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Arab Republic of Egypt Ministry of Education Book Sector 2016 ‫ ــ‬2017 ‫غري م�صرح بتداول هذا الكتاب خارج وزارة الرتبية والتعليم‬ Dear students, Dear students, We are pleased to introduce this book “ Mathematics for Primary stage - Year 4 “ to our We are pleased to introduce this book “ Mathematics for Primary stage - Year 4 “ to our children. We have done all what we can to make studying mathematics an interesting children. We have done all what we can to make studying mathematics an interesting job for you. We are confident in your abilities in understanding the subject of the jobbook, for you. We are confident in your abilities in understanding the subject of the but even seeking for more. book, but even seeking for more. Besides the interesting figures and drawings, we took into consideration to increase crossBesidescurricular the interesting figures drawings,applications, we took into consideration crossand real life and mathematics where you sense totheincrease value and curricular andof studying real life mathematics. mathematicsInapplications, where sensethat thewevalue and importance many situations, youyou will find ask you importance of studyingtomathematics. In manyoperations, situations, and you will find that you to use a calculator check mathematical invite you towe useaskthe tocomputer use a calculator to some checkoperations mathematical operations, and invite you to them. use the to conduct and draw some figures and decorate computer some operations and some drawactivities some figures and decorate them. Towards to theconduct end of every unit, you will find (sometimes may be closer to puzzles), in order to enjoy mathematics, where (sometimes you will findmay great, but Towards the end of every unit, studying you will find some activities be closer challenges alertsstudying your minds and develops youryou tendencies. tocalculated, puzzles), in order tothat enjoy mathematics, where will find great, but calculated, challenges that alerts your minds and develops your tendencies. Be careful to follow all what is written, conduct all activities and do not hesitate to question yourtoteacher whatis you may conduct face of any Be careful follow in allall what written, alldifficulties. activities and do not hesitate to question your teacher in all what you may face of any difficulties. Remember that many of the mathematics questions which have more than one correct answer, and studying it bears values that reflect this great humanitarian effort. Remember that many of the mathematics questions which have more than one correct answer, and studying it bears values that reflect this great humanitarian effort. May God help you and us to acheive what is good for our beloved nation Egypt. May God help you and us to acheive what is good for our beloved nation Egypt. The authors The authors Measurement Measurement Lesson 1: The Length Lesson Length Lesson 2: 1: TheThe Area Lesson 2: The Area Unit 4 Activities ........................................................................................ 74 ........................................................................................ ....................................................................................... 80 74 .......................................................................................87 80 ....................................................................................... .......................................................................................88 87 Unit 4Exercises Activitieson Unit 4 ....................................................................................... General General Exercises on Unit 4 ....................................................................................... 88 General Exercises General Exercises ....................................................................................... 89 ....................................................................................... 89 General Revision - For the first Term ............................................................................. 94 General Revision - For first................................................................................... Term .............................................................................10194 Model eixam - For the firstthe Term Model eixam - For the first Term ................................................................................... 101 74 80 74 87 80 88 87 88 89 89 Hundred thousands Millions, Milliards (Billions) Operations on Large Numbers Unit 1 Activities General Exercises on Unit 1 Lesson11 Lesson HundredThousands Thousand Hundred Lesson11 Hundred HundredThousands Thousands Lesson 99 999 99 999 + + 1 1 909 0 90 9 0 Tens Hundreds Units Tens Tens Hundreds Hundreds Thousands 9 909 09 0 0 + 1 1 thousand’ thousand’ and and can can bebe represented represented on on thethe abacus abacus figure figure opposite. opposite. thousand’ and can be represented on thousand’ be0 represented on0 11 asasin0inthe0theand 0can 0 0 0 0 0 Exercise Exercise 11 11 909 0 Hundreds Thousands 00 0 0 0 0 0 0 Ten Thousands Thousands 00 Units Units Ten Hundred Thousands 11 Thousands Thousands Thousands Thousands Hundred Thousands Hundred Hundred TenTen Thousands Hundreds Thousands Hundreds Tens Tens Hundred TenTenThousands Hundred Thousands Thousands Thousands Thousands Hundreds Thousands Hundreds TensTens UnitsUnits Units Hundred Thousands 99Thousands 99 999 999 +Hundreds 1+Hundreds =1 100 = 100 000 000 UnitsUnits Thousands Tens Tens Thousands Thousands Thousands Thousands Hundred Ten Thousands Thousands 999 1 100 = 100 000 9999 999 ++ 1= 000 « « « « This number is read as as hundred thousand This number is read hundred thousand 100100 000000 Hundred Hundred TenTen Ten Thousands Thousands 99999 100 000000 100 99 999 9999999 999 + +1 1 + + 1 100000 1 100000 Units Tens 9999 999 + 1+ =1 100 000 999 = 100 000 + Hundred Thousands Lesson Lesson1 1 Hundred Hundred Thousands Thousands This number is 0 is read read ‘hundred 1This 0 0 as 0‘hundred 1 number 0 0 0 as 0 00 thousand’ thousand’ and and can can bebe represented represented on on This This number number is is read read as as ‘hundred ‘hundred the the abacus abacus asas in in the figure opposite. This number isfigure read as ‘hundred This number isthe read asopposite. ‘hundred Thousands Hundreds Ten Thousands Thousands Units Tens Ten Thousands Thousands Units Units Tens Tens Hundreds Units Tens Hundreds Hundreds Thousands Hundred Ten Thousands Hundred Thousands Hundred Ten Thousands Hundred Thousands Units Tens Units Hundreds Tens Exercise1 1 Exercise Units Hundreds Tens Units Hundreds Tens Thousands Thousands Ten Thousands Hundreds Thousands Hundred Thousands Hundred Hundred Ten Thousands Thousands Thousands Hundred Ten Ten Thousands Thousands 1 1 Write Write thethe numbers. numbers. Thousands theabacus abacusasasininthe the figure opposite. the figure opposite. Exercise Exercise 11 1 1 Write Write thethe numbers. numbers. Ten Thousands Thousands Ten Thousands Thousands Hundred Ten Thousands Thousands Shorouk Press Units Hundred Ten Thousands Thousands Units Tens Units Thousands Hundreds Tens Hundreds Ten Thousands Thousands Units Tens Hundreds Thousands Hundred Ten Thousands Thousands Ten Thousands Hundred Thousands Thousands Hundred Ten Thousands Tens Hundreds Hundred Thousands Hundred Thousands Units Hundred Thousands Units Tens Units Tens Units Hundreds Tens Units Hundreds Tens Thousands Hundreds Thousands Hundreds Tens Units Units Tens Units Thousands Ten Thousands Thousands 22 Hundred Thousands Hundred Thousands Ten 26 2 Mathematics for Primary Stage-Year 4 Hundreds Tens Thousands Ten Thousands Thousands Hundreds Tens Thousands Hundreds Thousands Ten Thousands Hundreds Thousands Hundred Thousands Hundred Hundred Ten Thousands Thousands Thousands Hundred Ten Ten Thousands Thousands Hundred Thousands Hundred Thousands Ten Writethe thenumbers. numbers. 11 Write Complete according the place value each digit. 2 2 Complete Completeaccording accordingto tothe theplace placevalue valueof ofeach eachdigit. digit. 22 Complete according toto the place value ofof each digit. Hundred Hundred Ten Ten Hundred Ten Thousands Hundred Ten Thousands Hundreds Tens Tens Hundreds Number Number Thousands Thousands Hundreds Tens Tens Hundreds NumberThousands Number Thousands Thousands Thousands Thousands Thousands Thousands Thousands Units Units Units Units 752 341 752 341 752 341 752 341 605 618 605 618 605 618 605 618 78 539 78 539 539 7878 539 58 002 58 002 002 5858 002 Write thethe following number the following number Underline the correct number, digits, which express each 3 Underline correct number, 3 Write Underline the correct number,in indigits, digits,which whichexpress expresseach eachof of 33 Underline the correct number, inin digits, which express each ofof the following in words. the following in words. thefollowing followingwords. words. the one hundred sixty thousand, seven hundred and forty a a one onehundred hundredsixty sixtythousand, thousand,seven sevenhundred hundredand andforty forty......... ......... aa one hundred sixty thousand, seven hundred and forty (16740 740, ,740 740160 160, ,167 167040 040, ,160 160740) 740) (16 onehundred hundredthousand, thousand,three threehundred hundredand andseventy-five seventy-five...... ...... b b one onehundred hundredthousand, thousand,three threehundred hundredand andseventy-five seventy-five b b one seventythousand, thousand, five hundred and,nintythree ................. c c seventy five hundred and three ................. (10 375 100375 375 ,ninty375 375 100) (10 375 , ,100 1 1375 , ,375 100) seventythousand, thousand,five fivehundred hundredand andnintyninty-three three c c seventy (70593 593, ,700 700593 593, ,5959370 370, ,750 750093) 093) (70 Completeasasthe theexample. example. 4 4 Complete Complete asthe the example. 4 4 Complete as147 example. Example:147 962 962+ +147 147000 000 Example: 962 = =962 900+ +7 7000 000+ +4040000 000+ +100 100000 000 = =2 2+ +6060+ +900 Example:147 147962 962= =962 962+ +147 147000 000 Example: =2 2 60+ +900 900+ +7 7000 000+ +4040000 000+ +100 100000 000 =384 60…………………………………………… 672384 384 = =384 a a 672 + +…………………………………………… ………………………………………… = =4 4+ +8080+ +………………………………………… 672384 384 = =384 384+ +…………………………………………… …………………………………………… a a 672 4+459 +80 +………………………………………… ………………………………………… + …………………………………………… 126459 459 ===4=459 +…………………………………………… b b 126 +80 ……………………………………………… = =9 9+ +……………………………………………… 126459 459 = =459 459+ +…………………………………………… …………………………………………… b b 126 9+ +……………………………………………… 9 608 608 = =608 +…………………………………………… …………………………………………… c c 3535608 +……………………………………………… …………………………………………………… = =…………………………………………………… 608 = =608 608+ +…………………………………………… …………………………………………… c c 3535608 …………………………………………………… = =…………………………………………………… Shorouk Press First Term 73 3 33 Lesson 1 Hundred Hundred Thousand Thousands Lesson 1 99 999 Read the following numbers, then write them as the example. them in in words. Lesson 1 Hundred Thousands + 1 a 712365 Example: 370 634 three hundred seventy thousand, six 99999 100 000 99 999 99 999 +thirty-four 1 = 100 000 hundred + 1 b 105206 99 999 + 1 = 100 000 + 1 100000 «hundred thousand« This number is read as c 300418 Hundred Ten a 712 365 b +Hundreds 105 c 300100 418000 99 999 1 =206 100Tens 000 Units Thousands Thousands Thousands d Hundred 740 740 Ten e 85 069 Tens Hundreds Ten Thousands Hundred Thousands Tens Units Ten Thousands Hundreds Units Tens Hundreds Units Tens Hundreds Ten Thousands Tens Hundreds Thousands Hundred Thousands Ten Thousands Thousands Shorouk Press Units Ten Thousands Thousands Thousands Hundred Ten Thousands Hundred Thousands Hundred Thousands Units Tens Hundreds Thousands Ten Thousands Hundred Thousands 2 Tens Arrange the following numbers in an ascending order, then in a descending order. a 654 321 , 143 265 , 142 365 , 645 321 b 325 604 , 302 564 , 325 046 , 325 064 c 515 115 , 151 155 , 551 115 , 115 515 48 2 Mathematics for Primary Stage-Year 4 Thousands Ten Thousands 1 0 Units Tens Hundreds Units 9 0 Exercise 1 Units Tens Thousands Tens 9 0 Thousands 9 0 Units Hundreds Tens Hundreds Units Tens Hundreds Thousands 9 0 0Exercise 0 0 1 Ten Thousands Hundred Thousands Hundred Thousands 9 Hundreds Thousands Ten Thousands Ten Thousands Thousands Thousands Hundred 0 Ten Thousands Thousands 1 Hundred Ten Thousands Thousands 9 0 Hundred Thousands 1 Units 0 Write the value of the circled digit in each of the following numbers. This is read 1 number 0 0 0 as ‘hundred 0 0 a 27 351 b 156 348 thousand’ and can be represented con 7 2 3 6 0 8 d number 5 4 3 0 is 9 2read as e ‘hundred 230 045 f 467 900 This the abacus as in the figure opposite. This number is represented read as ‘hundred thousand’ and can be on 7 theComplete using theand suitable signbe < , represented > or = in each on . abacus as in the figure opposite. thousand’ can a 132 045 93 245 b 85 679 302 001 the abacus as in the figure opposite. c 100 074 74 001 d 321 587 321 587 Exercise 1 1e Write the numbers. 20 864 20 531 f 437 786 437 876 1 Write the numbers. 8 Write the greatest and the smallest number that can be formed from the number cards in each of the following. a1 4 Write greatest …………………… 1 5 the 3 2numbers. 6 smallest …………………… b 7 6 4 3 9 1 greatest …………………… smallest …………………… c 3 3 2 6 7 7 greatest …………………… smallest …………………… Hundred Thousands 0Tens 0Units Hundreds 0 Thousands 0 Units Ten Thousands 1 Tens Hundred Thousands 6 Thousands Hundreds Hundred Ten Thousands Thousands Thousands Hundreds Thousands Thousands Hundred Thousands 5 10 Completeaccording in the same pattern. 2 to the place value of each digit. 2 Complete Complete according to the place value of each a 710 654 , 720 654 , 730 654 , ………… digit. , ………… Hundred Ten Hundred Ten Number b 80 000 , 280 000 , Thousands 480 000 ,Hundreds ………… ,Tens …………Units Thousands Hundreds Tens Units Number Thousands Thousands Thousands Thousands c 100 568 , 100 578 , 100 588 , ………… , ………… 752 752 341 341 10 Complete in the same d 220 300 , 210 300pattern. , 200 300 , ………… , ………… 605 605 618 618 a 710 654 , 720 654pattern. , 730 654 , ………… , ………… 10 Complete in the same 78 78 539 539 b 80 000 ,pattern. 000 10 Complete in, the same a 654 , 280 720 654 , 480 730 654, , ………… …………, , ………… ………… 11 Join710 the000 cards with equal numbers. 58 58 002 002 10 b Complete in, the same c 80 100 568 100 578,pattern. 100000 588 a 710 654 , 280 720 654 , 480 730 654 , ………… ………… ………… 000 , , ………… 710000 710 1 ,710 + 70 000 a 710 654 , 280 720 654 730 654 ………… ………… d 100 220 300 210000 300 200000 300 b 80 000 , correct , , 480 , , ………… , , ………… c 568 100 578 100 588 Write the following number 3 Underline the number, in digits, which express each 3 Underline the, correct number, in300 digits, which express each of of b 80 000 280 000 , 480 000 , ………… , ………… c 100 568 100 578 100 588 d 220 300 , 210 300 , 200 , ………… , ………… 710 + 71 000 710 + 710 000 71 710 the following in words. the following words. c 100 568 100 578 100 588 11a Join the cards with equal numbers. d 220 300 , 210 300 , 200 300 , ………… , and ………… one hundred sixty thousand, seven hundred forty a one hundred sixty thousand, seven hundred and forty ......... 10 +220 700 + 710 000 10 + 700 + 71 000 d 300 , 210 300 , 200 300 , ………… , ………… 11 Join the cards with equal numbers. 710 710 1 710 + 70 000 (16 740 , 740 160 , 167 040 , 160 740) 11 Join710 the 710 cards with equal numbers. 710 + 70 000 b one hundred thousand, three 1hundred and seventy-five ...... 12 Underline the nearest number to 100 000 in each case. 11bJoin the cards with equal numbers. 710 + 71 000 710 + 710 000 71 710 710hundred 710 710 + 70 000 one thousand, three 1hundred and seventy-five a seventy 90 000 and 109710 000 b 710 101 000 and 100 900 + 71 000 + hundred 710 000 71 710 c710 thousand, five and three ................. 710 710 1 +,ninty70 000 (10 375 , 100 375 1 375 , 375 100) 10 + 710 10 000 + 700 + 71 000 71 710 c +200 and000 90710 000+ 710 710 +700 71000 000 10 ++700 710 000 10 000 + 700 + 71 000 71 710 71 + 000 710 c710 seventy thousand,710 five+ hundred and nintythree 12 Underline nearest to 100 000 in each case. + 700 +the 710 000 number 10 the + 700 + 71rectangles 000 13 10 Write suitable numbers inside empty on the (70 593 , 700 593 , 59 370 , 750 093) 4 Complete as the example. 10 +90 700 +the 710 000 10 to +b700 + 71000 a 000 and 109 000 and 100 12 Underline nearest number 100101 000 in000 each case.900 number line according to thier places. c 90 200000 000 and 90 000 12 a Underline the nearest number tob100101 000000 in each case. and 109 and 100 900 4 Complete as the Example: 147 962example. = 962 + 147 000 12 Underline the nearest number tob100101 000000 in each case. a 90 000 and 109 and 100 900 000 000 and 90 000 400c 000200 = 2 + 60 + 900 + 7 000 + 40 000 + 100 500 000 a 90suitable 000 109 b empty 101 000 and 100 13 c Write numbers rectangles on900 the 200 000and and 90 000inside the Example: 147 962 = 962 + 147 000 c 000 and 90 000 number line toinside thiernumber. places. 13 suitable numbers the empty rectangles on the 14 Write a 200 Write theaccording greatest 6-digit = 2 + …………………………………………… 60 + 900 + 7 000 + 40 000 + 100 000 a 672 384 = 384 13 number Write suitable numbersdifferent empty rectangles on the line toinside thier the places. b Write theaccording greatest 6-digit number. = 4 + 80 + ………………………………………… 13 Write suitable numbers6-digit the empty rectangles on the number line toinside thiernumber. places. c Write theaccording smallest 400 500 000 a 000 672 384 = 384 + …………………………………………… number to thier places. d Writeline theaccording smallest different 6-digit number. 400 500 000 + 80 + ………………………………………… b 000 126 459 == 4459 + …………………………………………… 14 6-digit numbernumber. different 6-digit number and 5 ae000Write the greatest 400 500 000 = 9 + ……………………………………………… b Write different 6-digit number. 14 a the greatest number. their sum is 15. 6-digit 400 500 000 b 000 126 459 = 459 + …………………………………………… c smallest different 14 b a 6-digit number. 6-digit f Write the greatest different 6-digit number. number and their sum is 9 + ……………………………………………… c 35 608 = 608 + …………………………………………… 14 c a 6-digit number. d Write b greatest different 6-digit number. 17. the smallest = …………………………………………………… b greatest different 6-digit number. e number different 6-digit number and of c 6-digit number. d g Write the smallest number and the sum c 35 608 = 608 + …………………………………………… c Write 6-digitis number. their sum is 15. d smallest different 6-digit number. e theand greatest number 6-digit number and its units tens digits 7.different = …………………………………………………… d smallest differentdifferent 6-digit number. fh their number and their sumofis e Writesum the greatest 6-digit number is 15. number the and sum greatest number 6-digit number 17. their sum is 15. fe Write theand smallest different 6-digit number and theirand sum is its units tens digits is 7.different 9 3 their sum is 15. different 6-digit number and the gPress 17. greatest Write the smallest theirsum sum 3is5 Shoroukf First Termof f Write smallest theirsum sumofis its units tens digits is 7.6-digit number and the 17. g theand greatest different 17.units h its smallest g Write theand greatest different tens digits is 7.6-digit number and the sum of g Write greatest different its units tens digits is 7.6-digit number and the sum of h theand smallest Lesson 1 Hundred Hundred Thousand Thousands Lesson 1 Second: Ten Millions 99 999 1 9 0 Tens Hundreds Thousands Ten Units Thousands Hundreds 9 0 Units 9 0 Tens 9 0 Hundreds 9 0 Thousands Ten 9 Units+ 1 Ten Thousands 1 Hundred Hundred Thousands Units 9 9 9 9 9 Hundred Ten Complete the following table to find Hundreds the Thousands Tens Hundred Ten Thousands Thousands 1 Thousands 0Thousands 0 sum of: 999 999 + 1 0Hundreds 0Tens 0Units Thousands Hundred ThousandsTens Thousands Ten Thousands 99 999 +Hundreds 1 = 100Tens 000 Thousands 9 Thousands Thousands Hundred Thousands Millions Lesson 1 following Hundred Lesson Millions, and + Complete2 the table to Ten findThousands theMillions sum of: 9 999 999 + 1 Hundred Millions 99999 100 000 99 999 99 999 + 1 = 100 000 + 1 Ten Hundred Ten 99 Thousands 999 +Hundreds 1 = 100 000 + 1 Millions Tens Units 100000 «hundred thousand« Millions Thousands Thousands This number is read as First: Millions 100 000 Hundred Ten 1 0 Units Tens Hundreds Thousands Ten Thousands Hundred Thousands Millions Ten Millions Thousands Hundreds Tens Units This number is read Thousands 0 1Thousands 0 0 as ‘hundred 0 0The sum is 1 000 000, and thousand’ on as ‘one million’ 9 is 109000and 9 can 9be represented 9 9 it is read The sum 000, This number is read as8-digit ‘hundred +1 the abacus as as in ‘ten the opposite. number and number is read million’, and can be represented This is figure read as ‘hundred Millions thousand’ and can be represented on and be represented on theopposite. on the abacus as in the thecan abacus as in the and figure thousand’ can be figure represented on abacus as in the figure opposite. above. 1 0 0Exercise 0 0 1 Units Thousands Units Thousands Thousands Units Millions Thousands Units Units Ten Thousands Units Ten Thousands Shorouk Press Hundred Thousands Units …… …… …… …… Hundreds Units Thousands Ten Tens Thousands Tens Hundreds Hundreds Thousands Thousands Hundred Thousands Millions Hundred Thousands Hundred Thousands Ten Ten Thousands Thousands Units Tens and and and and Tens Units Tens Hundreds Units Hundreds Tens Thousands Units numbers, then complete. …… million, …… thousand …… million, …… thousand …… million, …… thousand …… million, …… thousand Units Tens Tens Hundreds Hundreds Hundreds Thousands Ten Thousands 2 Hundred Thousands 8 10 6 2 Mathematics for Primary Stage-Year 4 Thousands Ten Thousands Hundred Thousands Ten Thousands Thousands Thousands Millions Hundred Thousands Hundred Hundred Thousands Ten Thousands Ten Thousands Thousands Read the following a 73 421 685 b 22 153 027 c 50 200 366 d 68 730 050 Exercise 3 Hundred Thousands Write the numbers. it is read from left to right as: 49 million, 136 thousand and 527 1 Tens Hundreds Tens Tens 527 Hundreds Hundreds Ten Exercise 1 136 Hundred Millions Thousands Hundred Ten Thousands Thousands Ten Thousands Thousands Hundred Thousands Tens Hundreds Units Units Tens Tens Hundreds Hundreds Thousands Ten Thousands Thousands Thousands 1 Millions Hundred Thousands Hundred ThousandsHundred Ten Ten Thousands Thousands Thousands below 1 thethe numbers. 1 Write Write numbers. 49 Units the abacus as in the figure opposite. Exercise 2 1 its digits as shown Exercise To read the number 49 136 527, we separate 1 Write the numbers. Ten Units Tens Units Units Tens Tens Units Hundreds Hundreds Units Units Tens Hundreds Thousands Thousands Ten Thousands Thousands Tens Tens Hundred Ten Hundred Thousands Thousands Thousands Millions Hundred Millions Millions Thousands Thousands Thousands Thousands Thousands Thousands Ten Ten Ten Thousands Millions Millions Millions Hundred Hundred Hundred Thousands Thousands Thousands 7 354 621 752 752 341 341923 508 605 4 561 009 605 618 618 78 539 8 000 300 78 539 Hundreds 1 Hundreds Hundreds Tens Tens Tens Units Units Units thousands thousands Hundred Ten Thousands Hundreds Number WriteThousands the numbers. numbers. 11 Write the Number Thousands Thousands Hundreds Thousands Thousands Hundreds Thousands Ten Thousands Millions Hundred Thousands 99 Thousands Ten Hundred 99 Units 99 Tens Hundreds Thousands 99 Ten Thousands Millions Hundred Thousands The sum sum is is 11 000 000 000, 000, and and The 99 itit is is read read as as ‘one ‘one million’ million’ ++ 11 and can can be be represented represented and on the the abacus abacus as as in in the the on figure above. above. figure 2 Completeaccording accordingtotothe theplace placevalue valueofofeach eachdigit. digit. 2 Exercise 2 Exercise 2 2 Complete Complete according to the place value of each digit. Number Millions Hundred Ten Thousands Hundreds Tens Units 99 58 58 002 002 Ten Hundred Units Units Tens Tens Hundreds Hundreds Thousands Thousands Millions Millions Hundred Hundred Thousands Thousands Ten Ten Thousands Thousands Units Units Tens Tens Hundreds Hundreds Thousands Thousands Hundred Hundred Thousands Thousands Ten Ten Thousands Thousands Millions Millions 3 Join the two cards which express the same number the the following 3 Underline correct number, 3 Write Underline the correctnumber number, in in digits, digits, which which express express each each of of the following in words. 1 170 650 words. one million, one hundred and fifty the following a sixty thousand, seven and thousand, six hundred and seventy a one one hundred hundred sixty thousand, seven hundred hundred and forty forty ......... 62Second: Ten Millions Write each of the following number in digits then put it in the (16 740 , 740 160 , 167 040 , 160 740) table according tohundred the placeand value of each digit. bcorresponding one 760 hundred thousand, three ...... 1 150 one million, one seventy Complete the following table to find hundred the sum and of: seventy-five b(a)one hundred three hundred and seventy-five thousand, six hundred fifty 17 million andthousand, 450 thousand and 46 and 9c 999seventy 999 + 1thousand, five hundred and ,nintythree ................. (10 375 , 100 375 1 375 , 375 100) Ten Units Units Tens Tens Hundreds Hundreds Thousands Thousands Ten Thousands Ten Thousands Hundred Thousands Hundred Thousands Millions Millions Ten Millions Hundred Millions Ten Millions Millions Units 1 170 560 one million, oneThousands hundredHundreds and fifty Tens thousand, Millions Thousands Thousands c seventy thousand, hundred nintythree sevenfive hundred andand sixty 9 the Millions 9 (70 593 9 , 7009593 , 59 9 370 , 9 750 093) 9 4 Third: Complete as example. Hundred + 1 one million , one hundred and seventy 66 1 150 670 4 Complete Complete asfollowing the Example:the 147 962example. = 962 + 147 000 table to find the sum of:sixty thousand, five hundred and 2 + 60 + 900 + 7 000 + 40 000 + 100 000 99 (b) 999105 999million + 1 and=11 Example: 147 = 962 + 147 000 4 Hundred Complete as 962 the example Hundred Ten Ten Units Millions = 2 60 + 900 + Thousands 7 000 +Hundreds 40 000 +Tens 100 000 a 672 384 = 384 + …………………………………………… The sum is 10 000 000, 8-digit Thousands Thousands Millions Millions = 4as +218 80 =+ 7………………………………………… number and is read ‘ten million’, Example: 7 435 million + 435 thousand + 218 9 9 9 9 9 9 9 a can 672be384 = 384 +on…………………………………………… and represented the 9 + 1 4 + 80 + ………………………………………… ba 126 459 +opposite. …………………………………………… abacus in396 the==figure 2 as 405 =459 ……… million + ……… thousand + ……… + ……………………………………………… b 4 691 508 ==9 ……… million + ……… thousand + ……… 3TobWrite the following number inwe digits. 126 459 = 459 + …………………………………………… read 136 527, its digits as shown c 8the 300number 597 =49 ……… million +separate ……… thousand + ……… (a) One million , one hundred and fifty thousand and twenty seven. 9 6+million ……………………………………………… cd 35…………… 608 = =608 + …………………………………………… below + 412 thousand + 576 The(b) sum is 100 000,thirty 9-digit Twenty four000 million, thousand and five. = …………………………………………………… 49 136 527two+hundred e …………… = 9 million + 18 thousand 72 number and is read as ‘hundred c(c) 608 608 + and …………………………………………… Five hundred= = million six thousand f 35 …………… 4represented million + 4hundred thousand +4 . million’, and can=be on …………………………………………………… Millions Thousands Nine hundred thousand eighty. Units the(d) abacus as in the figure and opposite. it is read from left to right as: 49 million, 136 thousand and 527 To read the number 714 326 518, we separate its digits asFirst Term Shorouk Press shown below Exercise 3518 714 326 7 3 311 Lesson 1 Hundred Hundred Thousand Thousands Lesson 1 Second: 99 999 1 Ten Millions sum in digits. Lesson 1 following Hundred Thousands 4 Write the + 9 0 Thousands Ten Thousands Thousands Hundreds Units Tens Hundreds Thousands Hundred Ten Thousands Hundred Thousands Units Tens Hundreds Exercise 1 Units Tens Hundreds Thousands Ten Thousands Thousands Hundred Ten Thousands Thousands Hundred Thousands Write thecards numbers. 3 1Join the two which express the same number 6 To1read the number 49 136 Write the numbers. 527, we separate its digits as shown below 1 170 650 one million, one hundred and fifty 49 136 527 thousand, six hundred and seventy c d Units Units Hundreds Thousands Ten Thousands Tens Hundreds Thousands Hundred Thousands Ten Thousands Units Tens Units Ten Thousands Hundred Thousands Units Shorouk Press ……… million + ……… thousand + ……… ……… million + ……… thousand + ……… ……… million + ……… thousand + ……… 6 million + 412 thousand + 576 Tens = = = = Hundreds 2 405 396 4 691 508 8 300 597 …………… Thousands Ten Thousands Hundred Thousands a Tens 7 435 218 = 7 million + 435 thousand + 218 12 8 2 Mathematics for Primary Stage-Year 4 2b Hundreds Read the following numbers, then complete. 1 150 670 one million , one hundred and seventy a 73 421 685 …… million, …… thousand and …… thousand, five hundred and sixty b 22 153 027 …… million, …… thousand and …… c 50 200 366 …… million, …… thousand and …… 4 Complete as the example d 68 730 050 …… million, …… thousand and …… Example: Ten Thousands Units Hundreds Tens Hundred Thousands Hundreds Thousands one million, one hundred and fifty thousand, Exercise 3 seven hundred and sixty Ten Thousands Thousands 1 Hundred Ten Thousands Thousands Hundred Thousands 1 170 560 Thousands Ten Thousands one million, one hundred and seventy thousand, six hundred and fifty it is read from left to right as: 49 million, 136 thousand and 527 Hundred Thousands 1 150 760 Hundred Thousands Write the numbers. Millions Thousands Units Tens 1 Tens 1 0on Tens Hundreds Thousands Ten Thousands Hundred Thousands Millions Ten Millions Exercise 1 Hundreds Hundred Thousands 9Tens Units 0 thousand’ and can be represented on b7 4691508 = ...million + ........thousand + ......... This number is read as ‘hundred 354 621 the abacus as in the figure opposite. The sum is 10 000 000, 8-digit This number is read as ‘hundred c 734216858 =can ...million + ........thousand thousand’ and be represented on + ......... 923 508 number and is read as ‘ten million’, thedthousand’ as in=the figure+ can opposite. 4abacus 561 009 168730050 ...million ........thousand + ......... be represented and can be representedand on the 8 000 300 abacus in the figure theasabacus asopposite. in the figure opposite. 0Exercise 0 0 1 Units 0 9 0 Units 1 9 0 thousands thousands Tens 9 0 Tens 1 Complete according to the place value of each digit. This number ismillion read 1Number 0 =Millions 0+ as 0 Ten 0+Thousands Hundred Hundreds 70 a 7435218 435‘hundred thousand 218. Units 2 0 9 + 1 Units Thousands Write following in digits. 1 the 0 0 sum 0 0 Thousands Thousands 9 Tens 9 Ten Thousands 5 Hundred Ten 9 9 Thousands 9 9 Hundreds Hundred Ten Thousands Thousands Thousands Hundreds Tens Units Hundred Thousands 4 Thousands Thousands Ten Thousands hundred thousandTens 100 000Units Hundreds This number is read as Ten Hundred Ten Millions Thousands Hundreds Hundred Ten 3 Millions Thousands 99 999Thousands +Hundreds 1 = 100 000 Units c million pound. Thousands Tens Thousands Complete the following a 41 million pound. table to find the sum of: 99999 100 000 99 999 99 999 + 1 = 100 000 9 999 999 + 1 + 1 1 99 999 + 1 = 100 000 + 1 b 2 million pound. 100000 « « Lesson 3 two Milliards (Billions) 2 Join the cards expressing the same number. 2 Complete according to the place value of each digit. Lesson 3 Milliards (Billions) 2 Complete according to the place value of each digit. Lesson 3 Milliards (Billions) Milliards ( Billions ) Hundred Ten 24 482 000 24 million and 482 Number Number Hundred Ten Thousands Hundreds Thousands Thousands Thousands Hundreds Thousands Thousands Tens Tens Units Units 752 341 Complete the following table to find the sum of: 752 341 24 400 082 24 million and Complete the following table to find the sum of:482 thousand 605 618 999 999 999 1 605 618 Complete the+ following table to find the sum of: 999 999 999 + 1 78 539 78 539 999 999 999 + Ten 1 Hundred Ten Hundred 58 002 Thousands Hundreds Tens Units Milliards Millions 24 040 082 24 million, 48 thousand and 200 58 002 3 3 Hundred Thousands Ten Hundred Ten Thousands Millions Millions Tens Units Milliards Hundred Millions Hundred Ten Thousands Hundreds Ten Units Milliards Millions Millions Millions Thousands Thousands Thousands Hundreds Tens Thousands Millions 9 theMillions 9 9 in Thousands 9 9 9 9each of9 Underline correct9number, digits, which express Write the the following Underline correctnumber number, in digits, which express each of 12 12 12 Shorouk Press Units Units Units Tens Tens Tens Hundreds Hundreds Hundreds Millions Millions Millions Hundred Hundred Hundred Thousands Thousands Thousands Ten Ten Ten Thousands Thousands Thousands Thousands Thousands Thousands Milliards Milliards Milliards Hundred Hundred Hundred Millions Millions Millions Ten Ten TenMillions Millions Millions 9 482 in9 words. 9 9 24 million, 9 9 thousand 9 9 82 9 24 000 40 and the 9 9 9 9 9 9 9 9 + 19 the following following words. + 1 a + 1 a one one hundred hundred sixty sixty thousand, thousand, seven seven hundred hundred and and forty forty ......... (16 740 24 , 740 160 400 , 167 040 , 160 24 048 200 million, thousand and740) 82 b one hundred thousand, three hundred and seventy-five ...... Milliards Millions Thousands Units b one hundred thousand, three hundred and seventy-five Milliards Millions Thousands Units c seventy thousand, five hundred and ,nintythree ................. Milliards Millions (10 Units 375 , Thousands 100 375 1 375 , 375 100) 3 Add one million to each of the following numbers. The sum is 1 000 000 000 which is 530 000 247 000 , which 28 900 The sum is 1610-digit 000 is 420 , 39 410 560 the smallest number and c seventy thousand, five hundred nintythree The sum is……………… 1 000 000 000 ……………… which is and ……………… the smallest 10-digit number and read as ‘milliard’, and be, 700 593 , 59 370 , 750 093) (70can 593 4isthe Complete as the example. smallest 10-digit number and is read as ‘milliard’, and can represented on the abacus asbe in is read as ‘milliard’, and can be 4 Add ten on millions to each as of the represented the abacus in following numbers. figure opposite. 4the Complete as the Example: 147 962example. = 962 + as 147in000 represented on the abacus 49 136 500 , 756 382 , 82 356 004 the figure opposite. = 2 + 60 + 900 + 7 000 + 40 000 + 100 000 the figure opposite. ……………… ……………… ……………… Example: 147 962 = 962 + 147 000 To aread672 the384 number digits as 000 =408 2 + 192 60 +357, 900 we + 7separate 000 + 40its 000 + 100 =6 384 …………………………………………… 5 Complete as the example. To readbelow the number 6 408 192 357, we separate its digits as shown = 4 6+ 408 80 +192 ………………………………………… To read the number 357, we separate its digits as shown below 6 408 192 357 a 672 384 = 384 + …………………………………………… shown below Example: 98 6230 156 230 000357 + 98 000 000 408= 156 + 192 + 80 + ………………………………………… b 126 459 ==64459 + 408 …………………………………………… 192 357 Milliards Thousands Units = 9 + Millions ……………………………………………… a 52 936 Milliards 147 = 147 + …………… + …………… Units Millions Thousands Units b 126 459 Milliards = 459 +Millions …………………………………………… Thousands Units b 23 600 156 = …………… + …………… + …………… andc it is35read right as: 6 Milliard, 408 million, 192 9 to + ……………………………………………… 608from =left 608 + …………………………………………… c 3 651 028left = …………… …………… …………… and it is read from to right as: 6+ Milliard, 408 +million, 192 thousand and 357 = …………………………………………………… anddit is10 read from left to right as: 6 Milliard, 408 million, 192 800357 900 = …………… + …………… + …………… thousand and c 35 608 = 608 + …………………………………………… thousand e 6and 000357 834 = …………… + …………… + …………… = …………………………………………………… First Term 9 3 313 3 a Which of the following numbers is the nearest to one milliard?Millions Represent the numbers Thousands Units on the number line. 1 000 000 090 , 999 999 990 or 1 100 000 000 Which ofright the following numbers the nearest two it is readbfrom left to as: 49 million, 136isthousand andto 527 milliard? Third: Hundred Millions 2 000 000 020 , 299 999 3 999 or 1 999 999 90099 999 Exercise Exercise 5 Lesson 1 Hundred Thousands + 1 the following table numbers to find thecomplete. sumthe of:difference between 4 a the Find two 10-digit with 1Complete Read following numbers, then 99999 100 000 99 999 99 999 + 1 = 100 000 1 Read the following numbers, then complete. 99 999 999 + 1 + 1 them is one milliard. a 73 421 685 …… million, ……+ thousand and …… 99 999 1 = 100 000 + 1 100000 a 8two 71910-digit 645 302 …… milliard, …… million, «hundred Find numbers with the difference between b b 22Ten 153 027 …… million, …… thousand and« …… This number is read as thousand Hundred Ten Hundred …… thousand and100 …… 000 Hundred them Ten Millions Thousands Hundreds 99 +Hundreds 1Thousands = 100 000 is Thousands one999 million. Tens Units c 50 200 366 …… million, …… thousand andTens …… Units Thousands Millions Millions Thousands Thousands b 6two 539 006 475 …… milliard, …… million, c Find numbers with the difference between Ten10-digit d Hundred 68 730 050 …… million, …… thousand and …… Thousands Hundreds Tens Units 9 9 9 9 9 9 9 9 …… thousand and …… Hundred Ten Thousands Thousands them is oneHundreds thousand. Thousands0 Tens Units 1 0 0 0 0 Thousands Thousands c 2 163 900 800 …… milliard, …… million,+ 1 13 …… thousand and …… is read as ‘hundred 8 This 1 number 0d 5 180 0 0 0 0 070 506 …… milliard, …… million, thousand’ and can be represented on …… thousand and …… This number is read as ‘hundred the abacus as in the figure opposite. The sum is 100 000can 000, This number is9-digit read as ‘hundred thousand’ and be represented on number and is read as ‘hundred 2 abacus Join the cards expressing the same number. the as two in the figure opposite. thousand’ and can be represented on million’, and can be represented on 7 000 600 900 7 million, 6 thousand and 900 the abacus as in the as figure the abacus inopposite. the figure opposite. Exercise 1 1 7Write the600 numbers. million, thousand and 900 70 600 900 To1read the the number 714 326 518, we separate its digits as Write numbers. 7 006 900 7 milliard, 600 thousand and 900 shown below 714 326 518 7 000 000 + 6 000 + 900 Lesson 1 Hundred Hundred Thousand Thousands Tens Units Tens Hundreds Units Tens Hundreds Thousands Hundred Ten Thousands Hundred Thousands Units 564 253 601 …… million, …… thousand and …… a Find two 10-digit with thousand the difference between 901 420 368 ……numbers million, …… and …… is one milliard. 987 them 654 321 …… million, …… thousand and …… b Find two 10-digit with thousand the difference between 123 456 789 ……numbers million, …… and …… is one million. 600 them 400 200 …… million, …… thousand and …… c Find two 10-digit with thousand the difference between 809 005 000 ……numbers million, …… and …… them is one thousand. Units Shorouk Press Units Tens Hundreds Units Thousands Ten Thousands Tens Hundreds Thousands Hundred Thousands Ten Thousands Hundred Thousands Units Tens Tens Hundreds Units Hundreds Thousands Thousands Tens Units Tens Ten Thousands Hundred Thousands Hundreds Ten Thousands Hundreds Thousands Hundred Thousands Ten Thousands Thousands Hundred Ten Thousands Thousands Hundred Thousands 142 Mathematics for Primary Stage-Year 4 10 Ten Thousands a 4 b c d e f Which of the following numbers is the nearest to one milliard? Represent the numbers the number line. it is read from left to right as: 417 million, 326on thousand and 518 1 000 000 090 , 999 999 990 or 1 100 000 000 b Which of theExercise following numbers 4 is the nearest to two milliard? 2 following 000 000 020 , 299then 999complete. 999 or 1 999 999 900 1 Read the numbers, Hundred Thousands a Ten Thousands Write the numbers. Millions Thousands Units 3 2 Hundreds Thousands Ten Thousands Tens Units Thousands Hundreds Units Hundreds Tens Thousands Ten Thousands Thousands 9 0 1 0 Ten Thousands Thousands Ten Thousands Millions Hundred Thousands Ten Millions Hundred Millions 9 0 Exercise 1 Units Tens Thousands Hundred 9 0 Hundred Thousands 1 Tens 0Exercise 0 0 1 Hundreds 0 Hundreds Thousands 1 Ten Thousands 9 0 Ten Thousands Thousands 9 0 Hundred Thousands 1 Hundred Thousands Hundred Thousands Lesson 1 13 b 1 000 000 090 , 999 999 990 or 1 100 000 000 Which of the following numbers is the nearest to two milliard? 2 000 000 020 , 299 999 999 or 1 999 999 900 2 the two expressing the number. between 4 Join a Find two cards 10-digit numbers withsame the difference 2 2 Complete Complete according according to to the the place place value value of of each each digit. digit. them is one milliard. Hundred Ten + 605 18 000 000 + 4 000 1 804 000Tens + 605 Units Hundred Ten Thousands Hundreds Number Thousands Hundreds Tens Units Number b Find two 10-digit numbers with the difference between Thousands Thousands Thousands Thousands them is one million. 752 752 341 341 1 800 000two + 410-digit 000 + 605 1 804 605 c Find numbers with the difference between 605 605 618 618 them is one thousand. 78 78 539 539 58 18 004 605 58 002 002 5 3 3 1 800 000 + 40 000 + 605 Write the following quantities of money in digits. 13 Write the the following number Underline correct number, Underline the correct number, in in digits, digits, which which express express each each of of a 1 milliard pound ............... 1 4840 605 in words. 1 840 000 + 605 the following the words. b 1following milliard pound ............... a a 2one one hundred hundred sixty sixty thousand, thousand, seven seven hundred hundred and and forty forty ......... c 3 milliard pound ............... (16 740 , 740 160 , 167 040 , 160 740) 4 3 b Complete using thousand, suitable numbers. one hundred three hundred and seventy-five ...... a one56hundred 340 608thousand, < ………………………… < seventy-five 56 430 608 three hundred and the following numbers in terms of million . ................. 6 bcExpress thousand, five hundred and ,nintythree b seventy 61 708 425 < ………………………… 61 425 (10 375 , 100 375 1 <375 , 807 375 100) c 500 600 700 < ………………………… < 500 700 600 a 2 milliard . 43 051 289 < ………………………… < 430 051 278 c d seventy thousand, five hundred and nintythree 1 b 3 2 milliard . example. (70 593 , 700 593 , 59 370 , 750 093) 4 Complete as the c 10 milliard . a Which theexample. following numbers 4 4 Complete asofthe Example: 147 962 = 962 + 147 000 is the nearest to five hundred million: = 2 + 60 + 900 + 7 000 + 40 000 + 100 000 500 147 000 962 900 =, 962 500+005 Example: 147000 000 or 499 999 000? = 2 + …………………………………………… 60 + 900 + 7 000 + 40 000 + 100 000 a 672 384 = 384 b Which of the numbers is the nearest to one = 4 following + 80 + ………………………………………… hundred a 672 384 million: = 384 + …………………………………………… 110459 000 000 100 900 000 or 101 000 000? == 4459 +, 80 + ………………………………………… b 126 + …………………………………………… = 9 + ……………………………………………… b 126 459 = 459 + …………………………………………… 5 c a 35Find with the difference between them 9 + numbers ……………………………………………… 608two 9-digit = 608 + …………………………………………… is one million. = …………………………………………………… c 35 608 = 608 + …………………………………………… b Find two 9-digit numbers with the difference between them = …………………………………………………… is one thousand. Shorouk Press First Term 15 3 311 Lesson 1 Hundred Hundred Thousand Thousands Third: Hundred Millions Lesson 1 Complete the following table to find the sum of: 99 999 999 + 1 99 999 Hundred Thousands Operations Milliards (Billions) on Large Numbers + 1 Hundred Ten Thousands Hundreds Tens Units Tens Hundreds Units Ten Hundred Thousands Thousands Thousands Ten Thousands Hundreds Thousands Units Tens Tens Hundreds Shorouk Press Units Hundred Thousands Hundreds Units Units Thousands Ten Thousands Tens Hundreds Thousands Hundred Thousands Ten Thousands Hundred Thousands Units Tens Hundreds Tens Thousands Tens Ten Thousands Hundred Thousands 2 Hundreds Hundreds Thousands Ten Thousands Thousands Hundred Ten Thousands Thousands Hundred Thousands To wecomplete. separate its digits as 1 read Readthe thenumber following numbers, then Example: 5 2 566408 7 0192 2 357, shown a below 564 +2536601 1 4 2 5…… 8 3 million, …… thousand and …… 408 192…… thousand 357 the and b 901 420 1 1368 369 9 2…… 8 5 million, (read sum)…… c 987 654 321 …… million, …… thousand and …… Milliards Units 123 456 789 bMillions …… million, …… thousand and ……200 a d 4 579 208 9Thousands 302 198 c 2 879 e 600 …… ……380 + 702400 354200 + million, 1 748 …… 327 thousand+ and 1 352 and = read005 from left to right 6 Milliard, 408 million, 192 fit is …………… 809 000 …… million, …… thousand …… = as: …………… = and …………… thousand and 357 10 d 5 208 107 + 9 274 305 = ………………… (read the sum) 162 Mathematics for Primary Stage-Year 4 12 14 Hundreds Thousands Units Tens Hundreds Thousands Tens Thousands Hundred Units Tens Hundreds Units Ten Thousands Hundred Thousands Units Tens Thousands Hundreds Exercise 1 Units Units Tens Hundreds Thousands Ten Thousands Ten Thousands Thousands Hundred Thousands Hundred Ten Thousands Thousands Hundred Thousands 1 0 Thousands 0Exercise 0 0 1 9 0 Ten Thousands Thousands Hundreds Thousands Ten 0 Hundred Thousands 1 1 9 0 Millions 9 0 Ten Millions 9 0 Hundred Millions 9 0 Milliards 1 Tens and sum in theisnext 642 thousand tons . The 100year 000produced 000, Hundred Ten9-digit Example: Thousands Hundreds Tens Units Thousands (a)This the production the two number isThousands read ‘hundred number read as ‘hundred 9 9of 9 0 as 9in 9 0years 9. 9 9 9 1Findand 0issum 0 0 (b)thousand’ Find and the amount increase million’, canand beofrepresented on + 1 can be .represented on 5 5is read as 4 ‘hundred 2 7 3 This number the the abacus as in the figure opposite. abacus as in the figure +This 3and 5is represented 2 6 number read0opposite. as ‘hundred thousand’ can be on 1 = 8 in the figure 9 2 8 7 9 the abacus as opposite. thousand’ can be represented To read the number 714and 326 518, we separate its digits as on the solution Milliards Millions Thousands Units shown below the abacus as in the figure opposite. 714 Exercise 326 518 1c 6 4 2 01 0256 a 1 3Write 785 421 the4 numbers. a 5b 0 0 0 04 891 243b 0 312 The +sum is 1 000 000 000 which is 210 0 287 1 Write the numbers. 6 4 2 0+ 0 03 102 315 -‫ــ‬ - 4 5+ 0 08 0341 +234 the smallest 10-digitMillions numberThousands and Units = …………… = 1 0 9 2= 0 0…………… = 1 9= 2 0…………… 00 0 is as 302 ‘milliard’, be d read 3 265 + 4 313and 491can = …………… represented onleft thetoabacus in million, 326 thousand and 518 it is read from right as: as 417 1 2:opposite. Write the numbers. the figure Drill Exercise 4 Add as the example. Hundred Thousands Millions Ten Millions Hundred Millions Hundred Ten Thousands HundredsHundred Tens TenUnitsThousands Thousands Thousands Thousands Thousands Millions Millions Hundred Thousands Hundred Ten Drill 1: Thousands Hundreds Tens Units Thousands Thousands Example : A Factory produced fertilizer in year 450 thousand tons Hundred Ten 0 0 0 0 0 Hundreds Tens Units Add as1the example. Milliards Millions Units Hundred Thousands Ten Thousands 99999 100 000 99 999 99 999 + 1 = 100 000 + 1 9 9 9 999999 9+ 1 =9 100 9000 9 + 1 100000 « « number is readtoasfind hundred thousand + 1 First:Hundred Complete Adding theThis following Large Numbers table the sumNumbers of: Adding and Subtracting Large 100 000 Ten 99 999 +Hundreds 1 = 100Tens 000 Units Thousands 999 Thousands 999 999Thousands +1 Thousands Thousands Tens Millions Millions Ten Thousands Millions Ten Thousands Lesson Lesson 4Ten1 3 Hundred Drill 3: In the 2008-09 governomental budget and in the context of the governomental efforts to support basic commodities, 2 milliard pounds were allocated for that perpouse, 405 million pounds to maintain the prices of medicines and 750 million pounds to reduce Drill 2: according the interest on housingto Find value the total sum for the three items Exercise 5of 2 Complete the each digit. 2If the Complete toloans. the place place value of each digit. budget according allocated to support drinking water increased in two in the governomental expenditure. Hundred Ten consecutive years from 250 000 pounds to 750 180 000 Hundred Ten270Thousands Hundreds Tens Units Number ‫ــ‬ Thousands-‫ــ‬ Hundreds Tens Units Number Thousands Thousands 1 Read the following numbers, then complete. Thousands Thousands pounds. Find the amount of increase. Complete the solution: 752 341 …… milliard, …… million, 752 341 a 8 719 645 302 Solution: basic 605 618 2 000 000 000 pounds ……support thousand andcommodities …… 605 The618 amount405 of increase = 750 180 000 – …………… …………… 000006 000475 pounds ……maintain prices of=medicine 78 539 b 6 539 milliard, …… million, 78 539the remainder, then write it in words) (read + ‫ ــ‬750 000 000 pounds ……reduce interest housing loans thousand and of …… 58 58 002 002 = c……………… pounds ……governomental expenditure 2 163 900 800 milliard, …… million, Exercise 7 the following number …… thousand and …… each 3 Underline the correct number, in digits, which express of d 9887000 -7115306 = ................. 31 Write Underline the correct in digits, which express each Find the3: difference innumber, each of the following Drill Exercise 6 …… million, of d 5 180 070 506 …… milliard, the following in words. the following words. 3 In the 2008-09 budget 6and in382 the context of the a a 2 256 912 governomental b 444 …… thousand and and ……forty one hundred sixty thousand, seven hundred a one hundred sixty thousand, seven hundred and ......... efforts to support basic commodities, 2 forty milliard 1 –governomental Add, then use the calculator to check your answer. 1 145 810 – 4 317 159 (16 740 , 740 160 , 167 040 , 160 740) pounds were allocated for thatbperpouse, 405000 million pounds to a 8 752 013 2 560 …………… =hundred …………… 2 b= Join the two cards expressing the same number. one hundred thousand, three and seventy-five ...... maintain the439 prices of medicines and 750 million pounds to reduce + 815 + 5 981 812 b7 one hundred thousand, three hundred and 000 600 900 7Find million, 6 thousand andthree 900 items the interest on housing loans. the…………… total sumseventy-five for the = …………… = thousand,(10 five hundred and ,nintythree ................. c c in seventy 9 000 100 375 , 100 375 1 375 , 375 100) the governomental expenditure. –7 million, 8 087 600 089 thousand and 900 70 600 900 c 1 465 789 …………… c=Complete seventy thousand, five hundred and nintythree solution: +9005the 984 078 7 006 7 milliard, 600 900 (70pounds 593 , 700 support 593 thousand , 59 370commodities ,and 750 093) 4 Complete2as the example. 000 000 000 basic d 9 887=000…………… – 7 115 306 = …………… 405 000 000 pounds maintain prices of medicine e (3 280 075 +7 5000 909000 138) 7 657 249 = …………… + 6– 000 + 900 d + 2 107 305 + =5000 760 = 000 ……………… 4 Complete as the example. 750 000 pounds reduce interest of housing loans Example: 147 962 962 +119 147 f (4 512 247 + 5 067 753) – (1 200 105 – 2 489 105) e = (3 ……………… 217 907 += 42814 + 5+152 917+=40 …………… governomental expenditure +pounds 60256) + 900 7 000 000 + 100 000 ……………….………………. 3 a = Which of the following numbers is the nearest to one Example: 147 962 = 962 + 147 000 milliard? Represent the to numbers on number line. Exercise 6 the 2a Circle the number the+correct answer, 4 = 2nearest 60 + 900 7 000 + 40 000without + 100 000 672 384 = 384 + …………………………………………… 2 Circle the number nearest to the correct answer, without 1 000 000 090 , 999 999 990 or 1 100 000 000 performing the operation. = 4usual + 80addition + ………………………………………… performing the usual subtraction b Add, Which of the following is the nearest to two then use the to operation. check your answer. 5 384 260 180 7 985 954numbers = …………… a 1a672 = +384 +calculator …………………………………………… a a 7milliard? 256 312 – 7013 056 300 = …………… b 000 , 13 million) million ,2 560 milliard == 4459 + 80 + (900 ………………………………………… b 126 459 8 752 + …………………………………………… (200 million , = 200 , 999 250 900 thousand) 020815 , 299 999 or 1 999 + 000 439 +thousand 5 981 812 b 28000 400 100 050999 …………… =+92+600 ……………………………………………… b 8 205 – 3 198 119 …………… = 107 …………… = , …………… (11=million 7 milliard , 6 milliard) b 126 459 = 459 + …………………………………………… (8 milliard , 6 milliard between , 5 million)15 4 a Find two 10-digit numbers with the difference 9 + ……………………………………………… c 35 608 = 608 + …………………………………………… 789 c c 459 –465 350 200 = …………… them212 is1one milliard. = …………………………………………………… 5 984 078 and ten thousand hundred thousandbetween , milliard) b(hundred Find+ two 10-digit numbers, with the difference c 35 608 = 608 + …………………………………………… = is …………… d 9them 575 100 4 275 090 = …………… one– million. = …………………………………………………… , the 5 million , 850 million) c d Find2 two numbers difference between 107 10-digit 305 + 5(two 760milliard 119 =with ……………… them one thousand. e (3 is 217 907 + 4 814 256) + 5 152 917 = …………… 17 Shorouk Press 2 First Term Circle the number nearest to the correct answer, without performing the usual addition operation. a 5 260 180 + 7 985 954 = …………… 1 3 313 d e f 9 887 000 – 7 115 306 = …………… (3 280 075 + 5 909 138) – 7 657 249 = …………… (4 512 247 + 5 067 753) – (1 200 105 – 2 489 105) = ……………….………………. Lesson 1 Hundred Hundred Thousand Thousands Lesson 1 Hundreds Thousands Units Ten Thousands Tens Hundreds Thousands Ten Thousands 9 0 Units Units Hundred Thousands Ten Thousands Tens Tens Hundreds Units Thousands Hundred Thousands Hundreds Units Tens Hundreds Ten Thousands Tens Hundreds Thousands Hundred Thousands Ten Thousands Ten Thousands Thousands Ten Thousands Thousands 1 0 Thousands Hundred Ten Thousands Hundred Thousands Units Units Hundred Thousands Tens Tens Hundreds Units Hundreds Thousands Tens Thousands 9 0 Exercise 1 Units Tens 9 0 Units Hundreds Tens Hundreds Units Tens Hundreds Thousands Ten Thousands Hundreds Thousands Ten Thousands Hundred Thousands Hundred Thousands Hundred Thousands Thousands Ten Thousands 0Exercise 0 0 1 Ten Thousands Thousands 0 Hundred 1 Ten Thousands Thousands 9 0 Hundred Ten Thousands Thousands 9 0 Hundred Thousands 1 Hundred Thousands Hundred Thousands a 57is260 256 312 – 056 300 =1 …………… first kind 97 pounds the of 100 one metre of the99second is 000 180 + 7and 985999 954price 99999 100 999 99 + = 000 3 Ifpounds. the income from advertisements African ( 900 million 13the million ) +3 1 (200the million 200, milliard thousand ,100 250 thousand) 158 If Mostafa bought 4, metres of the first kind and 99 999 +during 1 .= 000 + 1 «=hundred « 100000 Football Cup of – ‘Ghana 2008’did for Mostafa the Egyptian 400 100 +Nations 26 000 50 b of88 the 205 107 3 198 119 …………… metres second, how many pounds pay? This number is read as thousand 100)000 Hundred Ten was Channel Two million eight thousand 99 21 999 +Hundreds 1(8 = and 100 000 , hundred (11 million , Tens 7milliard . 6milliard Thousands milliard 6Units milliard , 5 million) Thousands Thousands pounds, for Nile Sports TV seven hundred thousand pounds cHundred 212 –Ten 350 200 = …………… 6459 005 218 + 3 095 235 = ............... Tens Solution: Thousands Hundreds Units and Youth Sports Radio Channel five hundred and eight) Hundred Ten and Thousands Thousands (hundred and ten thousand , hundred thousand , milliard) Price of first kind = …………………………………………… pounds Thousands0 Hundreds Tens , 8and . 10 million ( 9 million Unitsfalf million 1 0 0 0 0 Thousands Thousands cof second 005pounds. 218 095 the 235total …………… thousand income acheived by thepounds three d 96 575 100 275 090 == …………… Price kind–+ =43Find ………………………………………… million , 8 and million , 10 million) destinations from the advertisements. This number is (9 read asmilliard ‘hundred (two million , 850 million) Mostafa pounds 1 paid 0 = ………………………………………………… 0 0 0 , 0a5 half ………………………………………………………………………… thousand’ and can be represented on 17 This number is read as 3 If the income the‘hundred advertisements during the African 6 the abacus asfrom in the figure opposite. This number is read as ‘hundred thousand’ and can be represented on for the Egyptian Football Cup of Nations ‘Ghana Second: Subtracting Large Numbers b Multiplying by a 2-digit Number2008’ theChannel abacus Two as inwas the and figure opposite. 21 million and eight hundred thousand thousand’ can be represented on pounds, for Nile Sports TV seven hundred thousand pounds Drill 1: Drill 1:abacus the as in theChannel figurefiveopposite. Youth Sports Radio hundred and eight Subtract as the and example. Find and the product as the examples. Exercise 1 1thousand Write pounds. the numbers. 6 9 12 0 15three Find the total income acheived by the 1 destinations Write the 7 numbers. the advertisements. Example 1: 350 128 2: 9 2: 870 215 Example 1: 27from × 53 = 27 × (3 + Example 50) Example 5 3 3 3Drill Complete. Complete. ………………………………………………………………………… –2: 52 040 1153 – 7 818 408 256 712 = 7= 807 300 712 ++ …………… 7drinking 807 300water increased =3 256 27 ×+3…………… 27 to × 50 × 807 2 7in two allocated support 7 Ifa thea3 budget = 2 310 013 = 2 051 b b9 256 000 – …………… = 5= 312 989 9 256 000 –from …………… 5 312 989 to 750 180 000 consecutive years 270 250 000 pounds Second: Subtracting Large Numbers 1 Write the numbers. = 81 + 1 350 371 c c…………… – amount 7–218 305 = 6= 977 455 …………… 7 218 305 6 977 455 pounds. Find the of increase. a 6 215 108 b 8 167 105 = 104 1 431 + 104 1 060 Solution: Drill –1: 3 007 – 4 056 4The Ifamount the budget allocated to support medicine in two consecutive 8 4 If the budget allocated to support medicine in two consecutive of increase = 750 180 000 – …………… = …………… Subtract the example. = as…………… = …………… = 1 pounds 431 years increased from 380 million pounds to 405 million pounds years increased from 380 million pounds to 405 million (read the remainder, then write it in words) 6 9 12 0 15 to preserve prices of medicine. Find amount the to preserve thethe prices of medicine. Find thethe amount ofofthe Example 1: 7 350 128 Example 2: 9 870 215 c 7 423 856 d 3 255 202 (Notice that the product is the same even with different methods, increase. increase. Exercise 7 –– 27028 –018to 5 739 040 115 818139 408 – 5 use a calculator check your answer.) 1 =Find the2difference in each of the following =the 310 013 2 051 807 ……………… == …………… 5 Find number that 9 5 Find the number that if: if: from milliard, result 758 209 312. 24 43 subtracted = 24 ×from (……… +milliard, 40) 43 2 256 912 bresult 444 382 a ×aa subtracted oneone thethe is6 is 758 209 312. 215 108 b 8 167 105 ea added 96 000 – 9159, 211the 775result = ……………… to 7 ……… 812 ten million. 1312 –bebe 4 317 159 =– to 24 ×73it812 +810 × ……… ×million. 24 b badded it145 159, the result willwill ten – 3 104 007 – 4 05618 104 fc 270 6 505 789 – 4 327 558 = ……………… 408 is subtracted from result 200999. 999. …………… =the …………… c 270==408 213213 is+subtracted from it, it, the result willwill bebe 18 200 ……… ……… ……… = …………… = …………… = ……… + ……… Third: Multiplying a Whole Number by Another c 9 000 100 Third: Multiplying a Whole Number by Another 856 d = ……… 3 255 202 ac Multiplying by a 1-digit Number – 7 8 423 087 Multiplying by089 a 1-digit Number 2 a2 Mathematics 14 20 16 Stage-Year 4 Shorouk Press – 5 018 739 – 2 028 139 =for Primary …………… 2Drill = 1: ……………… = …………… Drill 1: d 9the 887 000 –as 7 115 306 = …………… Find product the example. Findethe(3product as the example. 280 075000 + 5–909 138) – 7= 657 249 = …………… e 9 312 9 211 775 ……………… Tens 6 005 + 3 095 235 to = …………… 25 cCircle the 218 number nearest the correct answer, without 99 999 Drill 4: Lesson 1 twoHundred Thousands (9 million , 8 and a halfofmillion , 10of+million) 1 performing usual subtraction Mostafa bought the kinds of cloth, theoperation. price one metre the a b c subtracted from one milliard, the result is 758 209 312. added to it 7 812 159, the result will be ten million. 270 408 213 is subtracted from it, the result will be 18 200 999. Third: Multiplying a Whole Number by Another a Multiplying by a 1-digit Number 2 the of : DMultiplying SComplete eSecond can3: d : according ividinto ga Wplace haolWhole e Nvalue umbNumber e by Andigit. oby theAnother r 2 Drill Complete according to the place value ofr each each digit. Inathe 2008-09 governomental budget and in the context of the by a 1-digit a Dividing Multiplying by a Number 1-digit Number Hundred Ten Hundred Ten Drill 1: Thousands Hundreds Tens Units Number c 6Thousands 005 218 + 3 095 235 = …………… Thousands Tens Units Number Thousands governomental efforts to support basicHundreds commodities, 2 milliard Thousands Thousands Find the product as the example. (9 million , 8 and a half million , 10 million) 752 341 pounds 752 341 were allocated for that perpouse, 405 million pounds to 605 618 maintain prices of medicines and 750 million pounds to reduce 605 618 the Example: Find the product of: 357 × 4 = …………… 3the If the income from the advertisements during African 78 539 interest on housing loans. Find the total sum the for the three items 78 539 Football Cup of Nations ‘Ghana 2008’ for the Egyptian 58 002 in expenditure. 58 the 002 governomental 357 7 + 21 50 million + 300 and eight hundred357 Channel Two was thousand × pounds, 4 × Sports 4 TV seven hundred thousand × 4 pounds for Nile 354 Write the following number 3 Underline the correct number, in digits, which express each Complete the solution: 3 Underline the+=correct number, in digits, which express each of of 28 + 200 + 1 200 = 1 428 300 + 50 4 andfollowing Youth and Sports Radio Channel five hundred and eight x 4 the in words. 2 000 000 000 pounds support basic commodities following 4 words. xthe thousand pounds. Find the total seven income acheived the three 16 a one hundred sixty thousand, hundred and forty 405 000 000 pounds maintain pricessixteen ofby medicine a one hundred sixty thousand, seven hundred and forty a 218 8+ …… + ……… + 200 218tens ......... 1200+200+16 =the ........ destinations from advertisements. 20 (16 740 , 740 160 ,interest 167 040 , 160 740) + 750 000 000 pounds reduce of housing loans × ………………………………………………………………………… 7354 x 4 = 1416 × 7 …… 12× hundreds +1200 354 ……………… pounds governomental expenditure...... b = 300 one thousand, hundred and= seventy-five +hundred 50 += 456 + …… +three ……… ……… 1416 x 4 xb one hundred 4 thousand, three hundred and seventy-five sixteen 16,nintySecond: Large Numbers cFind seventy thousand, five hundred and three ................. (10 375 , x100 1 375 , 375 100) Exercise 6 theSubtracting product of 9318 8 + 375 1200+200+16 = ........ 200 20 tens b 7346 6 + …… + ……… ……… 354 x 4 = 1416 +1200 12× hundreds × 61: × …… … 9318 Drill seventy thousand, five hundred and nintythree 1 c Add, then use the calculator to check your answer. 1416 8x = … (+8+....+....+....+) …… + ………x8=....+....+....+....=.... = ……… Subtract as the example. (70 593 , 700 593 , 59 370 , 750 093) 4 Complete as the example. a 8 752 013 b 2 560 000 18 ................. 6 9 12 0 15 Find+the product of 9318 x 8 439 815 + 5 981 812 + =1: 80 350 Example 2: 9 870 215 4Example Complete as 7the example. Example: 147 962 =128 962 + 147 000 = …………… 9318…………… + .............. – 5 040=115 – 000 7 818 408000 + 60 + 900 + 7 000 + 40 + 100 + .............. 8x ( 82+....+....+....+) x8=....+....+....+....=.... =1147 2 962 310 = 2 051 807 Example: 962 + 147 000 c 465 789=013 ................. = 2 + …………………………………………… 60 + 900 + 7 000 + 40 000 + 100 000 a+ 672 384 + 384 5 984 = 078 80 a 6 215 108 b 8 167 105 .............. + = …………… = 4 + 80 + ………………………………………… .............. – 384 3 104 007 – 4 056 104 a+ 672 = 384 + …………………………………………… d =2 107 305 + 5 760 119 = ……………… = …………… …………… == 4459 + 80 + ………………………………………… b................. 126 459 + …………………………………………… e (3 217 907 + 4 814 256) + 5 152 917 = …………… = 9 + ……………………………………………… 7 423 856 d 3 255 202 bc 126 459 = 459 + …………………………………………… 2 Circle the number nearest to the correct answer, – 608 5 018 739 – 2 without 028 139 9 + ……………………………………………… c 35 = 608 + …………………………………………… performing the usual addition operation. = ……………… = …………… = …………………………………………………… a 5 260 180 + 7 985 954 = …………… c 35 608 = 608 + …………………………………………… (900 million , milliard , 13 million) e 9 312 000 – 9 211 775 = ……………… = …………………………………………………… 100789 + 2 –600 050558 = …………… fb 8 400 6 505 4 327 = ……………… (11 million , 7 milliard , 6 milliard) Shorouk Press 16 First Term 3 3 315 32 + 160 + 2 400 + 56 000 + 400 000 b 9Drill × 784 =2:…… × (… + …… + ………) 458 592b 9 × 784 = …… × (… + …… + ………) ……… + ………… = …………… Find the product as +the example. = …… + ……… + ………… = …………… …………… 4 259 = 6 × (9 + …… + ……… + …………) c50 000) 6Example: 352 × 5 = (28 +× …… + ……… + …………) × 5 57 324 = …………… 00 + 7 000 = +54 +c…… + ……… + ………… = …………… 6 352 × =5= = ++…… ……… + …………) ×5 10 +(2(4 …… + ……… …………… 8× 20 ++300 ++ 7………… 000 + 50= 000) 00 + 56 000 + 400 000 99 999 c 6 005 218=+ =332 095 235 = 2…………… 10 + …… +400 ……… ………… = …………… + 160 + + 56+000 + 400 000 Drill 2: 784 = …… × (… + …… Lesson 1 + ………) Hundred Thousands million , 8 and a half million , 10 +million) 1 Drill 3: = (9458 592 If the budget allocated to support drinking water increased in two = ……Drill + ……… + ………… = …………… 3: the product the examples. 99999 100 000 consecutive yearsasfrom 270 250+ 000 pounds to 750 180 … + ……… +Find …………) 99 000 999 99 999 1 = 100 000 3 IfFind the income from the advertisements during the African + 1 2 6 1 2 2 3 3 4 the as 99 999 1 = 000 a =Find 6…………… × product 4the 259amount = the 6of×examples. (9 + …… ++ ……… +100 …………) pounds. increase. +52 ……… + ………… + 1 100000 × 5 = (2 +Football …… + ……… + …………) 5 2008’ for the Egyptian «×hundred Cup of Nations 2679 2 3 3 4 Example 1: This 9 308 8«354 =2 is 6read 54‘Ghana +as …… +Example ……… +2:………… =1 …………… number thousand Solution: = 10 + …… + ……… + ………… = …………… 100 000 Hundred Ten was Channel million and eight hundred 999821 999 1 =180 100000 000 Example 1: increase 308 Example 8 3545 679 Thousands Hundreds Tens ×Two Units × 2: thousand amount of =+ 750 – …………… = …………… … + ………) TheThousands Thousands pounds, for Nile Sports TV hundred thousand pounds Hundred × 8× 74 464 = × 41 773 395 5 b 9remainder, ×= 784 =Ten …… (…seven + in …… + ………) (read the then write it words) …… + ………… = …………… Thousands Hundreds Tens Units 3: and Youth Radio Channel hundred and eight395 Hundred Ten and Thousands Thousands = Sports 74 464 41 773 Thousands Hundreds Units = …… +Tens ……… + five ………… == …………… 1 0 0 0 0 0 Thousands Thousands e product as thethousand examples.pounds. Find the total income acheived by the three a 75 354 bExercise 83 204 7 c 3 605 421 ……… + …………) × 2 6 1 2 2 3 3 4 destinations the 0 advertisements. a 74difference 354 b c × × …… 8following × 6 421 This is read as ‘hundred c =number 6…………… 352 ×from 50 = (2 + +83 ……… + …………) × 53 605 1 0 08the 0204 1 Find the in each of +e……… + ………… 1: 9 308 ………………………………………………………………………… Example 2: 354 679 × 8 +on 6 = × ……… 4and=can =+ …… ………… = × …………… 10be + ……… ………… = …………… thousand’ represented × 8 × 5 aThis 2 256 912 b 6 444 382 number is read as ‘hundred = ……… = opposite. ………… = …………… the abacus as in the figure This number is read as ‘hundred = 74 464 = 41 773 395 –the 1calculator 145 810 can – on 4 317 159 thousand’ and beLarge represented Second: Subtracting Use to check yourNumbers answers. Drill 3: es. = …………… =answers. …………… theUse abacus as in the and figure opposite. calculator to check yourbe thousand’ can represented on Findthe as the examples. 1the 2 2 product 3 3 4 7 354 b 83 204 c 3 605 421 Drill 1:8 354 679 2 6 1 2 2 3 3 4 Example 2: the abacus as in the figure opposite. × 8 × 6 4 c 9as000 Subtract the100 example. Example 1: 2: 8 354 679 Exercise Example 1 × 5 9 308 1– Write the ……… = ………… 6 9 12 0 15 8 087 089 numbers. = …………… × 8 × 5 =Write 41 773 395 1 = numbers. …………… Example 1: the 7 350 128 Example 2: 9 870 215 = 74 464 = 41 773 395 19 e calculator to check your – answers. 5 040 115 – 7 818 408 d 9 – 7 421 115 306 = …………… 83 204 c 887 000 3 605 19 = 2 310 013 = 2 051 807 7 354 c 3 605 421 e (3a 280 + 5 909 – 7 657 83 249204 = …………… 8 × 075 6 138) b 1 512 numbers. 6 247 + 45the 067 753) – (1×200 105 8– 2 489 105) × ………… f (4 =×Write …………… a 6 215 108 b 8 167 105 ……… = ………… = …………… ==……………….………………. – 3 104 007 – 4 056 104 ur answers. = the …………… to check your answers. = …………… 19 Use 2 Circle thecalculator number nearest to the correct answer, without performing the usual subtraction operation. c 7 423 856 d 3 255 202 a 7 256 312 – 7 056 300 = …………… – 5 018 739 – 2 028 139 (200 million , 200 thousand , 250 thousand) = ……………… = …………… b 8 205 107 – 319 198 119 = …………… (8 milliard , 6 milliard , 5 million) 19 e 9 312 000 – 9 211 775 = ……………… c 459 212 – 350 200 = …………… f 6 505 789 – 4 327 558 = ……………… (hundred and ten thousand , hundred thousand , milliard) d 9 575 100 – 4 275 090 = …………… (two milliard , 5 million , 850 million) Lesson 1 Hundred Hundred Thousand Thousands Tens Units Hundreds Units Thousands Units Hundred Thousands Ten Thousands Tens Hundred Thousands Hundreds Units Tens Hundreds Ten Thousands Tens Hundreds Thousands Hundred Thousands Ten Thousands Tens 17 Shorouk Press Ten Thousands Thousands Ten Thousands Thousands 1 0 Thousands Hundred Ten Thousands Hundred Thousands Hundred Thousands Units Hundreds Thousands Units Ten Thousands Tens Hundreds Thousands Ten Thousands 9 0 Units Tens Tens Hundreds Units Hundreds Thousands 9 0 Exercise 1 Units Tens Thousands Tens Hundreds Ten Thousands Hundred Thousands 4 2 Mathematics for Primary Stage-Year 4 (2015 - 2016) 16 2 9 0 Units Units Tens Tens Hundreds Ten Thousands Hundreds Thousands Thousands Hundred Thousands Hundreds Thousands 0Exercise 0 0 1 Ten Thousands 0 Ten Thousands Thousands 1 Hundred 9 0 Ten Thousands Thousands 9 0 Hundred Ten Thousands Thousands 1 Hundred Thousands Hundred Thousands Lesson 1 Hundred Thousands = = Hundred Thousands e. c 6 352 × 5 = …… + ……… + ………… = …………… = = (2 + …… + ……… + …………) × 5 10 + …… + ……… + ………… = …………… 2 Complete Drill 2: according Drill 4: 3: Drill 4: 2 Complete according to to the the place place value value of of each each digit. digit. Drill 4: If the budget allocated to support drinking water increased in two Mostafa bought two kinds of cloth, the price of one metre of of the the Find thebought product as kinds the Mostafa two of cloth, of metre of the Hundred Tenexamples. Mostafa bought two kinds cloth, the the price price of one one Tens metre Hundred Ten of Thousands Hundreds Units Number Thousands Hundreds Units Number Thousands first kindis is97 97years pounds and the price of pounds one metre metre ofTens the second is consecutive from 270 250 000 to 750 180 2 Thousands 6 and 1 2second 2 000 3 3 4 first kind pounds the price of one of the is Thousands Thousands first kind is 97 pounds and the price of one metre of the second is 752 341 158 pounds. IfMostafa Mostafa bought 4 metres metres of the the2:first first kind kind and 679 3 pounds. Find the of increase. Example 1: IfIf 9amount 308bought Example 8 354 158 pounds. 44 of and 3 752 341 158 pounds. Mostafa bought metres of the first kind and 3 605 618 metres ofthe the×second, second,8how how many many pounds pounds did did Mostafa Mostafa pay? Solution: × 5 metres pay? metres of the second, how many pounds did Mostafa pay? 605 618of 78 The amount= of 74 increase …………… 464 = 750 180 000 – …………… = 41 =773 395 78 539 539 Solution: 58 (read Solution: Solution: 58 002 002the remainder, then write it in words) Price offirst first kind == = …………………………………………… …………………………………………… pounds a 7first 354 b97 × 483 204 = c 3 pounds 605 421 Price of kind pounds Price of kind …………………………………………… Price ofsecond second kind = ………………………………………… ………………………………………… pounds Write the4the following number 3 Underline correct number, each of Exercise ×of ×× 3 in 8 =7which × Price kind == pounds 158 Price of second kind ………………………………………… pounds 3 Underline the correct number, in digits, digits, which express express each of6 Mostafa paid = ………………………………………………… pounds following in words. 1 the the== difference in +each of the following =Find ……… = ………… = …………… Mostafa paid ………………………………………………… Mostafa paid ………………………………………………… pounds the following words. = a one hundred sixty thousand, seven hundred and forty hundred hundred a a one 2 256 912 sixty thousand, b seven 6 444 382 and forty ......... (16 your 740 ,answers. 740 160 , 167 040 , 160 740) Use the calculator to check – 1 145 810 – 4 317 159 b b Multiplying byaa athousand, 2-digit Number Number one hundred three hundred and seventy-five ...... bb Multiplying by 2-digit Multiplying by 2-digit Number = …………… = …………… b one hundred thousand, three hundred and seventy-five c 1: seventy hundred and ,nintythree ................. Drill 1: thousand,(10five375 , 100 375 1 375 , 375 100) Drill Drill 1: c 9 000 100 Findthe theproduct product as as the the examples. examples. Find the product as the examples. Find – 8 087 089 c seventy thousand, five hundred and nintythree 19 = …………… Example 1: as27 27 × 53 53 == =(70 27593 × (3 (3,++ +700 50) 593 Example Example 2: 5 3 , 59 3702: , 750 5 093) 4 Complete the example. Example 1: 27 × 53 27 × (3 50) 3 Example 1: × 27 × 50) 2 3 22 33 d 9 887 000 – 7 115 306 …………… = 27 27 ×× × 33 3 ++ + 27 27 ×× ×=50 50 × 2 2 7 7 = 27 27 50 × = × 4 e Complete as the example. Example: 147 962 = 962 + 147 000 (3 280 075 + 5 909 138) – 7 657 249 = …………… = 81 +067 1=350 350 371 2753) + 60–+(1900 7 000 40 000 100 f (4 512== 24781 +5 200+ 105 – 2+ 489 105)+ 3 81 350 371 ++ 11 7 000 1 Example: 962 = ……………….………………. =147 1 431 431 = 962 + 147 000 + 01 16060 060 = 1 431 + = 1 + 1 0 = 2 + …………………………………………… 60 + 900 + 7 000 + 40 000 + 100 000 a 672 384 = 384 = 1 431 = 4 +nearest 80 + ………………………………………… 2 Circle the number to the correct answer, without = = 1 41 431 3 1 a performing 672 384 the=usual 384 +subtraction …………………………………………… operation. (Notice that the product is the same even with different different methods, ==–4459 +300 ………………………………………… (Notice that the312 product is80 the same even with with b a that 126 459 +the …………………………………………… 7 256 7+056 = …………… (Notice the product is same even different methods, methods, use a calculator to check your answer.) useaacalculator calculator to to check check your answer.) answer.) =(200 9 + million ……………………………………………… , 200 thousand , 250 thousand) use your b b 126 459107 =– 459 + …………………………………………… 8 205 3 198 119 = …………… 24 × × 43 4335 = 24 24 × (……… (……… + 40) 43 24 40) 43 9 +++ ……………………………………………… = 608 +40) …………………………………………… (8 milliard , 6 milliard 43 , 5 million) 24 ×c43 == 608 24 ×× (……… = 24 × 3 + ……… ……… ……… × 24 …………………………………………………… c == 459 212 200×××=……… …………… 24 ……… × 24 24 ×× 33–++=350 ……… × 24 = 608 ……… +ten ……… ………, milliard) c (hundred 35= 608 + …………………………………………… and= thousand , hundred thousand ……… ……… ……… = ……… ++ ……… ……… d = 9 575 100 =– …………………………………………………… 4 275 090 = …………… + = ……… + ……… ……… ……… = ……… + ……… (two milliard , 5 million 850 million) = ,……… ……… = = ……… 20 20Shorouk Press First Term 5 3 317 Lesson 1 Hundred Hundred Thousand Thousands Lesson 1 3 99 999 1 Complete. Drill 2: 1712 +Hundred Lesson a 3 256 …………… = 7Thousands 807 300 Thousands Tens Units Ten Thousands Hundred Thousands Hundreds Thousands Ten Thousands 9 0 Units Hundred Thousands Ten Thousands Tens Shorouk Press Units Hundreds Units Thousands Ten Thousands Tens Hundreds Thousands Hundred Thousands Ten Thousands Tens Hundred Thousands Hundreds Units Tens Hundreds Thousands Hundred Ten Thousands Hundred Thousands Hundred Thousands Units Tens Hundreds Ten Thousands 2 Hundred Thousands 6 2 Mathematics for Primary Stage-Year 4 18 Thousands your teacher, discuss the annual Cairo bWith7346 6 + …… + benefits ……… of holding the……… International Book× Fair in Egypt and its annual timing. × 6 …… × … = … + …… + ……… = ……… 21 Ten Thousands Thousands Ten Thousands Thousands 1 0 Units Hundreds Units Tens Thousands Tens 9 0 Exercise 1 Units Tens 9 0 Units Hundreds Tens Hundreds Units Tens Hundreds Thousands Ten Thousands Hundreds Thousands Hundred Thousands Hundred Thousands Thousands Ten Thousands 0Exercise 0 0 1 Ten Thousands Thousands 0 Hundred 1 Ten Thousands Thousands 9 0 Hundred Ten Thousands Thousands 9 0 Hundred Thousands 1 Hundred Thousands 100 000 4 IfHundred the budget allocated medicine in two consecutive 99 999 to +Hundreds 1support = 100 000 Thousands (4 ×Thousands 12) × 25 4 Tens × (12 × Units 25) Thousands years increased pounds to 405 million pounds Tenfrom 380 million = 48Hundred × 25 4 × 12 × Tens (5 + 20) Units Thousands = Hundreds toThousands preserve the prices of medicine. Find the amount of the Hundred Ten Thousands Thousands0 Hundreds 0Tens = 0 Units = Thousands 481× Thousands (5 + ……) 4 × (12 × 5 + …… × ……) 0 0 increase. = …… × …… + …… × …… = 4 × (……… + ………) is read = This …… +0 …… = 0 …………… 4 × ……… + 4 × ……… 1 number 0 as ‘hundred 0 = 0 5 thousand’ Find the number that if: = ……… on + ……… = ……… and can be represented number from is read ‘hundred a This subtracted oneasmilliard, the result is 758 209 312. the abacus as in the figure opposite. This number is read as thousand’ and can be represented on bDrill added to it 7 812 159, the result will ‘hundred be ten million. 3: abacus as the and figure can opposite. cA the 270 408 isopportunity subtracted from it, therepresented result will be 18 200 999. thousand’ be on school took213 thein No. Quantity Unit Price Total Price of the Cairo International Book thesent abacus in the1 figure opposite. Third: a as Whole by Another 121 34 Fair andMultiplying delegates to Exercise buyNumber 1 Write the numbers. asome Multiplying by abook 1-digit Number 2 15 42 books for the 1 Write the numbers. 3 18 48 library. Using the part of the Drill 4 invoice 1: opposite, answer the Find the product as the example. following questions. Grand Total: ...................... a What the number 1 isWrite the ofnumbers. Example: Findcost the34 product of:each 357 × 4 = …………… books that pounds and what is their total price? 7 + 50 + 300 357 b 357 What is the number of books × that 4 cost 42 pounds × 4each and × 4 = 28price? + 200 + 1 200 = 1 428 what is their total c What is the number of books a 218 8 + …… ……… 218 that cost 48 pounds each+and × what 7 is their total × price? 7 × …… d Find the total =amount of money required from =the……… school. 56 + …… + ……… Hundreds «hundred thousand« This number is read as Ten Tens + Find the product of 4 × 12 × 25 using more than one method. b 9 256 000 – …………… = 5 312 989 99999 100 000 99 999 99 999 + 1 = 100 000 c …………… – 7 218 305 = 6 977 455 + 1 99 999 +1 = 100 000 First Method: Second Method: + 1 100000 58of 2 Complete the 2: according Exercise 2 Drill Complete according to toExercise the place place value value of each each digit. digit. Find the product as the example. Hundred Ten Hundred Ten Thousands Hundreds Tens Units Number Thousands Hundreds Tens Units Number Thousands Thousands 1 the following numbers, then complete. the product for each of the following. 1 FindRead Thousands Thousands 752 341 …… …… million, Example: × 57302 324 b = …………… a a1238×719 158 645 2 784milliard, ×8 c 5 467 × 84 752 341 605 …… thousand …… = ×849 × (4 + 20 e + 300 7 000 + 50and 000) d 23 278 475+ 209 × 23 f 3 785 × 17 605 618 618 53932006 475 …… milliard, 78 + 160 + 2 400 + 56 000 +…… 400 million, 000 Usebthe6= calculator to check your answer. 78 539 539 …… thousand and …… 58 = 458 592 58 002 002 c 2 163 900 800 ……inmilliard, using a suitable digit each …… . million, 2 Complete …… and …… 4 each following 3 Underline number, in express 259the 6 ×number (9 + …… ……… +c …………) 4 5=correct 3thousand 5 which 4 of 3 a Write Underline the correct number, in+ digits, digits, which express each of8 a6 × 4the b d 5 180 070 506 …… milliard, …… million, the following in words. = 54 + …… + ……… + ………… = …………… × 7 × 8 × 75 the following words. thousand and a hundred and forty = 4hundred 5 5 sixty = …… 7 4 seven = …… 170 2 0......... 40 a one one hundred sixty thousand, thousand, seven hundred and forty (16+740 , 7+ 740 b 9 × 784 = …… × (… +…… 0………) 0160 , 167+ 040 , 160 740) 2 bJoinone thehundred two cards expressing the same number. = thousand, …… + ……… + hundred ………… ==…………… three and seventy-five ...... b7 000 one600 hundred hundred and seventy-five 900 thousand, three 7 million, 6 thousand and 900 c seventy thousand, five hundred and nintythree 375 , 100 375 , bought 1 375 ,×18 375 100) 352 = happy (2 +(10 …… + ……… + …………) 5................. one ×of5their occasions, a family kilograms 3c 7In6million, 600 and+900 70 =thousand …… ……… ………… =900 …………… of meet for LE 3510a +kilogram and 16+litres of 600 juice for PT 400 a clitre. seventy thousand, five hundred and nintythree How many pounds7did the family pay? 7 006 900 milliard, 600 thousand 900093) (70 593 , 700 593 , 59 370and , 750 4 Drill Complete 3: as the example. product astothe examples. for his family. He bought 15 4FindA the man wanted build 4 7 000 000 +a6house 000 + 900 2 example. 6= 962 + 147 000 1 2 2 3 3 4 4 Complete as the Example: 147 962 tons of building steel for LE 7 356 a ton and 48 tons of cement = 2 + 60 + 900 + 7 000 + 40 000 + 100679 000 Example 1: 9 308 Example 2: 8 354 475of a the ton.following How much did theisman 3 afor LE Which numbers the pay? nearest to one Example: ×147 962 = 8 962 + 147 000 × 5 milliard? Represent the numbers on the number line. = 2 + …………………………………………… 60 + 900 +7 000 + 40 100395 000 672 384 384 = number 74=464 = 000 41 +773 to 990 the correct 5 aChoose 1 000the 000 090 , nearest 999 999 or 1 answer, 100 000 without 000 = 4 + 80 + ………………………………………… operation. bperforming Which ofthe themultiplication following numbers is the nearest to two 384 = 384 + …………………………………………… a aa 672 7 354 b 83 204 c 3 605 421 25 × 977 × 4 = …………… milliard? == 4459 + 80 +×………………………………………… b × 126 459 + …………………………………………… 4 × 6 (98 000 10 000 110 000) 2 000 000 020 , 299 999 999 or ,1 999 999 ,900 = 9= +…………… ……………………………………………… ……… = ………… = …………… b= 40 × 75 × 50 b 126 459 = 459 + …………………………………………… thousand , with 200 thousand , 500 thousand) 4 a Find two(300 10-digit numbers the difference between 9 + ……………………………………………… ccthe 35 608 = 608 + …………………………………………… Use calculator to check your answers. 100 ×is99 × 98 = …………… them one milliard. = …………………………………………………… (900 thousand , 800 one million) b Find two 10-digit numbers with thethousand difference, between cd 35 608 = 608 + …………………………………………… 125 ×is48 = …………… them one million. = …………………………………………………… (five thousand , six thousand , seven thousand) c Find two 10-digit numbers with the difference between them is one thousand. 22Shorouk Press First Term 7 13 3 319 Lesson 1 Hundred Hundred Thousand Thousands Lesson 1 9 0 Hundreds Thousands Units Ten Thousands Tens 9 0 Hundreds 9 0 Thousands 9 0 Ten Thousands 9 0 1 Hundred Thousands Hundred Thousands first kind is 97 pounds and the price of 100 one metre is 000 99999 100 999 99 999 +1= 000 of the99second +3 1 Example: 568bought ÷ 2 99 158 pounds. IfDivide Mostafa 4 metres first100 kind and 999 of+ the 1= 000 + 1 «hundred « 100000 metres of theThis second, how many pounds didthousand Mostafa pay? number is read as 100 000 Hundred Ten 99 999 +Hundreds 1 = 100Tens 000 Units Solution: Thousands Thousands Thousands Hundred Ten = 5 hundreds + 6 tens + 8 units We know that 568 Solution: Thousands Hundreds Tens Units Hundred Ten Thousands Thousands = 4 hundreds + 16 tens + 8 units Price of first kind = …………………………………………… pounds 1 Thousands0Thousands0Hundreds 0Tens 0Units 0 Thousands Price of second kind = ………………………………………… pounds Then, 568 =0 + +08) ÷ 20 This number is(400 read as ‘hundred Mostafa pounds 1 paid 0 ÷= 2………………………………………………… 0160 (400 ÷ 2)be + represented (160 ÷ 2) + (8 on ÷ 2) thousand’ =and can This number is read as ‘hundred = 200 + 80 + 4 = opposite. 284 the abacus as in the figure This number is read as ‘hundred be represented b thousand’ Multiplyingand by can a 2-digit Number on thethousand’ abacus figure can opposite. Drill 1: as in the and be represented on Tens Third : Dividing Dividing a Whole Number by Another99 999 Fourth: a Whole Number by Another Drill 4: Lesson 1 twoaby Hundred Thousands Dividing a 1-digit 1 aa Dividing 1-digit Mostafa boughtby kinds ofNumber cloth,Number the price of one metre of+ the 1 1 0 0 0 0 0 Exercise 1 out the division Follow the steps of the following example to carry Drill 1:abacus as in the figure opposite. the operation: 459as ÷ 3the examples. Find the product Exercise 1 1 Write the numbers. + = Tens Hundreds Units Ten Thousands Units Tens Hundred Thousands Hundreds Units Tens Hundreds Ten Thousands Tens Hundreds Thousands Hundred Thousands Thousands Shorouk Press 23 Ten Thousands × 43 24 ……… ……… ……… Hundred Thousands Units Tens Hundreds Ten Thousands 2 Hundred Thousands 8 2 Mathematics for Primary Stage-Year 4 20 Thousands 742+÷40) 2 24Example: × 43 = 24Divide × (……… 1 = 24 × 3 + ……… × ……… Solution: 7 4 2 + ÷……… 2 = 371 = ……… = ……… Ten Thousands Hundred Thousands Units Tens Units Tens Hundreds Hundreds Thousands Ten Thousands Thousands Hundred Ten Thousands Thousands Hundred Thousands Note:that You perform thesame previous write the (Notice thecan product is the evensteps with mentally different and methods, quotient as shown in the following example. use a calculator to directly check your answer.) Units Thousands Ten Thousands Thousands Thousands Hundred Units Tens Hundreds Ten Thousands Hundred Thousands Units Tens Thousands Hundreds Exercise 1 Units Tens Hundreds Thousands Ten Thousands Ten Thousands Thousands Hundred Thousands Hundred Ten Thousands Thousands Hundred Thousands 1 Write the numbers. Complete solution: Example 1: the 27 × 53 = 27 × (3 + 50) Example 2: 5 3 2 3 459 = 4 hundreds + 5 tens + …… units = 27 × 3 + 27 × 50 × 2 7 = 3 hundreds + 15 tens + …… units 1 Write numbers. = 81 +the 1 350 371 459 ÷ 3 = (300 + 150 + ……) ÷ 3 = 1 431 + 1 060 = (300 ÷ 3) + (……… ÷ 3) + (…… ÷ ……) = ……… + ……… + ……… = ……… = 1 431 Fourth: a Whole Number by Another 2 Complete according Drill 2: Dividing 2Drill Complete according to to the the place place value value of of each each digit. digit. 2: a Dividing by aof1-digit Number Find the product 4 × 12 × 25 using more than one method. Ten for each of the following division Write the Hundred quotient directly Hundred Ten Thousands Hundreds Tens Units Number Tens Units Number Thousands Thousands Thousands Hundreds Thousands Thousands operations, then use the calculator to check your answer. Example: Divide 568 ÷ 2 752 341 First Second Method: 752 341Method: 605 618 605 618 a 946 ÷ 2 b 486 ÷ 3 Solution: 78 539 (4 12) ÷× 725 4 × (12 78 × 539 c 847 d + 655 ÷ 5+×825) We know that 568 = 5 hundreds 6 tens 58 = 48 × 25 = 4 × 12 units × (5 + 20) 58 002 002 = 4 hundreds + = 16 tens + 8 ×units = 48 × (5and + ……) 4 × (12 5 + …… × ……) Dividend Divisor the following 3 Underline the in express each of = Write …… × …… +correct …… number ×number, …… =the4first ×which (……… + is ………) 3When Underline the correct number, in digits, digits, which express each the of dividing a number by another, number called Then, 568 ÷ 2 in == (400 + 160 + 8) ÷ =2 4 × ……… + 4 × ……… the following words. = …… + …… …………… the following words. dividend and the second the = (400 ÷ thousand, 2) is+ called (160 ÷seven 2) +divisor. (8 ÷ 2)+ ……… a one hundred sixty hundred and = ……… = ……… a one hundred sixty thousand, seven hundred and forty forty ......... = 200 +(16 80 + 4 = 284 740division , 740 160 , 167 54 040÷ ,9,160 740) For example, in the operation Drill 3:hundred b one three seventy-five ...... 54 is thousand, the dividend andhundred 9 is the and divisor. Drill 1: b onetook hundred thousand, three hundred and seventy-five A school the opportunity No. Quantity Unit Price Total Price Follow the steps of the following carry out the division c thousand, five hundred andto,nintythree ................. (10 375 , example 100 375 1 375 , 375 100) of the seventy Cairo International Book operation: 459 ÷ 3 1 12 34 Fair and sent to buy Quotient anddelegates Remainder c books seventy 2 and 15ninty- three 42 some forthousand, the book five hundred Complete the solution: 700 593 , 750 093) 18, 59 37048 4 library. Complete the example. Usingas the part of(70 the593 , 3 459 = 4 hundreds + 5 tens + …… units invoice opposite, answer the that4need to be distributed equally Example: We have 17 pens = 3 hundreds + 15 + …… units 4 following Complete as the Example: 147 962 = 962 tens + 147 000 questions. Grand ...................... among 3example. children. Find the Total: greatest number of pens = 2 + 60 + 900 + 7 000 + 40 000 + 100 000 a What is that the number of can be given to every child. 459 ÷ 3 = (300 + 962 15034 ……)+ ÷147 3 000 Example: 147cost =+ pounds 962 books that each =what (300 3)= +384 (……… ÷+ 3) + (…… ÷ ……) =total 2pens 60 and 900 + 7 000 +left 40 000 + 100 000 a and 672 384 + price? …………………………………………… is÷their Solution: Directly is 5 2 pens are = is ……… += ……… + ……… = ……… 45+×80 + ………………………………………… b What the number of books because 3= 15 and 17 – 15 = 2 a that 672 384 = 384 each + …………………………………………… cost 42 pounds and Note: You can total perform previous steps mentally and write the ==quotient 4459 + 80 + ………………………………………… 126 +the …………………………………………… what is459 their price? In b this example the is 5 in and the remainder is 2. quotient directly as shown the following example. = 9 + ……………………………………………… c What is the number of books b that 126 459 =2459 each + …………………………………………… cost 48 pounds and Then, 17 = 5 × 3 + Example: Divide 9price? + ÷……………………………………………… c what 35 is 608 =742 608 +2…………………………………………… their total 1 = …………………………………………………… d Find the total amount of money required from the school. Solution: 7 4 2 =÷ 608 2 += …………………………………………… 371 c 35 608 …………………………………………………… With your teacher,=discuss the benefits of holding the annual Cairo International Book Fair in Egypt and its annual timing. 24Shorouk Press First Term 9 23 3 321 Lesson 1 Hundred Hundred Thousand Thousands Hundreds Thousands Ten Thousands Hundred Thousands Drill 3: Drill 3:the following table as the example. Complete 99 999 Exercise 8 Drill 4: Complete the following table as the example. Lesson 1 The Hundred Thousands Relation between 1 Mostafa bought two kinds of cloth, the one metre of+ the The division The Theprice ofThe Drill 3: elements of Relation between division The for The The The of the second 1The Find the product each of the following. first kind is 97 pounds and the price of one metre is operation dividend divisor quotient remainder 99999 100 division operation Complete the following table as the example. elements 99 999 of 000 99 999 + 1 = 100 000 operation divisor +operation apounds. 123 ×Ifdividend 15 b 99 784 × 8of c division 5and 467 158 Mostafa bought 42quotient metres the first100 kind 3 ×184 999 +remainder 1= 000 + 1 100000 Relation 78 = 10 ×7 +8 «hundred «3elements 78 ÷ of 10 78 10 7 8 9 the 9many 8 ×did 6 9 between 817 6 The The The The ddivision 23 278 ×The 49 how e as475 209 23 f 78 785 × metres second, pounds Mostafa pay? This number is read thousand of = 000 10 × 7 + 8 78Hundred ÷ 10 78 10 7 8 100 Ten operation dividend divisor quotient 99 999 +Hundreds 1 =your 100 000 remainder Thousands Tens division operation Units Use the calculator to check answer. 43 ÷ 2 ......... ......... 21 ......... ......... Drill 3: Drill 3:43 Thousands Thousands ÷2 Hundred Ten Tens Lesson 1 Units Tens 9 0 Hundreds 9 0 Thousands 9 0 Ten Thousands 9 0 1 Hundred Thousands Solution: Complete following ......... Complete the table as Thousands the Hundreds 78 =Units 10 × 7 + 8table as 78 10 78 10 example. 7 76 5 Ten ......... ......... 77 ÷÷following 5 28Tens the Hundred Thousands Thousands 2 Thousands Complete using a suitable digit in each . Price of first kind = …………………………………………… pounds Thousands0 Hundreds 0Tens 76 1 ÷ 5Thousands 0......... 0Units 0Relation between......... ......... ......... 43 ÷ 2 68 ÷ 4 64 The The The division The The The The The0division Price of second kind = ………………………………………… 4 5 3 5 4 8 elements 4 of pounds a b c 68 dividend ÷4 dividend divisor operationThis divisor remainder operation division operation is read as Mostafa pounds ......... ......... 1 ÷ ×paid 0 = ………………………………………………… 0quotient 0 ......... 76 5number ………… 10 7960 × ‘hundred 80 × 75 9 0 1 + 7opposite. 0a 02-digit + the abacus as in the figure This number is read as ‘hundred bthousand’ Dividing aand Whole Number by Number can be represented on bb Multiplying by a 2-digit Number = a Whole Number by a 2-digit Number theDividing abacus as in the figure opposite. thousand’ and can be represented on 0 0Exercise 0 0 0 Drill 1 4: 0261 1 ………… 96and can 10be thousand’ on =4784 5 = The 5 7 quotient+ 4 =÷= 10 1 ×7 70+2878 040 78remainder 10 78 78 ÷ The 10This 10 7 represented 8 The 68 ÷ dividend divisor x=The number is read as ‘hundred 10 Dividing a Whole 43 with ÷ 2 remainder 43 ÷ 2 ………… 96 Number 10 by a 2-digit Number 76 ÷ 5 76 ÷ 5 Drill 1: Drill 4:abacus as in the figure opposite. the Find the product as35 thea examples. remainder 3915 ÷ 15 and 16 litres Exercise 1 of juice for15PT 39 1 5a of meet forexample. LE kilogram 400 Divide as the 1 Write the numbers. 1 _2960 ………… ………… 96 10 Solution How did the family pay? Drill 4: _3 0 1 litre. Write the numbers. Example: 1many 320 ÷pounds 11 = 120 11 1 13 22 00 Example: Find the quotient of theby division without one of their happy occasions, family bought a Whole Number a 2-digit Number 68 ÷ 4 18 kilograms 68 ÷3Divide 4b InDividing as the example. 10 Dividing a Whole Number by a 2-digit Number 25 Ten Thousands Units Ten Thousands Tens Shorouk Press Hundred Thousands Hundreds Units Thousands Ten Thousands Tens Hundreds Tens Hundred Thousands Hundreds Units Tens Hundreds Units Thousands Ten Thousands Thousands Thousands Hundred Thousands Hundred Thousands Units Tens Ten Thousands Hundred Thousands Units Tens Hundreds Units Hundreds 10 Ten Thousands Hundred Thousands Units Tens Thousands Tens Hundreds Tens Hundreds Exercise 1 Units Thousands 96 Units Tens Hundreds Thousands Hundreds Thousands Ten Thousands Ten Thousands Ten Thousands Thousands Hundred Thousands b Hundred Thousands Hundred Thousands ………… 2 Ten Thousands Hundred Thousands Ten Thousands Thousands Hundred Ten Thousands Thousands Hundred Thousands 3915 ÷ 15 = 261 Example 27 ÷ × 11 53 = 120 27 × (3 + 50) Example 2: 5 3 Divide as1:the example. Example: 1 320 = 11 – 11 31 29 01 2 3 4Note: A man wanted to3build a×a house forNumber his family. He–bought 15 b Dividing b Dividing a We Whole Number by 2-digit 1_2Whole 2 0 7 Number 1×12a =start 27 × + 27 50 with the division 920 tons We of building LE 7 356 a ton and 4811tons1 of cement Example: 1 320with ÷steel 11 120 Note: start the=for division 0 operation as shown opposite, – 223 222 1 5 1 Write the numbers. = 81 + 1 350 371 475we a ton. did the manDrill pay? 4: Drill 4:for LEoperation as How shown opposite, –– 1 201 20 then write the much quotient. 15 Divide as the+02example. Note: We=start with the the quotient. division Divide as the example. then we1 write 012 431 060 5a Choose the number nearest to the correct answer, without operation as shown opposite, 0 00 1182 –0 2 42 32 2 430 ÷ 18 = ……… = 1 performing the multiplication operation.11 Example: then we the quotient. Example: 320 11 120 182 02140320 30431 0÷ 11 = 120 a 21430 ÷÷18 ==write ……… 13 Drill 3: a 25 the × 977 × 4 = …………… Complete following table as the example.– 1 1 (Notice that the product is even 000with , different 10 2000 182 4110 3 with 0000) Note: We ,2methods, start the division 430with ÷ 18the = ……… Note: a We 2start divisionthe same (9 Relation between use adivision calculator to50 check your answer.) Theb The The The The 40 ×÷as75 ×= =opposite, …………… operation – 2152 3elements 9 1 5asofshown oppo boperation 3 915 15shown ……… operation dividend divisor quotient remainder (300 thousand , 200 thousand ,0 500 division then we write the quotien quotient. 150 3 thousand) 9 1operation 5 bthen 3 we 915write ÷ 15 the = ……… 24 ×c43 100 = 24 × (……… + 40) 43 × 99 × 98 = …………… 78 = 10 × 7 + 8 78 ÷ 10 78 10 7 8 == ……… + ……… × ……… × 430 thousand , 800 thousand one million) a 2 ……… 318 9= 1 5 18 4153, 0÷24 b ÷318 915 ÷2415× =3 (900 ……… a 2 430 43 2= ……… d ÷ 125 ×answer 48 = + …………… ……… ……… (check your by using the calculator or any other method.) (five thousand , six thousand , seven thousand) (check your answer by using the calculator or any other method.) 76 ÷ 5= ……… + ……… 25 = ……… 25 68 ÷ 4 10 b 915 ÷ 15 = ……… 15 3 9 1 5 (check your answer by using the calculator or any other method.) b 320 915 ÷ 15 = ……… 22 2 Mathematics for Primary Stage-Year 4 equals the remainder of 678 ÷ 13. ( ) and correct the wrong statement. 000 000 000 pounds support basic commodities c 2 When dividing 13, 26, 39, 52, … etc. by 13, the remainder a is If405 79 × 18 = 1 422, then 1 422 ÷ 79 = 18. 000 000 pounds maintain prices of medicine(( zero. )) 678000 = 52 × 13 + 2, then the remainder ÷ 52loans + b If750 000 pounds reduce interestof of 678 housing equalsusing the remainder 678 13. ( ) ……………… governomental expenditure 2 = Complete apounds suitableofsign <,÷>, or = in each without c When dividing 13, 26, 39, 52, … etc. by 13, the remainder performing the division operation. 99 999 Fourth: Dividing a Whole Number by Another 2 according the is zero. ( ) 2 Complete Complete according to toExercise the place place value value6of of each each digit. digit. a Dividing by a 1-digit Number a 2 538 ÷ 18 2 538 ÷ 37 + 1 Hundred Ten ands 9 1 en Hundred Ten Thousands Hundreds Tens Number Hundreds Tens Number b Thousands 780 ÷ using 9 Thousands (78Thousands ÷ 9)sign × 10 2 Complete a suitable <, >, or = in each Thousands Thousands 1d Add, then use the calculator to check your answer. 100 000 Example: Divide 568 ÷ 2 Hundreds Thousands Ten Thousands Units 752 the division operation. 752 341 341 c 100 × (287 865 ÷ 24) 282786 aperforming 8 752 013 b 560500 000÷ 24 605 605 618 618 439 + 375 981 812 a ÷ 18 2 538 ÷ d +2 If 538 1 288 =815 56 × 23, then: Solution: 78 539 78 539 = …………… = …………… 2 ÷ 568 b 780 9 divide (78 ÷ 9) We know that = 5 hundreds + 10 6 the tensremainder + 8 units will be when we 12 293 ÷× 56 58 002 58 002 Hundred Thousands Units Units without 5 Units Units Tens Tens Thousands Thousands Units Tens =865 4 hundreds + 16 tens +500 8 units c when 100 × we (287 ÷1 24) 28 786 ÷ 24 2448 24480 divide 283 ÷ 23 the remainder will be 5 c 1 465 789 following 3 Underline number, d +the If 15the 288 =078 56 ×number 23, then:in 3 Write Underline the correct number, in digits, digits, which which express express each each of of 984correct Then, 568the ÷ 2quotient = (400 + 160 +of 8)the ÷ 2following division operations, following in words. e3the Find of each the following words. = when …………… we divide 1 293 ÷ 56 the will be 5 = (400 ÷ thousand, 2) + (160 ÷seven 2) + remainder (8 ÷ 2) and a one hundred sixty hundred forty without using the calculator. a onewhen hundred sixty thousand, seven hundred and forty .........5 we divide 1 283 ÷ 23 the remainder will be = 200 + 80 + 4 = 284 da 2 3107 305 + 5 760 119 ……………… (16 740 , 740b160 167÷040 654 ÷ 3 18, 905 5 , 160 740) (3350 217 907÷+thousand, + 5 hundred 152 917 and = …………… 714 74 814 256) d 390 130 ÷ 13 becone hundred three VHYHQW\¿YH 3b Find the quotient of each of the following division operations, Drill 1: one hundred thousand, three hundred and seventy-five without using calculator. f45cCircle Follow thethe steps of the thenearest following to,nintycarry out the division seventy thousand, ¿YH hundred andfor three ................. Find the quotient and remainder of the following. 2 number to the answer, without (10 375 , example 375 1each 375 , the 375 100) Find the quotient of 18the 936 ÷100 24correct without using calculator, a 654 ÷3 18 905 operation: 459the 2use 312 68 b to 3423 3find 415 ÷ b62 c5 9327 9 of 000 performing the usual addition operation. then3 quotient the quotient of ÷each the÷ 28 714 77 985 130three dseventy 96 ÷÷+48 e 70 ÷dand 35390 f÷ 13 64 064 ÷ 16 5 350 260960 180 954 =070 …………… cac thousand, five hundred nintyfollowing without carrying the division operations. the940 ,18,milliard , , 13 (70 (900 593 , million 700b593 59 370 750million) 093) 4 Complete Complete assolution: the example. a 18 ÷ 24 931 ÷ 24 4 Find the quotient of 18 936 ÷ 24 without using the calculator, 459 = 4 hundreds + 5 tens + …… units number that 050 if: = …………… 8 400 100 + 2 600 g6 bFind then find ofthe each the 17. 3use hundreds 15 tens + the …… a =divided byquotient 48, theto quotient isquotient 625 remainder (11 million ,units 7and milliard , of 6 milliard) 4 Complete asthe the example. Example: 147 962 =+962 + 147 000 a is , the358 quotient is following without operations. b 7KHQXPEHUWKDWLIGLYLGHGE\ divided by 69, quotient and = carrying 2the + 60 +the 900division + 72 000 + 40 the 000remainder + 100 0000.15 7KHQXPEHUWKDWPXOWLSOLHGE\ b,isthe product a 18 940+ 962 ÷150 24 931 ÷ is24 459 ÷b (300 ……) 3 000 c3 = multiplied by=+54, the product 418158. Example: 147 962 + ÷147 = (300 + (…… ÷ ……) 26a 672 =(……… 2 + …………………………………………… 60 ÷+ 3) 900 + 7 000 + 40 000 + 100 000 384 ÷ 3)= +384 = ……… += ……… = ……… 4 + 80 + + ……… ………………………………………… 7a The a 672daily 384 production = 384 + of …………………………………………… Note: You can perform previous steps mentally and write the producing == 4459 + garments 80 + ………………………………………… b factory 126 459 +the …………………………………………… 26 from quotient directly as shown one clothing is 732 in the following example. = 9 +item ……………………………………………… a second item b units 126 and 459 from = 459 + …………………………………………… Example: Divide ÷……………………………………………… 956 units. The used for 9 +box c is35 608 =742 608 +2…………………………………………… 1 packaging the= actory …………………………………………………… Solution: 7 4 2for=÷export 2 += …………………………………………… 371 can c production 35 608 608 hold 18 units =of…………………………………………………… the first kind or 15 units of the second. Find: 11 323 Shorouk Press First Term 3 a The number of boxes consumed by the factory daily. b The daily remainder from each kind produced. Hundreds Tens Ten Thousands Thousands Units Ten Thousands Hundreds 8 Hundreds 0 on a b c divided by 48, the quotient is 625 and the remainder 17. divided by 69, the quotient is 2 358 and the remainder 0. multiplied by 54, the product is 4 158. Lesson 1 Hundred Hundred Thousand Thousands Lesson 1 1 0 0Exercise 0 0 1 9 0 Hundreds Thousands Ten Thousands Units 9 0 Tens 9 0 Hundreds 9 0 Thousands 9 0 Ten Thousands 1 Hundred Thousands Hundred Thousands from one clothing item is 738 732 operations, then use the your answer. 99999 100 000 99 999 99calculator 999 + 1to=check 100 000 + 1 units and from a second item 99 999 + 1 = 100 000 + 1 100000 «forhundred is 945 956 The box used a 946 ÷ 2 units. b 486 ÷ 3 thousand« This number is read as 100 000 Hundred Ten 99 999 +Hundreds 1 =d100 000 packaging the Thousands actory Tens c Thousands 847 ÷ 7Thousands 655 ÷ 5 Units Hundred production forTen export can Thousands Hundreds Tens Units Hundred Tenunits Thousands Thousands hold 18 of the first Dividend and Divisor 1 Thousands0Thousands0Hundreds 0Tens 0Units 0 Thousands or 15aunits of the Whenkind dividing number by another, the first number is called the This number is read ascalled ‘hundred dividend and the0 second 1second. 0 Find: 0is 0 the0divisor. a The number boxes by the thousand’ andofcan be consumed represented onfactory daily. This is read asin‘hundred b number The remainder from each kind Fordaily example, the division operation 54 ÷ 9, the abacus as in the figure opposite. This number is read as ‘hundred thousand’ and can be represented on produced.54 is the dividend and 9 is the divisor. thethousand’ abacus as in the and figure can opposite. be represented on Tens 99 999 1 production of a h7 The2:daily Drill Lesson 1 Hundred Thousands producing garments Writefactory the quotient directly for each of the following division + 1 0 the abacus as in the figure opposite. Units Tens Hundreds Tens Hundreds Units Tens Directly is 5 pens and 2 pens are left because 5 × 3 = 15 and 17 – 15 = 2 27 Ten Thousands Thousands Ten Thousands Thousands Thousands Hundred Units Hundred Thousands Hundreds Ten Thousands Hundred Thousands Units Tens Hundreds Tens Hundreds Thousands Exercise 1 Units Thousands Solution: Ten Thousands Ten Thousands Thousands Hundred Thousands Hundred Ten Thousands Thousands Hundred Thousands bought a flat in aExercise housing tower 1 i8 1AdelWrite Quotient and Remainder numbers. for LE 168the 940. He paid LE 100 000 1 as Write the payment numbers.and the rest on a down 18 equal Find theneed value Example: Weinstallments. have 17 pens that to be distributed equally of eachamong installment. 3 children. Find the greatest number of pens 1 Write numbers. that canthe be given to every child. Units Ten Thousands Shorouk Press Hundred Thousands Tens Hundreds Units Thousands Ten Thousands Tens Hundreds Thousands Hundred Thousands Ten Thousands Hundred Thousands Units Tens Units Hundreds Tens Units Thousands Ten Thousands 2 Hundred Thousands 122 Mathematics for Primary Stage-Year 4 24 Tens Then, 17 = 5 × 3 + 2 Hundreds Hundreds Thousands Ten Thousands Thousands Hundred Ten Thousands Thousands Hundred Thousands In this example the quotient is 5 and the remainder is 2. ands 99 999 Units Tens Units Units Tens Hundreds Thousands 28Shorouk Press Hundreds Thousands Tens Ten Thousands Hundreds Thousands Hundred Thousands Tens Ten Thousands Thousands Units Ten Thousands Hundreds 0 Unit Activities 2 Complete to value 3: according 2 Drill Complete according to the the1place place value of of each each digit. digit. + CompleteHundred 1 the following table as the example. Ten Hundred Ten Thousands Hundreds Tens Units Number Tens Units Number Thousands Thousands Thousands Hundreds Activity 1 Thousands Thousands Relation between The division The The The The 100 000 and 752 341 Numerals Numbers elements of 752 341 operation dividend divisor quotient remainder division operation a 618 Find the smallest number formed from 10 different digits. 605 605 618 b Find number different 78 539 78digits. = 10 × 7 + 8 ÷ 10the greatest 78 10 formed 7 from 10 8 78 78 539 c Find the smallest even number formed from 10 different digits. 58 58 002 002 43 ÷ 2 d Find the greatest odd number formed from 10 different digits. 76 ÷ 5 the Find smallest number formed fromwhich 10 different digits following number 3 Underline correct number, in express each of the the 3e Write Underline the correct number, in digits, digits, which express eachand of the sum of its units and tens digit numbers equals 3. the following in words. 68 ÷following 4 the words. f a greatest number formed fromhundred 10 different and one hundred sixty thousand, seven and forty aFind onethe hundred seven hundred anddigits forty ......... ………… 96 sixty thousand, 10 the sum of its units and tens, digit equals (16 740 740numbers 160 , 167 040 , 9.160 740) b one hundred thousand, three hundred and seventy-five ...... one hundred thousand, three and seventy-five b b Dividing a Whole Number by ahundred 2-digit Number c seventy five hundred and ,nintythree ................. Activity 2 thousand,(10 375 , 100 375 1 375 , 375 100) Write Drillthree 4: numbers each is formed from four different digits of 9, 6, 5,seventy 4 and 0thousand, such that:five hundred the firstand is nearest to 4 000 c nintythree Divide as the example. second nearest (70 593 the , 700 593 ,is59 370 , to 750 093) 4 Complete as the example. 15 2000 0 the third is nearest to 6 000 Example: 1 320 ÷ 11 = 120 11 1 3 2 0 4 Complete as the Example: 147 962example. = 962 + 147 000 –11 2 +division 60 + 900 + 7 000 + 40 000 + 2100 Note: We start with=the 2 000 Activity 3 147 962 Example: = 962 +opposite, 147 000 operation as shown – 22 Notice and deduce =the 2 +quotient. 60 + 900 + 7 000 + 40 000 + 0100 a 672 384 = 384 …………………………………………… then we write 0 000 In the figure opposite, = 4 + 80 + ………………………………………… geometric were 672 ÷shapes 384 = 384drawn + …………………………………………… 18 2 4 3 0 a a 2 430 18 = ……… to b express the number == 4459 + 80 + ………………………………………… 126 459 + …………………………………………… 21 003 005. Deduce = 9the + ……………………………………………… possible numerical b 126 459 =value 459 +of…………………………………………… each 9shapes. + ……………………………………………… 35the 608 = 608 + …………………………………………… 15 3 9 1 5 b c 3 of 915 ÷ following 15 = ……… 21 003 005 = …………………………………………………… …………… = …………… c 35= 608 = 608 + …………………………………………… = …………………………………………………… = …………… = or …………… (check your answer by using the calculator any other method.) Units 9 1 First Term 13 3 325 Lesson 1 Hundred Hundred Thousand Thousands Lesson 1 Units Hundreds Units Thousands Units Hundred Thousands Ten Thousands Tens Hundred Thousands Hundreds Units Tens Hundreds Ten Thousands Tens Hundreds Thousands Hundred Thousands Ten Thousands Tens 29 29 Shorouk Press Ten Thousands Thousands Ten Thousands Thousands 1 0 Thousands Hundred Ten Thousands Hundred Thousands Hundred Thousands Units Hundreds Thousands Units Ten Thousands Tens Hundreds Thousands Ten Thousands 9 0 Units Tens Tens Hundreds Units Hundreds 9 0 Exercise 1 Units Tens Thousands Tens Thousands Hundreds 9 0 Units Units Tens Hundreds Ten Thousands Hundred Thousands 142 Mathematics for Primary Stage-Year 4 26 20 2 Tens Hundreds Thousands Ten Thousands Hundreds Thousands Hundred Thousands Hundred Thousands Thousands Ten Thousands 0Exercise 0 0 1 Ten Thousands Thousands 0 Hundred 1 Ten Thousands Thousands 9 0 Hundred Ten Thousands Thousands 9 0 Hundred Thousands 1 Hundred Thousands Hundred Thousands 11 (✔) forresult the correct statement for the one first kind isthe 97 pounds the ofand one(✗)metre of incorrect the99second is 000 1 Put Find Find the result for forand each each of ofprice the the following. 99999 100 999 99 999 + 1following. = 100 000 the 158 and pounds. If Mostafa 4 metres of first kind and 3 1 99 999 + the 1 000 a a correct 87 87 562 562 ++ 55wrong 429 429bought ==statement. ……… ……… b b 39 39 057 057= –– 100 14 14 583 583 == +……… ……… + 1 100000 «1hundred «……… ac If3379 ×second, 18 422, then 422 = 014 18. ÷÷ 77 == ( ) metres the how many pounds didthousand Mostafa pay? c of 478 478 ××number 99===1……… ……… d d÷ 79 721 721 014 ……… This is read as 100 000 Hundred Ten 99 999 +Hundreds 1 = 100 Units ÷ be 678 52==Thousands ×……… 13 + 2, then thefTens remainder 678 ÷ 52 e If267 267 ××=18 18 ……… f000 62 62 550 550 ÷of25 25 == ……… ……… Thousands Thousands Hundred equals theTen remainder of 678 ÷ 13. ( ) Solution: Thousands Hundreds Tens Units Hundred Ten Thousands Thousands cComplete. dividing 26,0 39, … by 13, the remainder Price of first kind = …………………………………………… pounds 2 2Thousands Complete. Thousands Hundreds Tens52, 0 Unitsetc. 0 1When 0 013, Thousands zero.the ( ) Pricea second kind = ………………………………………… pounds aof is Write Write the value value of of the the underlined underlined digit digit in in each each of of the the This number is read Mostafa pounds following following numbers. numbers. 1 paid 0 = ………………………………………………… 0 0 as ‘hundred 0 0 2 thousand’ Complete a suitable >, or each without 33 256 256using 812 812 159 159 ,, 958 958 214 214<,100 100 ,, =77inon 100 100 279 279 312 312 and can besign represented This number is read as ‘hundred performing the operation. ……………… ……………… ,, ……………… ……………… ,, ……………… ……………… the abacus asdivision in the figure opposite. This number is read as ‘hundred thousand’ and can be represented on b Multiplying bynumbers a 2-digit2of Number ab 2Write 538 ÷the 18 538 37 babacus Write the a a in in÷words. words. thethousand’ as innumbers the and figureofcan opposite. be represented on bc ÷ 9×× 29 (78 ÷ 9)then: × 10 c 780 IfIf 458 458 29 == 13 13 282, 282, then: Drill 1:abacus the the 28 figure opposite. ii ×13 13 282 282865 ÷÷ as 29 29 =in …… …… ii ii 786 13 13500 282 282 458 458 == …… …… (287 ÷ =24) ÷÷÷24 Findcthe100 product as the examples. Exercise 1 1 Write iii iii 13 13the 291 291numbers. == …… …… ×× 29 29 ++ …… …… d If 1 288 = 56 × 23, then: 1 Write the numbers. Examplewhen 1: we27divide × 53 1 = 293 27 ×÷(356+ 50) Example the remainder will2:be 5 35 3 3 Circle Circle the the number number nearest nearest to to the the correct correct answer. answer. 2 3 127 283 ÷ 23 the remainder will be = we 27divide ×++311+475 ×987 50 × 2 75 a a when 77 815 815 100 100 475 987 == …………… …………… (9 (9 million million ,, milliard milliard ,, 990 990 million) million) 1 Write numbers. = 81 +the 1 350 371 3 Find the quotient each000 of the following division operations, b b 9 9 145 145 000 000 –– of 88 142 142 000 == …………… …………… without using = 1 the 431calculator.(3 1 060 (3 000 000 ,, million million ,, 200 200+million) million) ac 3 ×× 125 b 18 905 ÷ 5 c 388654 ×× 66÷958 958 125 == …………… …………… = 1 431 c 350 714 ÷ 7 d 390,, 130 ÷ 13 ,, 55 million) (7 (7 million million 66 million million million) d d (4 (4 000 000 ÷÷ 4) 4) ×× 999 999 == …………… …………… (Notice that the product is the same even with different methods, 4 Find the quotient of 18 936 ÷ 24,, without using the calculator, (one (one million million one one milliard milliard ,, 900 900 thousand) thousand) use a calculator to check your answer.) then use the quotient to find the quotient of each of the without the are division operations. 4 4 following a a IfIf 756 756 pupils pupilscarrying in in aa school school are distributed distributed equally equally among among 18 18 24 × 43 = 24 × (……… + 40) 43 a 18 940 ÷ 24 18 931 ÷ 24class. classes, classes, find find the the number number of ofbpupils pupils in in each each class. = 24 × 3 + ……… × ……… × 24 b b Find Find the the number number that that ifif multiplied multiplied by by 17, 17, the the product product will will be be =11 156. ……… + ……… ……… 156. = ……… + ……… = ……… Tens 99 999 Exercise 9 Drill 4: General Exercises on Unit 1 Lesson 1 Hundred Thousands 1 Mostafa bought two kinds of cloth, the price of one metre of+ the Exercise 5 1 Choose the correct answer. a 7 251 309 + 748 691 = …… (8 milliard , 8 million , 8 thousand) b 5 000 000 – 324 067 = …… (95 324 076 , 91 675 933 , 4 675 933) c 8 × 641 × 125 = ... (641 thousand , 641 hundred , 641 million) Relation Between Two Straight Lines d The number 2 100 is divisible by …… (35 , 11 , 13 , 17) e XYZPolygons is a triangle in which m(∠X) = 40° and m (∠Y) = 30°, Triangle thenThe ∆XYZ is …… triangle. (a right-angled , an obtuse-angled , an acute-angled) Applications f TheUnit L.C.M. of 15 and 35 is …… (15 , 105 , 35 , 5) 2 Activities 2 General on side Unit length 2 Draw the squareExercises XYZL whose 3 cm. Join its diagonals XZ and YL. 3 a b c d e 4 a b Multiples of 6 are ……, …… and …… Prime factors of 350 are ……, …… and …… The perimeter of a rectangle whose dimensions are 7 cm and 11 cm = ………………………… = …… cm The H.C.F. of 18 and 30 is …… 1 4 of a day = …… hours = …… minutes. Calculate 2 106 425 + 894 075 – 3 000 500. Find the number that if subtracted from 256 412 307, then the remainder will be 255 million. 93 Lines ur ngle, Two straight straightlines, lines,intersecting intersecting Two and not not perpendicular perpendicular. . and Twostraight straightlines, lines,intersecting intersecting Two andperpendicular. perpendicular. and (you can can use useyour yourgeometric geometricinstruments.) instruments.) 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Draw in which AB to = -5draw cm, b geometric Do∆ABC you expect expect these b Do you these - The Thetwo twoedges edgesofofthe theruler. ruler. as shown in the figure opposite. BC straight =straight 4 cm and = 60˚. linesm(∠B) to lines to ………………………………………………………… - - ………………………………………………………… A intersect B C intersectififthey theywere were - - ………………………………………………………… ………………………………………………………… extendedfrom fromboth both extended ………………………………………………………… gure opposite. .etisoppo erugif eht t-e- g………………………………………………………… ot senil thgiarts eht etelpmoC 4 b cm sides? sides? ………………………………………………………… - - ………………………………………………………… b Complete -the straight lines to get the figure opposite. - ………………………………………………………… ………………………………………………………… b Complete lines to get the A )) B figure opposite. yes ,the ,no nostraight (( yes era toNote: g u o y t a h Note: t senil thgiarts owt ehT c60˚ Write the greatest fo rebnumber mun tseof taerg eht etirW .senil thgiarts ralucidnAeprep5dcm ellac B Youcan can draw two parallel lines You draw two parallel lines c The two straight lines that you got are Notice and draw. 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Draw ∆XYZ in which XY = 7 cm, YZ = 5 cm and m(∠Y) e h t t a h t d n i f l l i w u o y , n o itof cesre= tn40˚. i that you can se - The edges of the d Measure angles resulted fromat their the lines point eht fo sthe egdefour ehT - two straight lines that you can see in your environment. . ˚ … … … = m e h t f o h c a e f o e r u s a e m 32 right angle in32 a setthe lines at their you pointwill of findenvironment. that the -testwo a ni straight elgna thgiintersection, r - The edges of the Drill 4: r u o y n e h t , ˚ 0 9 s i e r u s a e m r u o y fi( square. intersection,.eryou will find that the measure of each of them = ………˚. auqs - The edges ofgeometric the right angle in a se Join each figure to the suitable statement, use your Exercies tcerro c si gniward - The vertical and measure them = ………˚. (if of measure is 90˚,2)then your dna laciof treeach v ehT -your right angle in a set- square. instruments to be sure. Draw s∆DEF in which ∠D is right, DE = 3 cm and EF = 4 cm. horizontal edges (if your egdemeasure latnozirodrawing h is 90˚, yais sthen ncorrect) acyour ew ,stniop ssquare. uoiverp lla mo- rFThe e vertical and Measure the length of DF, then answer the following questions. of the door. drawing.ris oodcorrect) eht fo t - we Thecan vertical and:tahhorizontal ethe From all previous points, say a Calculate perimeter of ∆DEF, given that the perimeter of edges - ……………………………… ……………………………… sewe nil can thgiasay rts raluchorizontal idneprepedges owt ehof t the door. e From all previous points, that: any polygon = the sum of its side lengths. - ……………………………… ……………………………… - .˚……… erusaem htiw lglines ndoor. a na eka of ethe -m ……………………… that: the of twothe perpendicular straight b What is the type triangle, according to the measures of - ……………………………… ……………………………… ……………………………… ……………………… theitstwo perpendicular straight make an anglelines with measure ………˚. angles? …………… 1 an angle with 2 3- ……………………………… 4- ……………………… make measure ………˚. (acute-angled , obtuse-angled or right-angled) o straight lines is si senil thgiarts owt neewteb elgna eh-t f……………………………… o erusaem eht fI c What is the type of the triangle, according to the length of its en the two straight thparallel giarts olines wt ehIft nthe ehtmeasure ,lines, )esutb o of rothe etuangle ca( ˚09between ot lalines, uqetwo tostraight n Two Two intersecting Two intersecting lines is sides? …………… ndicular. . r a l u c i d n e p r e p t o n d n a g n i t c e s r e t n i e r a s e n i l andequal not perpendicular and perpendicular If the measure of the angle between two straight linesthen is the two straigh not to 90˚ (acute or obtuse), (isosceles , equilateral or scalene) 31 to 90˚ 1344Mathematics not equal or obtuse), thenand thenot twoperpendicular. straight lines are intersecting for Primary Stage-Year 4 (acute Shorouk Press Drill 5:intersecting and not perpendicular. lines are How to draw a perpendicular to a straight line from a point on 31 it. 1 0 05 6 1 14 23 32 41 4 5 3 4 50 0 2 3 1 2 0 0 1 0 0 A A 1 2 3 A 4 5 1 2 31 4 5 4 5 6 7 8 80˚80˚ 30˚30˚ CC 4 cm 4 cm Noticeand anddraw. draw. Notice Notice and draw. BB TheSum SumofofMeasures Measuresofofthe theAngles Anglesofofthe theTriangle Triangle DrillThe 6: How to draw a perpendicular to a straight line from a point outside it. Drill7:7: Drill B B Two straight lines, intersecting Draw anytriangle triangle pieceofof Two straight lines, intersecting aa Draw any onona apiece and not perpendicular and perpendicular. cardboard paper. . cardboard paper. C Colour theangles angles thetriangle triangle bb Colour ofofthe atat (you can the use your geometric instruments.) verticesinAinred, red,green greenand andyellow yellow itsitsvertices A A shown figureopposite. opposite. asasshown Drill 3: ininthethefigure c Use the scissors cutthe the three c the scissors totocut three a Use Draw two straight lines Notice and draw. Write the greatest number of examples of parallel angles and fix them on a piece angles and fix them on a piece ofof two we lines of your In thison case, write AB ⊥ BC. lines that you can see arround you. paper as shown in the figure. paper as shown in the figure. copybook, as shown 33 in the figure below. Notice: The Thethree threeangles anglestogether togetherformed formeda astraight straightangle angleand and Notice: weknow knowthat thatthe themeasure measureofofthe thestraight straightangle angleisis we 180˚.Then, Then,we wededuce deducethat: that: 180˚. 0 0 1 2 3 1 2 3 4 5 4 5 6 7 8 B Draw∆ABC ∆ABCininwhich whichBC BC= =4 4cm, cm, Draw AA Drill= =30˚ 2:30˚and m(∠B) andm(∠C) m(∠C)= =80˚. 80˚. m(∠B) Join each figure to the suitable statement. 3 … Drill6:6: Drill 3 … Length of OneSide Side Length One How to draw a perpendicular toof aor straight linethen fromthe a point on it. not equal to 90˚ (acute obtuse), two straight Alines are intersecting A and not perpendicular. A 2 … Drawing TriangleGiven Given theMeasure Measure Two Angles and the Drawing a aTriangle ofof Two Angles and Drill 5: If the measure of thethe angle between two straight lines isthe 1 … - perpendicular ……………………………… and 2 … and not perpendicular 0 0 el of the door. 2 3 4 that: - ……………………………… the two perpendicular straight lines - ……………………………… Two parallel lines Two with lines,measure intersecting lines, intersecting make an angle ………˚.Two 1 g 1 - The lines of the copy-book. Thesum sum measures theinterior interiorangles anglesofofany anytriangle triangle= =180˚. 180˚. The ofofmeasures ofofthe b Do you expect these - The two edges of the ruler. straight lines to - ………………………………………………………… intersect if they were - ………………………………………………………… Drill Drill 8:8: from both - ………………………………………………………… extended Drawthe thetriangle triangleABC ABCininwhich which ∠Bisisa aright rightangle, angle,m(∠C) m(∠C)= =60˚ 60˚ Draw ∠B sides? - ………………………………………………………… andBC BC= =4 4cm. cm.Measure Measure∠A, ∠A, thencheck checkthat thatthe thesum sumofof and then - ………………………………………………………… measures triangleisis180˚. 180˚. measures ( yesofofangles , angles no of ) ofa atriangle Note: 45 45 You can draw two parallel lines Shorouk Press First Term These two straight lines are called parallel lines. using the two edges of your ruler, as shown in the figure opposite. Two Two straight straight lines, lines, intersecting intersecting Two straight lines, intersecting and and not not perpendicular perpendicular . .. and not perpendicular Two Two straight straight lines, lines, intersecting intersecting Two straight lines, intersecting and and perpendicular. perpendicular. and perpendicular. (you (you can can use use your your geometric geometric instruments.) instruments.) (you can use your geometric instruments.) c c What What is type of of thethe ∆DEF ∆DEF according according to its: to its: Drill Drill 3:3: 3:isthethetype Drill side lengths? lengths? ………… ………… angles angles measures? measures? ………… ………… a aa side Draw two straight lines Draw two straight lines Draw two straight lines Write thethe greatest number of of examples of of parallel Write the greatest number ofexamples examples of parallel Write greatest number parallel d d What What islines is the the type of of thethe ∆NKM ∆NKM according according to its: to its: onon two oftype your on two lines of your two lines of your lines that you can see arround you. lines that you can see arround you. lines that you can see arround you. side side lengths? lengths? ………… ………… angles angles measures? measures? ………… ………… copybook, asas shown copybook, as shown copybook, shown inin the figure below. in the figure below. the figure below. Drawing Drawing a Triangle a Triangle given given thethe Length Length of two of two Sides Sides andand thethe Measure Measure of of thethe Included Included Angle Angle Drill Drill5:5: - -The - The The lines lines ofof the ofthe the copy-book. copy-book. lines copy-book. Draw ∆ABC inexpect which AB = 5=- cm, Draw ∆ABC in which AB cm, bb you expect these b Do Do you expect these Do you these The - The The two two edges edges ofof the ofthe the ruler. ruler. -5 two edges ruler. BCBC =straight 4 cm and m(∠B) =straight 4 cm and = -60˚. lines tom(∠B) lines to = 60˚. straight lines to - ………………………………………………………… ………………………………………………………… -………………………………………………………… A A intersect B B C C if ifthey were intersect ifthey they were - -………………………………………………………… intersect were - ………………………………………………………… ………………………………………………………… extended from both extended from both - -………………………………………………………… extended from both ………………………………………………………… - ………………………………………………………… 4 cm4 cm sides? sides? sides? - -………………………………………………………… - ………………………………………………………… ………………………………………………………… A A ) )) ( yes yes , no no (( yes ,,no - -………………………………………………………… - ………………………………………………………… ………………………………………………………… B B Note: Note: Note: 60˚ 60˚ A A parallel 5 cm 5lines cm You can draw two parallel lines You can draw two lines B B You can draw two parallel Notice and draw. Notice and draw.lines These two straight These two straight lines These two straight lines using the two edges ofofyour using the two edges ofyour your using the two edges are called parallel lines. are called parallel lines. are called parallel lines. ruler, asas shown ruler, as shown inthe the ruler, shown Exercies 1 1ininthe Exercies opposite. figure opposite. Draw ∆XYZ in in which XYXY = 7=figure cm, YZ =opposite. 5=cm andand m(∠Y) = 40˚. Draw ∆XYZ which 7figure cm, YZ 5 cm m(∠Y) = 40˚. 32 32 32 Drill Drill4:4: Join Join each each figure figure to to thethe suitable suitable statement, statement, your your geometric geometric Exercies 2 use Exercies 2 use instruments instruments to in to bewhich be sure. sure. Draw ∆DEF in which ∠D∠D is right, DEDE = 3=cm andand EF EF = 4=cm. Draw ∆DEF is right, 3 cm 4 cm. Measure thethe length of of DF, then answer thethe following questions. Measure length DF, then answer following questions. a a Calculate thethe perimeter of ∆DEF, given thatthat thethe perimeter of of Calculate perimeter of ∆DEF, given perimeter any polygon = the sum of its side lengths. any polygon = the sum of its side lengths. b b What is is thethe type of of thethe triangle, according to the measures of of What type triangle, according to the measures itsits angles? …………… angles? …………… 1 1 2 2 3 right-angled) 3 4 4 (acute-angled , obtuse-angled or or right-angled) (acute-angled , obtuse-angled c c What is is thethe type of of thethe triangle, according to the length of its What type triangle, according to the length of its Two parallel lines lines, intersecting TwoTwo lines, intersecting Two parallel lines Two Two lines, intersecting lines, intersecting sides? …………… sides? …………… andand notnot perpendicular perpendicular perpendicular (isosceles , equilateral orperpendicular scalene) (isosceles , equilateral or scalene) andand 44 44Mathematics for Primary Stage-Year 4 Shorouk Press Drill Drill5:5: How to to draw a perpendicular to a lineline from a point on it. How draw a perpendicular tostraight a straight from a point on it. A A A A A A AA AA Draw∆ABC ∆ABCininwhich whichBC BC= =4 4cm, cm, Draw m(∠B)= =30˚ 30˚and andm(∠C) m(∠C)= =80˚. 80˚. m(∠B) AA 3 4 5 6 7 8 1 2 3 3 4 3 4 5 5 4 5 6 7 8 80˚80˚ 30˚30˚ CC 4 cm 4 cm Notice and draw. Notice Noticeand anddraw. draw. Notice and draw. BB The SumofofMeasures Measuresofofthe theAngles Anglesofofthe theTriangle Triangle The Drill 6:Sum Drill 6: Howtotodraw drawa aperpendicular perpendiculartotoa astraight straightline linefrom froma apoint pointoutside outsideit.it. How Drill7:7: Drill BB Drawany anytriangle triangleonona apiece pieceofof a a Draw cardboardpaper. paper. cardboard Colourthe theangles anglesofofthe thetriangle triangleatat b b Colour verticesinAinred, greenand andyellow yellow itsitsvertices Ared,green AA shownininthe thefigure figureopposite. opposite. asasshown c Use the scissorstotocut cutthe thethree three c Use the scissors Notice and draw. Notice and draw. angles and fix them apiece pieceofof angles and fix them onon this case, we write AB BC. InInthis case, we write AB ⊥a⊥BC. paperasasshown shownininthe thefigure. figure. paper BB 0 0 2 3 CC 4 5 6 AA 7 8 2 3 0 0 11 1 1 2 2 3 3 4 4 5 5 4 5 6 7 8 B A DrillA6: 6: Drill 2 … Two lines, intersecting Two lines, intersecting and perpendicular and perpendicular Length OneSide Side Length of One Howtotodraw drawa aperpendicular perpendicular astraight straight linefrom froma apoint pointononit.it. How toto aof line 2 … 44 Drawing TriangleGiven Giventhe theMeasure MeasureofofTwo TwoAngles Anglesand andthe the Drawing a aTriangle Drill Drill 5:5: 2 … Two lines, intersecting Two lines, intersecting and not perpendicular and not perpendicular 0 0 … 33 11 … Two parallel lines Two parallel lines 22 0 0 el 11 1 g 33 33 Notice: The Thethree threeangles anglestogether togetherformed formeda astraight straightangle angleand and Notice: weknow knowthat thatthe themeasure measureofofthe thestraight straightangle angleisis we 180˚.Then, Then,we wededuce deducethat: that: 180˚. Thesum sumofofmeasures measuresofofthe theinterior interiorangles anglesofofany anytriangle triangle= =180˚. 180˚. The Drill8:8: Drill Drawthe thetriangle triangleABC ABCininwhich which∠B ∠Bisisa aright rightangle, angle,m(∠C) m(∠C)= =60˚ 60˚ Draw andBC BC= =4 4cm. cm.Measure Measure∠A, ∠A,then thencheck checkthat thatthe thesum sumofof and measuresofofangles anglesofofa atriangle triangleisis180˚. 180˚. measures Shorouk Press 45 45 First Term Two straight straightlines, lines,intersecting intersecting Two and not not perpendicular perpendicular. . and Twostraight straightlines, lines,intersecting intersecting Two andperpendicular. perpendicular. and (you can can use useyour yourgeometric geometricinstruments.) instruments.) (you cDrill c What What is type of of thethe ∆DEF ∆DEF according according to its: to its: Drill 3:isthethetype Drill 3: 7: side lengths? lengths? ………… ………… angles measures? measures? ………… ………… Draw two straight lines aa side Draw two lines How to draw a straight line parallel togreatest aangles given straight line from aparallel Writethe the greatest number examples Write number ofofexamples of of parallel dpoint d What What is is the the type type of thethe ∆NKM ∆NKM according to its: to its: you. on two two lines ofof your on lines of your outside it. linesthat thataccording youcan cansee seearround arround you. lines you A A side side lengths? lengths? ………… ………… angles angles measures? measures? ………… ………… copybook, asshown shown copybook, as D in the the figure figurebelow. below. in Drawing Drawing a Triangle a Triangle given given thethe Length Length of two of two Sides Sides andand thethe Cof of Measure thethe Included Included Angle C B Measure BAngle 8 7 6 8 5 7 4 6 3 Drill Drill5:5: 5 2 4 1 00 1 Thelines linesofofthe thecopy-book. copy-book. - - The 3 Draw Draw ∆ABC in which which AB AB = 5=cm, cm, b Do Do∆ABC youinexpect expect these b you these Thetwo twoedges edgesofofthe theruler. ruler. -5- The BCBC = straight 4 =straight cm 4 cm and and m(∠B) m(∠B) = 60˚. lines to = 60˚. lines to ………………………………………………………… - - ………………………………………………………… A A intersect B B C C intersectififthey theywere were - - ………………………………………………………… ………………………………………………………… extendedfrom fromboth both extended ………………………………………………………… - - ………………………………………………………… 4 cm4 cm sides? Noticesides? and draw. ………………………………………………………… - - ………………………………………………………… In this case, we write AB // CD. ………………………………………………………… - - ………………………………………………………… A A )) B B yes ,,no no (( yes Note: Note: 60˚ 60˚ Exercise 1 A A parallel 5 cm5lines cm Youcan candraw drawtwo twoparallel lines B B Notice Notice and and draw. draw. lines These two straight lines You These two straight usingthe thetwo twoedges edgesofofyour your areWrite called parallel lines.using called parallel lines. 1are the relation between each two straight lines under each ruler,as asshown shown the ruler, Exercies Exercies 1 1 ininthe figure. figure opposite. Draw Draw ∆XYZ ∆XYZ in in which which XYXY = 7=cm, 7figure cm, YZYZ =opposite. 5=cm 5 cm andand m(∠Y) m(∠Y) = 40˚. = 40˚. 2 3 2 4 5 1 00 1 2 3 4 5 32 32 Drill 4: Join each figure to theExercies suitable statement, Exercies 2 2 use your geometric instruments to be sure. Draw Draw ∆DEF ∆DEF in in which ∠D∠D is right, is right, DE2DE = 3=cm 3 cm andand EF EF = 43=cm. 4 cm. Figure 1 which Figure Figure Measure Measure thethe length length of of DF, DF, then then answer answer thethe following following questions. questions. ………………… ………………… ………………… a a Calculate Calculate thethe perimeter perimeter of ∆DEF, of ∆DEF, given given thatthat thethe perimeter perimeter of A of any polygon polygon = the = the sum sum ofCE its of on its side side lengths. lengths. 2 any Draw the perpendicular b b What What is is thestraight the type type ofline of thethe triangle, triangle, according according to the to the measures measures of C of the given AB. itsits angles? angles? …………… …………… Then, complete. 1 2 3 4 (acute-angled (acute-angled , obtuse-angled , obtuse-angled or or right-angled) right-angled) m(∠BCE) =type m(∠………) = ………˚. c c What What is is thethe type of of thethe triangle, triangle, according according to the to the length length ofB its of its Two parallel lines Two lines, intersecting Two lines, intersecting sides? sides? …………… …………… and not and perpendicular (isosceles (isosceles , equilateral , equilateral orperpendicular or scalene) scalene) 34 44 44Mathematics for Primary Stage-Year 4 (2015 - 2016) Shorouk Press Drill 5: How to draw a perpendicular to a straight line from a point on it. A A A 4 Two lines, intersecting and perpendicular Drawing TriangleGiven Given theMeasure Measure TwoAngles Anglesand andthe the Draw perpendicular from the point X on 3 Drawing the ofof Two Drill 5:a aTriangle Y Length of One Side One Side the given straight Length line YZ, then complete. How to draw a perpendicular toof a straight line from a Xpoint on it. A A Drill 6: Drill 6: If O is the point of intersection of the A Drawdrawn ∆ABCperpendicular whichBC BC= and =4 4cm, cm, Draw ∆ABC ininwhich the straightAline A m(∠B) = 30˚ and m(∠C) = 80˚. m(∠B) = 30˚ and m(∠C) = 80˚. YZ, then m(∠XOY) = m(∠………) = ……˚. 2 3 4 3 Z 5 4 5 6 7 8 … Two lines, intersecting and not perpendicular 1 … 3 2 … Two parallel lines 2 0 0 el 1 1 g 80˚80˚ 30˚30˚ CC 4 cm 4 cm Noticeand anddraw. draw. Notice Notice and draw. 4 Draw a straight line parallel to the given BB N TheSum Sum Measures theAngles Angles theTriangle Triangle The ofof the Drillstraight 6: lineofof LMeasures and passing through the ofofthe How topoint drawN.a perpendicular to a straight line from a point outside it. Drill7:7: Drill B Drawany anytriangle triangleonona apiece pieceofof a a Draw … cardboardpaper. paper. cardboard C … Colourthe the anglesofofthe thetriangle triangleatat bb 5 Colour Notice theangles figure opposite, then complete. A verticesinAinred, red,green greenand andyellow yellow itsitsvertices A a AB ……… BC (⊥ or B shownininthe thefigure figureopposite. opposite. //) asasshown band AB ……… YZ (⊥ or //) c Use Use the scissors cutthe thethree three c the scissors totocut Notice draw. angles and fixthem them apiece piece of //) angles and fix onon ccase, XY ……… BC (⊥ofor In this we write AB ⊥aBC. paper shownininthe thefigure. figure. paper asasshown d AY intersects with BZ at the point L B 0 0 1 2 3 1 2 3 4 5 4 5 A 6 7 8 33 ……… X Y Notice: The Thethree threeangles anglestogether togetherformed formeda astraight straightangle angleand and Notice: e YCwe intersects with BX at the point weknow knowthat thatthe themeasure measureofofthe thestraight straightangle angleisis ……… 180˚.Then, Then,we wededuce deducethat: that: 180˚. B Z C Thesum sumofofmeasures measuresofofthe theinterior interiorangles anglesofofany anytriangle triangle= =180˚. 180˚. The Drill8:8: Drill Drawthe thetriangle triangleABC ABCininwhich which∠B ∠Bisisa aright rightangle, angle,m(∠C) m(∠C)= =60˚ 60˚ Draw andBC BC= =4 4cm. cm.Measure Measure∠A, ∠A,then thencheck checkthat thatthe thesum sumofof and measuresofofangles anglesofofa atriangle triangleisis180˚. 180˚. measures Shorouk Press 45 35 45 First Term Two straight straightlines, lines,intersecting intersecting Two and not not perpendicular perpendicular. . and Twostraight straightlines, lines,intersecting intersecting Two andperpendicular. perpendicular. and (you can can use useyour yourgeometric geometricinstruments.) instruments.) (you c What Drill 3:is the type of the ∆DEF according to its: Drill 3: Lesson 2two Polygons side ………… angles measures? ………… Drawlengths? twostraight straight lines Write aa Draw lines Writethe thegreatest greatestnumber number examples parallel ofofexamples of of parallel d on What the type of the lines ∆NKM to its: you. on two twoislines lines ofyour your of linesthat thataccording youcan cansee seearround arround you. you side lengths? ………… angles measures? ………… copybook, asshown shown copybook, as in the the figure figurebelow. below. in Drill 1: Drawing a Triangle given the Length of two Sides and the Notice the followingMeasure polygons,of then thecomplete. Included Angle Drill 5: Thelines linesofofthe thecopy-book. copy-book. - - The Draw in which AB = -5- The cm, b Do Do∆ABC you expect expect these b you these Thetwo twoedges edgesofofthe theruler. ruler. BC straight =straight 4 cm and = 60˚. linesm(∠B) to lines to ………………………………………………………… - - ………………………………………………………… 1 Figure 2 Figure 3 C AFigure B intersectififthey theywere were - - ………………………………………………………… intersect ………………………………………………………… extendedfrom fromboth both extended ………………………………………………………… - - ………………………………………………………… 4 cm sides? sides? ………………………………………………………… - - ………………………………………………………… yes (( yes noA )) ,,no ………………………………………………………… - - ………………………………………………………… B Note: Note: 60˚ A parallel B 5lines cm Youcan drawtwo twoparallel lines You Figure 5candraw Figure 6 Figure 4 straight Notice and draw. lines These two straight lines These two using thenumber twoedges edges ofyour your the two The number of The of of The number of are called called parallel parallel lines.using are lines. Figure number ruler, as shown in the ruler, as shown in the 1 Vertices SidesExercies aertices angles figure opposite. opposite. Draw ∆XYZ in which XY = 7figure cm, YZ = 5 cm and m(∠Y) = 40˚. 1 ………… ………… ………… Drill2 4: ………… ………… ………… 32 32 3 ………… Join each figure to………… the suitable statement, geometric Exercies 2 use your………… instruments to which be sure. 4∆DEF in ………… ………… Draw ∠D is right, DE = 3 cm and EF………… = 4 cm. Measure of DF, then answer the following………… questions. 5 the length………… ………… a Calculate the perimeter of ∆DEF, given that the perimeter of 6 ………… ………… ………… any polygon = the sum of its side lengths. What do you notice? b What is the type of the triangle, according to the measures of The relation between the number of sides of a polygon with its angles? …………… 1to the number 3 number of its angles. 4 respect its2vertices and (acute-angled , of obtuse-angled or the right-angled) Notice that, for type any polygon: c What is the of the triangle, according to the length of its Twosides? parallel lines …… Two lines, of intersecting Two lines, Number of sides Number vertices …… Number ofintersecting angles …………… and not perpendicular and perpendicular (isosceles , equilateral or scalene) 36 44Mathematics for Primary Stage-Year 4 Shorouk Press Drill 5: How to draw a perpendicular to a straight line from a point on it. A A A 1 g 3 4 5 4 5 m(∠B) = m(∠…) = m(∠…) = m(∠…) = …˚.B C 7 8 b 6 Notice that m(∠B) can be written instead of (∠B) for simplicity. 80˚measure30˚ Notice and B a ……… Notice and draw. draw. 4 cm c From all the above, it can be said Cthat the square is (pentagon , quadrilateral , hexagon) that has ……… sides The Sum of Measures the Angles of the Triangle Drillthat 6:are ……… in length of and ……… angles that are ……… in How to draw a perpendicular to a of straight from a point outside measure and the measure each line is ………˚ (check by it. Drilldrawing 7: other squares onB graph paper). B a d Draw any triangle on a piece of Using your geometric instruments, check that AC = BD and for cardboard paper.that you drew on graph paper, Cyou will find that other squares b Colour the angles of the triangle the diagonals of the square areatalways equal in length. its vertices inAred, green and yellow A A Notice: the diagonal is the line segment as shownIn in any the quadrilateral, figure opposite. joining two non-consecutive vertices. c Useand thedraw. scissors to cut the three Notice angles them on⊥aBC. piece of In this case,and wefix write AB the above, deduce that the diagonals of the paperFrom as shown in thewe figure. 33 square are equal in length. 0 0 1 2 3 1 2 3 4 5 4 5 6 7 8 B 3 … One Side How to drawdrawing a perpendicular toof a straight line from a point on it. Complete theLength square ABCD, then answer A the following (consider A the unit of A Drill 6: length = 1 cm). Draw ∆ABC in which BC = 4 cm, A m(∠B) = 30˚ and m(∠C) = 80˚. a AB = BC = …… = …… = …… cm 2 … Drawing a Triangle Given the Measure of TwoAAngles and the Drill Drill5:2: 1 … Two lines, intersecting and perpendicular 2 … Two lines, intersecting and not perpendicular 4 0 0 … Two parallel lines 3 1 el 2 Notice: The three angles together formed a straight angle and e Using the set-square, or the protractor, check that AC ⊥ BD we know that the measure of the straight angle is and similarly for other squares that you drew on graph paper. 180˚. Then, we deduce that: From the above, we deduce that the diagonals of the The sum of measuressquare of the interior angles of any triangle = 180˚. are perpendicular. f If M is the point of intersection of AC and BD, use the instruments to check that MA = MB = MC = MD and Drillgeometric 8: for other squares thatisyou drewangle, on graph paper. Draw similarly the triangle ABC in which ∠B a right m(∠C) = 60˚ and BC = 4 cm. Measure ∠A, then check that the sum of From the above, we deduce that the diagonals of the measures of angles of a triangle is 180˚. square bisect each other. Shorouk Press 37 45 First Term Two straight straightlines, lines,intersecting intersecting Two and not not perpendicular perpendicular. . and Twostraight straightlines, lines,intersecting intersecting Two andperpendicular. perpendicular. and (you can can use useyour yourgeometric geometricinstruments.) instruments.) (you c What Drill 3:is the type of the ∆DEF according toA its: Drill Drill 3:3: side ………… angles measures? ………… Drawlengths? twostraight straight lines Write aa Draw two lines Writethe thegreatest greatestnumber number examples parallel ofofexamples of of parallel Complete drawing the rectangle ABCD, d on What the type of the lines ∆NKM to its: you. on two twoislines lines ofyour your of linesthat thataccording youcan cansee seearround arround you. you then answer the following (consider the unit side lengths? ………… angles measures? ………… copybook, asshown shown copybook, as B C of length = 1figure cm). below. in the the figure below. in Drawing a Triangle given the Length of two Sides and the a AB = …… = …… = …… cm and BC = …… = …… = …… cm Measure of the Included Angle i.e. In the rectangle, every two opposite sides are ……… in length. Drill 5: Thelines linesofofthe thecopy-book. copy-book. - - The Draw in which AB = 5 cm, b Do Do∆ABC you expect expect these b you these Thetwo twoedges edgesofofthe ruler. b m(∠B) = m(∠…) = m(∠…)- -=The m(∠…) = …˚.theruler. BC straight =straight 4 cm and = 60˚. linesm(∠B) to lines to ………………………………………………………… - - ………………………………………………………… A i.e. B C intersect ifthey theywere were intersect In the ifrectangle, all angles are ……… in measure and ………………………………………………………… - - ………………………………………………………… extendedfrom from both extended theboth measure of each is ……˚. ………………………………………………………… - - ………………………………………………………… 4 cm sides? sides? ………………………………………………………… - - ………………………………………………………… c From all the above, it can be said that the rectangle is a ……… ………………………………………………………… - - ………………………………………………………… that has ………A sides and every twoB opposite sides are ……… yes ,,no no )) (( yes in length and ……… angles that are ……… in measure and the Note: Note: 60˚ A parallel B measure of each is ………˚ (check bytwo drawing other 5lines cm Youcan candraw draw twoparallel lines Notice andstraight draw. These two two straight lines You These lines rectangles on graph paper). usingthe thetwo twoedges edgesofofyour your are called called parallel parallellines. lines.using are ruler,as asshown shown the ruler, ininthe Exercies 1 the d Use the geometric instruments to identify relation between figure opposite. opposite. Draw ∆XYZ which XY = for 7figure cm, YZ = 5 cm and m(∠Y) = 40˚. AC and BDinand similarly other rectangles that you drew on 32 graph paper. 32 Drill 4: Joini.e. each figure to the suitable statement, use your geometric In the rectangle, the diagonals are2……… in length. Exercies instruments to which be sure. ∆DEF in ∠Doristhe right, DE = 3 check cm and EFAC = 4and cm.BD e Draw Using the set-square, protractor, that Measure length of DF, answer the following questions. are not the perpendicular andthen similarly for other rectangles (not a squares) Calculate the perimeter of ∆DEF, given that the perimeter of that you drew on graph paper. any polygon = the sum of its side lengths. Theisdiagonals of the the triangle, rectangleaccording are not perpendicular. b i.e. What the type of to the measures of its angles? …………… f If N1 is the point of intersection of AC and 2 3 BD, use the 4 (acute-angled , obtuse-angled or right-angled) geometric instruments to check that NA = NC and NB = ND c What is the type of the triangle, according to the length of its andparallel similarly that you drew onlines, graph paper. Two linesfor other Tworectangles lines, intersecting Two intersecting sides? …………… andof notthe perpendicular and perpendicular (isosceles , equilateral orrectangle scalene)bisect each i.e. The diagonals other. 3844Mathematics for Primary Stage-Year 4 Shorouk Press Drill 5: How to draw a perpendicular to a straight line from a point on it. A A A 1 g 8 7 6 4 5 4 5 5 3 A B 4 3 2 2 1 0 0 1 2 3 4 5 1 7 5 6 0 0 1 2 8 4 7 6 3 3 4 5 80˚ 30˚ 3 cm A B Notice C B Notice and and draw. draw. 4 cm Notice and draw. DrillThe 6: Sum of Measures of the Angles of the Triangle How to draw Drill 5: a perpendicular to a straight line from a point outside it. Drill 7:using graph paper orB squared paper, can you draw Without B a a rectangle, Draw any triangle on a piece of D C given its dimentions? cardboard paper. ABCD in which C Draw the rectangle b ABColour angles = 5 cmthe and BC =of4 the cm.triangle at its vertices inAred, green and yellow A cm A 4 4 cm A B as shown in the figure opposite. c Useand thedraw. scissors to cut the three Notice A B angles and fix them on⊥aBC. piece of InNotice this case, we write AB and draw. 5 cm paper as shown in the figure. 0 0 1 2 1 2 3 4 3 5 4 5 6 7 8 B 8 3 … 2 … Length One Side How to draw a perpendicular toof a straight line from point on ait. Without using graph paper or squared paper, can ayou draw square, A given its side length? A A Drill 6: Required: Draw the square ABCD whose side length 3 cm long. Draw ∆ABC in which BC = 4 cm, D C A m(∠B) = 30˚ and m(∠C) = 80˚. 1 … Two lines, intersecting and perpendicular Drawing a Triangle Given the Measure of Two Angles and the Drill Drill5:4: 2 … Two lines, intersecting and not perpendicular 4 0 0 … Two parallel lines 3 1 el 2 33 Drill 6: Notice: The three angles together formed (use a straight angle and Notice, then answer the following questions your geometric we know that the measure of the straight angle is instruments). 180˚. Then, we deduce Xthat: L E F The sumA of measures ofD the interior angles of any triangle = 180˚. Figure 2 Drill 8: Figure 1 Figure 3 Z Y Draw the triangleC ABC in which ∠B is a right angle, B N m(∠C) = 60˚ M and BC = 4 cm. Measure ∠A, then check that the sum of measures of angles of a triangle is 180˚. Shorouk Press 39 45 First Term Two straight straightlines, lines,intersecting intersecting Two and not not perpendicular perpendicular. . and Twostraight straightlines, lines,intersecting intersecting Two andperpendicular. perpendicular. and (you can can use useyour yourgeometric geometricinstruments.) instruments.) (you a Drill c Is What figure a rhombus? type of the ∆DEF ………according Why? ……………………… to its: Drill 3:is1 the 3: side ABstraight ≠ …………… ………… angles measures? ………… Drawlengths? two straight lines Write aa Because Draw two lines Writethe thegreatest greatestnumber number examples parallel ofofexamples of of parallel d on What the type of the lines ∆NKM according to its: you. on two twoislines lines ofyour your of lines that you cansee seearround arround you. that can b In figure 1, AB // ……… and AD //you ……… side lengths? ………… angles measures? ………… copybook, asshown shown copybook, as i.e. Each two opposite sides are ………………………………… in the the figure figurebelow. below. in • The figure is called a parallelogram. Drawing a Triangle given the Length of two Sides and the c Is figure 2 a parallelogram? Measure of ……… the Included Why? ……………………… Angle Because XY // ……, but XL is not parallel to …… Drill • This 5:figure is called a -trapezium. - The Thelines linesofofthe thecopy-book. copy-book. Draw in which AB = -5- The cm, b Do Do∆ABC you expect expect these b you these Thetwo twoedges edgesofofthe theruler. ruler. d Is figure 3 a parallelogram? ……… Why? ……………………… BC straight =straight 4 cm and = 60˚. linesm(∠B) to lines to ………………………………………………………… - - ………………………………………………………… Because MN // …… and MF // …… A intersect B C intersectififthey theywere were - - ………………………………………………………… ………………………………………………………… e Inextended figure 3, from MN NE = …… = …… extended from=both both ………………………………………………………… - - ………………………………………………………… 4 cm i.e. Figure 3 is a quadrilateral and its sides are ……… in sides? sides? ………………………………………………………… - - ………………………………………………………… length. ………………………………………………………… - - ………………………………………………………… • (( yes This figure four sides areB equal in length is called a yes noAwhose ,,no )) Note: Note: 60˚ rhombus. A parallel B 5lines cm Youcan candraw drawtwo twoparallel lines Notice andstraight draw. lines These two two straight lines You These usingthe thetwo twoedges edgesofofyour your Drill 7: parallel are called called parallellines. lines.using are ruler, asshown shown the ruler, as Join each figure to the suitable name. Exercies 1 ininthe figure opposite. opposite. Draw ∆XYZ in which XY = 7figure cm, YZ = 5 cm and m(∠Y) = 40˚. 32 32 Drill 4: the suitable statement, geometric Parallelogram Trapezium Square Triangle Exercies 2 use your instruments to be sure. Draw ∆DEF in which ∠D is right, DE = 3 cm and EF = 4 cm. Join eachRhombus figure to Rectangle Exercise 2 the following questions. Measure the length of DF, then answer a Calculate the perimeter of ∆DEF, given that the perimeter of 1 Join figure= to the suitable anyeach polygon the sum of its name. side lengths. b What is the type of the triangle, according to the measures of its angles? …………… 1 2 3 4 (acute-angled , obtuse-angled or right-angled) c What is the type of the triangle, according to the length of its Twosides? parallelTrapezium lines Two lines, intersecting Two lines, intersecting Rectangle Triangle Rhombus Square Parallelogram …………… and not perpendicular and perpendicular (isosceles , equilateral or scalene) 40 44Mathematics for Primary Stage-Year 4 Shorouk Press Drill 5: How to draw a perpendicular to a straight line from a point on it. A A A 4 5 4 5 6 7 8 0 0 1 2 3 1 2 3 4 5 4 5 6 7 8 B and correct the wrong statement. Length One Side How to draw a perpendicular toof a straight line from a point on it. aA The angles of a rectangle are right. ( ) A A Drillb 6:The sides of a square are equal in length. ( ) Draw ∆ABC in which BC = 4 cm, c The opposite sides of a parallelogram are parallel. ( ) A m(∠B) = 30˚ and m(∠C) = 80˚. d The measure of any angle of the square = 45˚. ( ) e Any of the four angles formed from the intersection of two 30˚ straight lines is a right angle. C80˚ ( ) Notice and draw. B Notice and draw. 4 cm f Any angle of the four angles formed from the intersection of perpendicular straight is a of right ) Sum of Measures of thelines Angles theangle. Triangle ( DrillThe 6:two g draw Twoa parallel straighttolines are two straight How to perpendicular a straight linenon-intersecting from a point outside it. ( ) Drill 7:lines. B B a Draw any triangle on a piece of lines on the same straight line h Two perpendicular straight are intersecting straight lines. ( ) cardboard paper. C b Colour thetwo angles of the of triangle at i The diagonals the square are perpendicular. ( ) vertices Ared, green A 3 itsDraw the in square ABCDand withyellow sideAlength 4 cm, then complete. asashown the figure AB =in…… = ……opposite. = …… = …… cm. c Use the scissors to cut the three Noticeband ABdraw. // …… and BC // …… angles and fix them on aBC. piece ccase, AB ⊥ ……, CD ⊥⊥…… andofBD ⊥ …… In this we write AB shown in theXYZL figure. 4 paper Drawas the rectangle in which its two dimensions are 5 cm 3 … Two lines, intersecting and perpendicular 3 … 4 2 Put for the correct andof (�)Two for the incorrect Drawing a Triangle Given statement the Measure Angles and one the Drill 5:(�) 2 … Two lines, intersecting and not perpendicular 1 … 3 2 … Two parallel lines 2 0 0 el 1 1 g 33 and 2 cm, then complete. Notice: three a XYThe = …… = angles …… cmtogether and YZformed = …… a= straight …… cm.angle and knowand thatXY the⊥measure of the straight angle is b XYwe // …… …… c YZ180˚. // …… and we YZ deduce ⊥ …… that: Then, 5 Complete the following. In the quadrilateral: The sum of measures of thesides interior ofinany triangle = 180˚. a Each two opposite areangles parallel ………, ………, ……… and ……… b Each two opposite sides are equal in length in ………, Drill 8:………, ……… and ……… fourABC sidesinare equal ……… and ……… Draw c the The triangle which ∠Binislength a rightinangle, m(∠C) = 60˚ d The four angles are right in ……… and ……… and BC = 4 cm. Measure ∠A, then check that the sum of e The two diagonals in ……… and ……… are equal and measuresbisect of angles of a triangle is 180˚. ………. Shorouk Press 41 45 First Term Two straight straightlines, lines,intersecting intersecting Two and not not perpendicular perpendicular. . and Twostraight straightlines, lines,intersecting intersecting Two andperpendicular. perpendicular. and (you can can use useyour yourgeometric geometricinstruments.) instruments.) (you c What Drill 3:is the type of the ∆DEF according to its: Drill 3: Lesson 3two The Triangle side ………… angles measures? ………… Drawlengths? twostraight straight lines aa Draw lines Writethe thegreatest greatestnumber number examples parallel Write ofofexamples of of parallel d on What the type of the lines ∆NKM to its: you. on two twoislines lines ofyour your of linesthat thataccording youcan cansee seearround arround you. you side lengths? ………… angles measures? ………… copybook, asshown shown copybook, as in the the figure figurebelow. below. in Drill 1: Drawing a Triangle given the Length of two Sides and the A Notice the figure opposite, then Measure of complete. the Included Angle a The sides of the triangle ABC are C AB, …… Drill 5: and …… Thelines linesofofthe thecopy-book. copy-book. - - The bb The vertices of the triangle are A, … and … Draw in which AB = -5- The cm, b Do Do∆ABC you expect expect these you these Thetwo twoedges edgesofofthe theruler. ruler. B c BC The angles of the triangle ABC are ∠A, ∠… and ∠… =straight 4 cm and = 60˚. linesm(∠B) to straight lines to ………………………………………………………… - - ………………………………………………………… d AThe triangle is ……… (a polygon , an open curve), it hasC… B intersectififthey theywere were - - ………………………………………………………… intersect ………………………………………………………… sides and …from angles. extended from both extended both ………………………………………………………… - - ………………………………………………………… 4 cm sides? sides? ………………………………………………………… - - ………………………………………………………… Identifying the Type of the Triangle According to the ………………………………………………………… - - ………………………………………………………… Measure of its Angles B yes ,,no noA )) (( yes Note: Note: 60˚ A parallel B 5lines cm Youcan candraw drawtwo twoparallel lines Drill Notice andstraight draw. lines These2: two straight lines You These two usingcomplete. thetwo twoedges edgesofofyour your using the Notice the following triangles, then are called parallel lines. are called parallel lines. A D as ruler, asshown shown the ruler, X Exercies 1 ininthe figure opposite. opposite. Draw ∆XYZ in which XY = 7figure cm, YZ = 5 cm and m(∠Y) = 40˚. 32 32 B Drill 4:C E F Z Y Join each figure to the suitable statement, geometric Exercies 2 use your Figure 1 Figure 2 Figure 3 instruments to which be sure. Draw ∆DEF in ∠D is right, DE = 3 cm and EF = 4 cm. a In ∆ABC, ∠……… is a right angle, for that the triangle is called Measure the length of DF, then answer the following questions. a right-angled triangle. a Calculate the perimeter of ∆DEF, given that the perimeter of Question: Can you a triangle with lengths. two right angles? any polygon = draw the sum of its side thethree typeangles of the are triangle, according measures of b b In What ∆DEF,isits ………, for that to thethe triangle is its angles? …………… triangle. called an acute-angled 1 2 3 4 , is obtuse-angled or right-angled) c In (acute-angled ∆XYZ, ∠……… an obtuse angle, for that the triangle is c called Whatanisobtuse-angled the type of the triangle, according to the length of its triangle. Twosides? parallel …………… lines Two lines, intersecting Two lines, intersecting Question: Can you draw with two obtuse and a nottriangle perpendicular and angles? perpendicular (isosceles , equilateral or scalene) 42 44Mathematics for Primary Stage-Year 4 Shorouk Press Drill 5: How to draw a perpendicular to a straight line from a point on it. A A A 1 g A A Notice the following triangles, Draw ∆ABC in which BC = 4 cm,then complete. A A m(∠B) = 30˚ and m(∠C) = 80˚. 3 4 5 4 D X 5 6 7 8 Notice Notice and and draw. draw. E F C B 80˚ C 30˚ 4 cm Y B 1 Figure 3 The of MeasuresFigure of the2 Angles of the Triangle DrillFigure 6: Sum Z How perpendicular to a straight line from point outside a to In draw figurea 1, use the compasses to check that aDE = DF. Thisit. Drilltriangle 7: is called an isosceles triangle. B B a Draw any triangle on a piece of b In figure 2, use the compasses to check that AB = BC = CA. cardboard paper. C i.e. the sides of the triangle b Colour thethree angles of the triangle at are ……… in length. This an equilateral itstriangle verticesisincalled and yellow Ared, green A triangle. A as shown in the figure opposite.triangle Isosceles? …………… Questions Is the equilateral c Useand thedraw. scissors to isosceles cut the three Is the triangle equilateral? …………… Notice angles and fix them on⊥aBC. piece of Incthis AB Incase, figurewe 3,write use the compasses to check that the three sides of paper as shown in the figure. the triangle are different in length. This triangle is called a 33 scalene triangle. Notice: The three angles together formed a straight angle and know that the measure of the straight angle is Drill 4:we 180˚. Then, we deduce that: N Notice the following triangles, then complete. 0 0 1 2 1 2 3 4 3 5 4 5 6 7 8 B DrillA6:3: Drill 3 … of its Sides Length One Side How to draw a perpendicular toof a straight line from a point on it. 2 … Identifying the Type of the to theand Length Drawing Given theTriangle MeasureAccording of Two Angles the Drill 5:a Triangle 1 … Two lines, intersecting and perpendicular 2 … Two lines, intersecting and not perpendicular 4 0 0 … Two parallel lines 3 1 el 2 D X The sum A of measures of the interior angles of any triangle = 180˚. C Drill 8: B Z Y F E M K a What is the type ∆ABC to its: m(∠C) = 60˚ Draw the triangle ABC of in the which ∠B according is a right angle, side ………… angles and BC = 4lengths? cm. Measure ∠A, then check thatmeasures? the sum of ………… b Whatofis angles the typeofofa the ∆XYZis according to its: measures triangle 180˚. side lengths? ………… angles measures? ………… Shorouk Press 43 45 First Term Two straight straightlines, lines,intersecting intersecting Two and not not perpendicular perpendicular. . and Twostraight straightlines, lines,intersecting intersecting Two andperpendicular. perpendicular. and (you can can use useyour yourgeometric geometricinstruments.) instruments.) (you c Drill c What What is type of of thethe ∆DEF ∆DEF according according to its: to its: Drill 3:isthethetype 3: side lengths? lengths? ………… ………… angles angles measures? measures? ………… ………… Draw twostraight straight lines Write aa side Draw two lines Writethe the greatest number examples parallel greatest number ofofexamples of of parallel d d What What is is the the type type of thethe ∆NKM ∆NKM according to its: to its: you. on two two lines ofof your on lines of your linesthat thataccording youcan cansee seearround arround you. lines you side side lengths? lengths? ………… ………… angles angles measures? measures? ………… ………… copybook, asshown shown copybook, as in the the figure figurebelow. below. in Drawing Drawing a Triangle a Triangle given given thethe Length Length of two of two Sides Sides andand thethe Measure Measure of of thethe Included Included Angle Angle Drill Drill5:5: Thelines linesofofthe thecopy-book. copy-book. - - The Draw ∆ABC which AB = 5=cm, Draw in which AB cm, b Do Do∆ABC youinexpect expect these b you these Thetwo twoedges edgesofofthe theruler. ruler. -5- The BCBC = straight 4 cm and m(∠B) =straight 4 cm and m(∠B) = 60˚. lines to = 60˚. lines to ………………………………………………………… - - ………………………………………………………… A A intersect B B C C intersectififthey theywere were - - ………………………………………………………… ………………………………………………………… extendedfrom fromboth both extended ………………………………………………………… - - ………………………………………………………… 4 cm4 cm sides? sides? ………………………………………………………… - - ………………………………………………………… yes (( yes A A )) no ,,no ………………………………………………………… - - ………………………………………………………… B B Note: Note: 60˚ 60˚ A A parallel 5 cm5lines cm Youcan candraw drawtwo twoparallel lines B B You Notice and draw. Notice and draw. lines These two straight lines These two straight usingthe thetwo twoedges edgesofofyour your are called called parallel parallellines. lines.using are ruler,as asshown shown the ruler, Practice (1) Exercies 1 1:ininthe Exercies figure opposite. Draw ∆XYZ in in which XYXY = 7=cm, YZYZ =opposite. 5=cm andand m(∠Y) = 40˚. Draw ∆XYZ which 7figure cm, 5 cm m(∠Y) = 40˚. 32 32 Drill 4: Join each figure to Practice theExercies suitable statement, (2) 2 2:use your geometric Exercies instruments to which be sure. Draw ∆DEF in in which ∠D∠D is right, DEDE = 3=cm andand EF EF = 4=cm. Draw ∆DEF is right, 3 cm 4 cm. Measure thethe length of of DF, then answer thethe following questions. Measure length DF, then answer following questions. a a Calculate thethe perimeter of ∆DEF, given thatthat thethe perimeter of of Calculate perimeter of ∆DEF, given perimeter any polygon = the sum of its side lengths. any polygon = the sum of its side lengths. b b What is is thethe type of of thethe triangle, according to the measures of of What type triangle, according to the measures itsits angles? …………… angles? …………… 1 2 3 4 (acute-angled , obtuse-angled or or right-angled) (acute-angled , obtuse-angled right-angled) c c What is is thethe type of of thethe triangle, according to the length of its What type triangle, according to the length of its Two parallel lines Two lines, intersecting Two lines, intersecting sides? …………… sides? …………… and not and perpendicular (isosceles , equilateral orperpendicular scalene) (isosceles , equilateral or scalene) 44 44Mathematics for Primary Stage-Year 4 Shorouk Press Drill 5: How to draw a perpendicular to a straight line from a point on it. A A A A A Draw∆ABC ∆ABCininwhich whichBC BC==44cm, cm, Draw m(∠B)==30˚ 30˚and andm(∠C) m(∠C)==80˚. 80˚. m(∠B) AA 4 5 4 5 6 7 8 80˚ 30˚ 80˚ 30˚ CC cm 4 4cm Noticeand anddraw. draw. Notice Notice and draw. BB The SumofofMeasures Measuresofofthe theAngles Anglesofofthe theTriangle Triangle DrillThe 6: Sum How to draw a perpendicular to a straight line from a point outside it. Drill7: 7: Drill B Drawany anytriangle triangleon onaapiece pieceofof aa Draw cardboardpaper. paper. cardboard Colourthe theangles anglesofofthe thetriangle triangleatat bb Colour itsvertices verticesinin red,green greenand andyellow yellow its Ared, A asshown shownininthe thefigure figureopposite. opposite. as c Use Use the scissorstotocut cutthe thethree three c the scissors Notice and draw. angles and fixthem them on apiece pieceofof angles on In this case,and wefix write AB ⊥aBC. paperas asshown shownininthe thefigure. figure. paper B 0 0 1 2 3 1 2 3 4 C 5 4 5 A 6 7 8 B DrillA6: 6: Drill 3 … Length OneSide Side Length One How to draw a perpendicular toof aofstraight line from a point on it. 3 … Two lines, intersecting and perpendicular Drawing TriangleGiven Giventhe theMeasure MeasureofofTwo TwoAngles Anglesand andthe the Drawing Drill 5:aaTriangle 2 … 4 Two lines, intersecting and not perpendicular 1 … 3 2 … Two parallel lines 2 0 0 lel 1 1 g 33 Notice: The Thethree threeangles anglestogether togetherformed formedaastraight straightangle angleand and Notice: weknow knowthat thatthe themeasure measureofofthe thestraight straightangle angleisis we 180˚.Then, Then,we wededuce deducethat: that: 180˚. Thesum sumofofmeasures measuresofofthe theinterior interiorangles anglesofofany anytriangle triangle==180˚. 180˚. The Drill8: 8: Drill Drawthe thetriangle triangleABC ABCininwhich which∠B ∠Bisisaaright rightangle, angle,m(∠C) m(∠C)==60˚ 60˚ Draw andBC BC==44cm. cm.Measure Measure∠A, ∠A,then thencheck checkthat thatthe thesum sumofof and measuresofofangles anglesofofaatriangle triangleisis180˚. 180˚. measures Shorouk Press First Term 31 43 45 45 Two straight lines, intersecting and not perpendicular . Two straight lines, intersecting and perpendicular. (you can use your geometric instruments.) c What Drill Drill 9:3:is the type of the ∆DEF according to its: side measures? ………… a ∆XYZ Drawlengths? two straight lines Writem(∠X) the angles greatest number of examples Draw in which =………… XY = 7cm, = 100˚, and m(∠Y) =of parallel d Measure What the type of answer: the ∆NKM its: you. on twoislines ofthen your lines thataccording you can seeto arround 50˚. (∠Z), side angles measures? ………… copybook, as shown a What islengths? the sum of………… the measures of angles of ∆XYZ? ………˚ in the figure below. b What is the type of the triangle XYZ according to the measures Drawing a Triangle of its angles? ………given the Length of two Sides and the Measure of the Included Angle Drill 10: Drill 5:set-squares in Use the two - The lines B ofZthe copy-book. X Draw in which AB = 5- cm, b geometric Do∆ABC you expect these The two edges of the ruler. your instruments BCto=straight 4 cmtwo and m(∠B) = 60˚. lines to - ………………………………………………………… box draw triangles A intersect if they were B C - ………………………………………………………… as shown in the figure extended from both Y - ………………………………………………………… opposite, then answer: 4 cm C A sides? - ………………………………………………………… - triangle, ………………………………………………………… a Measure the angles of each then complete. B , no i ( yes The sum ofA the) measures of angles of ∆ABC equals Note: 60˚ ………˚ + ………˚ + ………˚ = ………˚A B You can draw two parallel5 cm lines Notice andsum draw. These two straight lines ii The of the measures of angles of ∆XYZ equals using the two edges of your are called parallel lines. ………˚ + ………˚ + ………˚ = ………˚ ruler, as shown in the Exercies b What is the type of ∆ABC according to 1 its side lengths? ……… figure opposite. Draw ∆XYZ in which XY = 7 cm, YZ = 5 cm and m(∠Y) = 40˚. (scalene , equilateral , isosceles) c32 What is the type of ∆XYZ according to its side lengths? ……… Drill 4: (scalene , equilateral , isosceles) Join each figure to the suitable statement, Exercies 2 use your geometric instruments to which be sure. Draw ∆DEF in ∠D is right, DE = 3 cm and EF = 4 cm. Exercies 3 Measure the length of DF, then answer the following questions. 1 a Put (✔) for the statement andgiven (✗) forthat thethe incorrect one of Calculate thecorrect perimeter of ∆DEF, perimeter and correct the =wrong statement. any polygon the sum of its side lengths. There can type be two righttriangle, angles in one triangle. ( ) of b a What is the of the according to the measures b itsThere can…………… be three acute angles in one triangle. ( ) angles? 1There can be, aobtuse-angled 2 angle andor 3 4 c (acute-angled right an right-angled) obtuse angle in one triangle. ( of its ) c What is the type of the triangle, according to the length Two parallel lines intersecting Two of lines, d sides? The measure ofTwo thelines, straight angle = the sum theintersecting …………… and not perpendicular and perpendicular measures, of the angles a triangle. ( ) (isosceles equilateral orof scalene) 44 30 30 46 44Mathematics for Primary Stage-Year 4 Shorouk Press Drill 5: How to draw a perpendicular to a straight line from a point on it. A A A 4 5 4 5 6 7 8 80˚ 30˚ ∆XYZ in which XY = 5 cm, m(∠X) m(∠Y) =B 45˚. Notice and 3 Draw C Notice and draw. draw. 4=cm a Without using the protractor find m(∠Z). type of the according the measures Sumisofthe Measures of triangle the Angles of theto Triangle DrillbThe 6:What of its angles? How to draw a perpendicular to a straight line from a point outside it. triangle according to its side Drillc 7:What is the type of the B B (measure the lengths of its sides) a Draw lengths? any triangle on a piece of cardboard paper. C Draw the ∆ABC in which ACtriangle = 7 cm,atm(∠A) = 45˚, and m(∠C) = b 4 Colour angles of the 5˚. its7vertices inAred, green and yellow A A Calculate, m(∠B), then check your answer using asashown in the mentally, figure opposite. the protractor. c Useand the scissors to cut the three Notice draw. bcase, What the type the triangle according to the measures angles and fix them on⊥ofaBC. piece of In this weis write AB angles? paperofasitsshown in the figure. 33 c What is the type of the triangle according to its side (measure lengths of theasides) Notice: lengths? The three anglesthe together formed straight angle and we know that the measure of the straight angle is in which = 5 cm, EF = 6 cm and m(∠B) = 80˚. 180˚. Then, weDE deduce that: 5 Draw ∆DEF a What is the sum of the measures of the two angles ∠FDE ∠DFE? of the interior angles of any triangle = 180˚. The sum and of measures b use the protractor to find m(∠DFE). c Calculate m(∠FDE). (without measuring) Drilld 8:What is the type of ∆DEF according to the measures of its lengths? Draw the angles triangleand ABCitsinside which ∠B is a right angle, m(∠C) = 60˚ and BC = 4 cm. Measure ∠A, then check that the sum of measures of angles of a triangle is 180˚. 0 0 1 2 3 1 2 3 4 5 4 5 6 7 8 B 7 0draw ˚ . a perpendicular Length One Side How to toof a straight line from a point on it. a Without using the protractor, find m (∠L). DrillbA6:What is the type of Athe triangle according to theAmeasures of its Draw ∆ABC in angles? which BC = 4 cm, A Whatand is the type =of80˚. the triangle according to its side m(∠B)c = 30˚ m(∠C) lengths? (measure the lengths of the sides) 3 … Two lines, intersecting and perpendicular 3 … 4 2 Draw in which MN =6 cm, m(∠M) = 40˚Angles and m(∠N) = Drawing Triangle Given the Measure of Two and the Drill 5:a∆LMN 2 … Two lines, intersecting and not perpendicular 1 … 3 2 … Two parallel lines 2 0 0 el 1 1 g Shorouk Press First Term 31 45 47 45 Two straight lines, intersecting and not perpendicular . Two straight lines, intersecting and perpendicular. (you can use your geometric instruments.) c What Drill 3:is the type of the ∆DEF according to its: Lesson 4two straight Applications ………… measures? ………… a side Drawlengths? lines Write the angles greatest number of examples of parallel d What the type of the ∆NKM its: you. on twoislines of your lines thataccording you can seeto arround side lengths? ………… angles measures? ………… copybook, as shown in the figure below. Question How to make a solid using cardboard paper? Drawing a Triangle given the Length of two Sides and the Measure of the Included Angle Drill 1: You can make a cube-shaped box without a lid as follows. Drill 5: - The lines of the copy-book. a Draw a square of (choose a proper side length, Draw in which AB = 5- cm, b Do∆ABC you expect these The two edges of the ruler. for example 30 cm, on cardboard paper. BC =straight 4 cm and = 60˚. linesm(∠B) to b ADivide the large square into- 9………………………………………………………… small squares, B C intersect if they were - ………………………………………………………… as in the figure. extended from both ………………………………………………………… c Use the scissors to cut the- four blue squares 4 cm sides? - ………………………………………………………… in the four corners of your drawing. - ………………………………………………………… d Fold the remaining figure on the dotted lines B ( yes , noA ) e Glue the edges, to get the Note: solid opposite 60˚ (a cube-shaped box withoutYou a lid). B can draw twoA parallel5 cm lines Notice and straight draw. lines These two are called parallel lines. using the two edges of your Drill 2: ruler, as shown in the Exercies 1 You can make a opposite. Draw ∆XYZ in which XY = 7figure cm, YZ = 5 cm and m(∠Y) = 40˚. cuboid-shaped box 32 a lid by drawing a with Drill 4: figure suitable Joinwith each figure to the suitable statement, use your geometric Exercies 2 dimensions (astoinbe thesure. instruments Draw ∆DEF in which ∠D is right, DE = 3 cm and EF = 4 cm. figure opposite) on Measure the length of DF, then answer the following questions. cardboard paper, fold a Calculate the perimeter of ∆DEF, given that the perimeter of on the dotted lines any polygon = the sum of its side lengths. then glue the edges to b What is the type of the triangle, according to the measures of get the resulted solid its angles? …………… as in the 1 figure 2 3 4 (acute-angled , obtuse-angled or right-angled) below. c What is the type of the triangle, according to the length of its Twosides? parallel …………… lines Two lines, intersecting Two lines, intersecting and not perpendicular and perpendicular (isosceles , equilateral or scalene) 46 30 30 48 44Mathematics for Primary Stage-Year 4 Shorouk Press Drill 5: How to draw a perpendicular to a straight line from a point on it. A A A 4 5 4 5 6 7 Exercies80˚4 8 30˚ Notice and draw. C B Notice 4 cmA 1 aand Ondraw. the lattice, draw the square ABCD whose side length is 4 cm. Sum of Measures of the Angles of the Triangle DrillbThe 6:Draw AC and BD. How to draw a perpendicular to a straight c Into how many triangles was theline from a point outside it. Drill 7:square ABCD divided? B B a Draw any triangle on a piece of d Are these triangles congruent? cardboard paper. C e Divide each of these triangles into B b Colour the angles of the triangle at two congruent triangles. its vertices inAred, green and yellow A A f Colour the resulted triangles in two different colours as shown in the figure opposite. consecutively to get an ornamental nice figure. c Useand thedraw. scissors to cut the three Notice g With the aid of your teacher, use the ‘Paint’ program in angles and fix them on⊥aBC. piece of In this case, wecomputer write AB your to do the final figure. paper as shown in the figure. 0 0 1 2 3 1 2 3 4 5 4 5 6 7 8 B Length One Side How draw a perpendicular toof a straight line from a point on it. Youtocan make a pyramid with square-shaped base A by drawing a figure with A suitable A Drill 6: dimensions as in the figure on cardboard Draw ∆ABC BC = lines 4 cm,then glue the paper, fold in onwhich the dotted A m(∠B) = 30˚ and m(∠C) = 80˚. edges and you will get the solid opposite. 3 … Two lines, intersecting and perpendicular 3 … 4 Drawing a Triangle Given the Measure of Two Angles and the Drill Drill5:3: 2 … Two lines, intersecting and not perpendicular 1 … 3 2 … Two parallel lines 2 0 0 el 1 1 g 33 2 The figure opposite represents a Notice: The three angles together formed a straight angle and rectangular-shaped hall. Its two we know that the measure of the straight angle is dimensions are 6 m and 8 m. Two types 180˚. Then, we deduce that: of tiles were used to tile the hall as shown in the figure. Complete tiling in the The sum of measures of the interior angles of any triangle = 180˚. same pattern, then answer the questions. a How many squared tiles are needed? b How many rectangular tiles are needed? Drill 8: Draw the triangle ABC in which ∠B is a right angle, m(∠C) = 60˚ 3 A square-shaped room of side length 4 metres. On squared and BC = 4 cm. Measure ∠A, then check that the sum of paper, design a pattern of your choice where you use 2 or 3 measures of angles of a triangle is 180˚. different kinds of tiles to cover its floor. Shorouk Press First Term 31 47 49 45 Two straight lines, intersecting and not perpendicular . Two straight lines, intersecting and perpendicular. (you can use your geometric instruments.) c What of the2∆DEF according to its: Drill 3:is the type Unit Activities ………… measures? ………… a side Drawlengths? two straight lines Write the angles greatest number of examples of parallel d What the type of the ∆NKM its: you. on two of your lines thataccording you can seeto arround Activity 1 islines lengths? angles measures? copybook, as In the side multimedia labshown in………… your school and with the aid of your………… in the below. to draw the following geometric figures. teacher, use figure the computer Drawing a Triangle givenbtheSquare Length of two Sides and the a Rectangle Measure ofdtheOther Included Angle figures c Triangle ornamental Drill 5: - The lines of the copy-book. Activity 2 ∆ABC in which AB =straight 5- cm, bthe Do youopposite, expect these The two edges of the ruler. In Draw figure three BC intersect =straight 4 cm and m(∠B) = 60˚. lines to points. - ………………………………………………………… lines at three A intersect if they were B C - ………………………………………………………… a What is the greatest number of extended points from both ………………………………………………………… intersection can you- get 4 cm sides? using four straight lines? - ………………………………………………………… - ………………………………………………………… b What is the greatest number of A )can you get B ( yes , no intersection points Note: 60˚ using six straight lines? B You can draw twoA parallel5 cm lines and draw. These straight lines c Notice Whattwo is the greatest number of intersection points can you get using the two edges of your are called lines. using sixparallel straight lines, if four of them are parallel? ruler, as shown the Exercies 1 inpoints d What is the greatest number of intersection can you get figure opposite. Draw ∆XYZ in which XY = 7 cm, YZ = 5 cm and m(∠Y) using ten straight lines, if seven of them are parallel? = 40˚. 32 Drill 4: Join each figure to the suitable statement, Exercies 2 use your geometric instruments to which be sure. Draw ∆DEF in ∠D is right, DE = 3 cm and EF = 4 cm. Measure the length of DF, then answer the following questions. a Calculate the perimeter of ∆DEF, given that the perimeter of any polygon = the sum of its side lengths. b What is the type of the triangle, according to the measures of its angles? …………… 1 2 3 4 (acute-angled , obtuse-angled or right-angled) c What is the type of the triangle, according to the length of its Twosides? parallel …………… lines Two lines, intersecting Two lines, intersecting and not perpendicular and perpendicular (isosceles , equilateral or scalene) 48 30 30 50 44Mathematics for Primary Stage-Year 4 (2015 - 2016) Shorouk Press Drill 5: How to draw a perpendicular to a straight line from a point on it. A A A 4 5 4 5 6 7 8 0 0 1 2 3 1 2 3 4 5 4 5 6 7 8 B Length One Side How to draw a perpendicular toof a straight line from a point on it. 1 Put and (✗) for the incorrect one A (✔) for the correct statement A A Drilland 6:correct the wrong statement. If ABC is a triangle which m(∠B) = 98˚, then it is Draw a ∆ABC in which BC = 4 in cm, A possible to be a right-angled triangle. ( ) m(∠B) = 30˚ and m(∠C) = 80˚. b If XYZ is a triangle in which m(∠X) = 100˚ and m(∠Y) = 58˚, then m(∠Z) = 30˚. ( ) 30˚ sides are equal c The rhombus is a quadrilateral 80˚ in which all Notice and draw. C B Notice and 4 cm in draw. length. ( ) d It is possible to draw a triangle given the measures of each of Measures of the Angles of the Triangle ( DrillThe 6:ofSum its angles. ) How to draw a perpendicular to a straight line from a point outside it. Drill 7:each figure to the suitable 2 Join name. B B a Draw any triangle on a piece of cardboard paper. C b Colour the angles of the triangle at its vertices inAred, green and yellow A A asParallelogram shown in the figure opposite. Rhombus Rectangle Square Trapezium c Use the scissors to cut the three Notice and draw. angles them on⊥aBC. piece of each of the following. In3this case,and wefix write AB Write only one difference between paper as shown thethe figure. a The squareinand rectangle. 33 b The triangle and the circle. Notice: The three angles together formed a straight angle and c The rhombus and the parallelogram. wesquare know that of the straight angle is d The and the the measure cube. 180˚. Then, we deduce that: 3 … Two lines, intersecting and perpendicular 3 … 4 Drawing Given the Measure of Two Angles Drill 5:a Triangle General Exercises on Unit 2 and the 2 … Two lines, intersecting and not perpendicular 1 … 3 2 … Two parallel lines 2 0 0 el 1 1 g 4 Draw The triangle ABC in which AB = 3 cm, BC = 4 cm and The sum m(∠B) of measures the interior anglesof ofAC, any then triangle = 180˚. = 90˚. of Measure the length complete the rectangle ABCD and answer. a Calculate the perimeter of each of the rectangle ABCD and Drill 8:the triangle ABC. Draw b the What triangle in which is a right m(∠C) is ABC the type of the∠B triangle ABCangle, according to: = 60˚ and BC =i4 cm. ∠A, then check thatmeasure the sum of of its angles. its Measure side lengths. ii the measures of angles of a triangle is 180˚. Shorouk Press First Term 31 49 51 45 Two straight lines, intersecting and not perpendicular . Two straight lines, intersecting and perpendicular. (you can use your geometric instruments.) c What Drill 3:is the type of the ∆DEF according to its: ………… measures? ………… a side Drawlengths? two straight lines Write the angles greatest number of examples of parallel d What the type of the ∆NKM its: you. on twoislines of your lines thataccording you can seeto arround side lengths? ………… angles measures? ………… copybook, as shown in the figure below. Drawing a Triangle given the Length of two Sides and the Measure of the Included Angle Drill 5: - The lines of the copy-book. Draw in which AB = 5- cm, b Do∆ABC you expect these The two edges of the ruler. BC =straight 4 cm and = 60˚. linesm(∠B) to - ………………………………………………………… A intersect if they were B C - ………………………………………………………… extended from both - ………………………………………………………… 4 cm sides? - ………………………………………………………… ( yes , noA ) - ………………………………………………………… B Note: 60˚ B You can draw twoA parallel5 cm lines Notice and straight draw. lines These two are called parallel lines. using the two edges of your ruler, as shown Exercies 1 in the opposite. Draw ∆XYZ in which XY = 7figure cm, YZ = 5 cm and m(∠Y) = 40˚. 32 Drill 4: Join each figure to the suitable statement, Exercies 2 use your geometric instruments to which be sure. Draw ∆DEF in ∠D is right, DE = 3 cm and EF = 4 cm. Measure the length of DF, then answer the following questions. a Calculate the perimeter of ∆DEF, given that the perimeter of any polygon = the sum of its side lengths. b What is the type of the triangle, according to the measures of its angles? …………… 1 2 3 4 (acute-angled , obtuse-angled or right-angled) c What is the type of the triangle, according to the length of its Twosides? parallel …………… lines Two lines, intersecting Two lines, intersecting and not perpendicular and perpendicular (isosceles , equilateral or scalene) 30 30 44Mathematics for Primary Stage-Year 4 Shorouk Press Drill 5: How to draw a perpendicular to a straight line from a point on it. A A A g el … … … … … B Multiples Divisibility Factors and Prime Numbers Common Factors (H.C.F.) Common Multiples (L.C.M.) Unit 3 Activities General Exercises on Unit 3 Factors and and Prime Prime Numbers Numbers Lesson Lesson 3 13 1 Factors Multiples Multiples Lesson Lesson 1 1 Multiples Multiples 8 9 9 1010 First: of of thethe Number First: Factors Factors Number Drill 1:that Drill 1:thatwewe We know can write a number in the form of the product of of We know can write a number in the form of the product atwo, Complete the following table. a or Complete the following table. two, more, numbers. or more, numbers. • • With respect the we can write With respect 6,6 we it as: 0 0 1to1to 2number 34 456, 5 67 can 7 89it as: 910 10 2 the 3 number 8 write × 2× 2 6= then thethe numbers 1, 2, 6 are 6 1= ×1 6× 6or or6 =6 2= ×2 3, × 3, then numbers 1, 32,and 3 and 6 are 0 0 2 24 4 called thethe factors of of thethe number 6. 6. called factors number toset the 35,35, wewe cancan write it as: the number write it as: 4• b 5With 0 1 1 2 2 3 3• b 4With 5 6respect 6respect Opposite is a ofnumber consecutive Opposite is ato set of consecutive 0 1 2 45 5 0 1 2 3 75,3and 47 and 6 6 35 = 1 × 35 or 35 = 5 × 7, then the numbers 1, 5, 35 35 = 1 × 35 or 35 = 5 × 7, then the numbers 1, 35 numbers in a numbers arranged intable. a table. 7 8 8 9 91010111112 12 1313 arranged 78 89 910 10 735. 11 11 12 12 13 13 are called the factors of the number 35. are called the factors of the number Complete colouring using the Complete colouring using the 4151516161717181819192020 Complete. Complete. With respect to to thethe number 12, we can write it18as: With respect number 12, we can write it18 as:19 14 15 16 17 14 15 16 17 19 20 20 same pattern. same pattern. 1212 =1 1212 = 2= ×2 …… or or 12 12 = 3=×3……, then thethe factors of of = ×1 ……, × ……, × …… × ……, then factors the 1212 areare ………………………… number ………………………… cthe Complete. cnumber Complete. uares are 0, 0, 2, 2, 4, 4, …… quares are …… The numbers written in the coloured squares are 0, …… The numbers written in the the coloured are 0, 2, 4, …… The process of writing number insquares the form of 2, the Note: The process of writing the number in the form of4, the nonbyby …… …… Note: and they are the results of numbers multiplication …… and they are the of numbers multiplication by …… product of two orresults more is called factorization product of two or more is by called factorization thethe number into factors. number into factors. es ofof the number 2 2of of ples the number These numbers areare called thethe multiples of the number 2 2 These numbers called multiples of the number Drill Drill is is 0, 2, 2, 4, 4, 61: enumbers numbers 0, 61: Note: 1 The units digit of these numbers isinto 0, 4, Note: 1factorizing The units digit ofthe each of these numbers is 2, 0, 2,64, 6 Complete factorizing each ofofthe following numbers into factors Complete each ofeach following numbers factors or 8. or 8. of of and write thethe factors each. and write factors each. bers that you studied mbers that you studied 2 2 Multiples of of 2 are thethe even numbers thatthat youyou studied Multiples 2 are even numbers studied a a 1818 = 1= ×1 before. … = 2= ×2 … = 3=×3…, then thethe factors of the number × before. … ×… × …, then factors of the number 1818 areare ……… ……… b Generally: 4242 = 1= ×1 …… = 2= ×2 …… = 3=×3…… = 6=×6……, then the the b Generally: × …… × …… × …… × ……, then roduct is is a multiple of of product a multiple of of the number 42by are …………… the 42 are Iffactors aIffactors number is multiplied 2, then thethe product is aismultiple of of a number is number multiplied by 2,…………… then product a multiple 2 c c 2424 = 1= ×1 …… = 2= ×2 …… =the 3=the ×number = 24=×24……, then the the × …… × …… 3…… ×number …… × ……, then factors of of thethe number 2424 areare …………… factors number …………… ple ofof the number 2 =2 1= ×1 …… ultiple the number d = 2= ×2 …… = 3=×3…… = 4=×4…… = 5=×5…… = = d 120 120 × …… × …… × …… × …… × …… Example: × 2× =2 34, hence 34 34 is aismultiple of the number 2 2 Example: 1717 = 34, hence a multiple of the number 1010 × ……, then thethe factors of the number 120120 areare …………… × ……, then factors of the number …………… 52 6252 62Mathematics for53 53 Primary Stage-Year 4 53 53 Shorouk Press n1 Drill2: 3: Drill 3: 2: a Complete Complete the following table. aa Complete the following table. Complete the following table. a the following table. 5 53 × ×3 6 3 0 f … 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 1010 5 53 00 3 b Opposite Opposite is aset set of consecutive bb Opposite isis ofof consecutive Opposite set consecutive b is aa aset of consecutive numbers arranged in atable. table. numbers arranged inin numbers arranged table. numbers arranged in aa atable. Complete colouring using the Complete colouring using the Complete colouring using the Complete colouring using the same pattern. same pattern. same pattern. same pattern. 0000 1111 2222 3333 4444 5555 6666 1011 1112 1213 13 10 11 12 13 10 11 12 13 7777 8888 999910 1415 1516 1617 1718 1819 1920 20 14 15 16 17 18 19 20 14 15 16 17 18 19 20 14 2122 2223 2324 2425 2526 2627 27 21 22 23 24 25 26 27 21 22 23 24 25 26 27 21 2828292930303131323233333434 Complete. c c Complete. Complete. c c The Complete. The numberswritten writtenininthe thecoloured colouredsquares squaresare are0,0,3,3,6,6,…… …… numbers The numbers written colouredsquares squares are0,0,5,5,10, 10,…… …… The numbers written ininthe coloured are and they arethe the results ofmultiplication multiplication …… and they are results ofthe byby…… andthey theyare arethe theresults resultsofofmultiplication multiplicationbyby…… …… and Thesenumbers numbersare arecalled calledthe themultiples multiplesofofthe thenumber number3 3 These Thesenumbers numbersare arecalled calledthe themultiples multiplesofofthe thenumber number5 5 These Generally: Generally: Generally: Generally: number ismultiplied multiplied byby 5,then then the product isaisaamultiple multiple ofthe If IfIfaIfaanumber isis byby 5,3, the product isis ofof anumber number ismultiplied multiplied 3,then then the product amultiple multiple ofthe the product number number 5 35 3 the number the number Example: 21 32 ×5 3= 5=== 160, hence 160 isamultiple amultiple multiple ofthe the number Example: 32 160, hence ofthe number Example: 21 63, 63is isaisamultiple number Example: ×× ×3 63, hence 63160 ofofthe number 3 35 5 Note: Forthe themultiples multiplesofofthe thenumber number5,5,the theunits unitsdigit digitofofeach eachofof Note: For c Complete. c Complete. d d these numbers is these numbers 0 0oror5 5ofof3 3 because The number amultiple multiple because3030= =…… ……× ×3 3 The number 3030isisa is Thenumber number2424isisa amultiple multipleofof…… because because2424= =…… ……× ×3 3 The Complete. c c Complete. …,then thenthe thenumber number……isisa amultiple multipleofofthe thenumber number5 5 1717× ×5 5= =…, …,then thenthe thenumber number……isisa amultiple multipleofofthe thenumber number5 5 4242× ×5 5= =…, 54Shorouk Press 53 54 First Term 53 53 55 55 Drill2: 3: Drill Factors and Prime Numbers 1the a Multiples Complete3 thefollowing followingtable. table. aLesson Complete Lesson 1 Multiples 10 00 11 22 33 44 55 66 77 88 99 10 ××35 00 35 of the Number First: Factors Drill We know1: that we can write a number in the form of the product of a or Complete the following table. two, more, numbers. 00 11 22 33 44 55 66 8 9 10 bb Opposite a set of consecutive isis a set of consecutive • Opposite With respect to the number 6, we can 0 1 2 3 4 5 6 7 write 8 9it as: 10 × 2 numbers arranged in a table. 7 8 9 10 11 12 12 13 numbers arranged in a table. 7 8 91, 2, 10 13 6 = 1 × 6 or 6 = 2 × 3, then the numbers 3 11 and 6 are 0 2 4 Complete colouring using the Complete colouring called the factors using of thethe number 6.14 14 15 15 16 16 17 17 18 18 19 19 20 20 same pattern. same pattern. theofnumber 35, we21 can22 write as:25 0 1 2 3 •b 4 With 5 6respect 21 22 23it24 24 25 26 26 27 27 6 23 Opposite is atoset consecutive 0 1 2 3 4 5 35 = 1 × 35 or 35 =in5a×table. 7, then the numbers 1, 5, 7 and 35 numbers arranged 7 8 9 10 11 12 13 28 29 830 931 10 32 11 33 12 34 13 7 are called the factors of the number 35. Complete colouring using the c 18 Complete. 4 15 16 17 19 20 Withwritten respect to the number 12, can as:19 20 14we15 16 176,it18 same pattern. cComplete. Complete. The numbers in the coloured squares are 0,write 3, …… 12and = 1they × ……, 12written =results 2 × in …… or 12 = 3squares ×by ……, then factors The numbers themultiplication coloured are 0, the 5, 10, ……of are the of …… the number 12 are c and Complete. they are the ………………………… results of multiplication by …… quares are 0, 2, 4, …… TheThe numbers written in the coloured are 0, These numbers are the multiples of 3 Note: process ofcalled writing the numbersquares in the the number form of 2, the4, …… on by …… andproduct they are results ofthe multiplication These numbers are multiples ofby the…… number 5 of the two orcalled more numbers is called factorization ples of the number 2 of the number into factors. These numbers are called the multiples of the number 2 Generally: Generally: IfDrill number is multiplied by 5, then the product is a multiple of the Ifaa e numbers is 0, 2,number 4, 61: is multiplied by 3, then the product is a multiple of Note: 1factorizing The unitseach digitthe each of53these numbers is 0, 2, 4, 6 number Complete ofofnumber the following numbers into factors 8. and write theor factors of each. mbers that you studied 2 Multiples ofhence 2 are numbers you studied Example: 32 × 5 = 160, 160 ismultiple a multiple of that the number Example: 21 × 3 = 63, hence 63the is aeven of the number 3 5 a 18 = 1 × before. … = 2 × … = 3 × …, then the factors of the number 18 are ……… For the multiples of the number 5, the units digit of each of cNote: Complete. b The 42number = 1 × numbers …… × …… = 6 × 30 ……, then×the Generally: these is 0 or 5=of3 3× …… 30 is= a2 multiple because = …… 3 product is a multiple of of the number 42by are …………… Iffactors anumber number multiplied then the product is a multiple of The 24isis a multiple of2,… because 24 = …… ×3 2 cc Complete. d 24 = 1 × …… = 2 × …… =the 3 ×number …… = 24 × ……, then the 17 × 5 = of …,the then the number is a multiple of the number 5 factors number 24 are……………… 42 × 5 = …, then the number … is a multiple of the number 5 ultiple of the number 2 = 1 × …… = 2 × …… = 3 × …… = 4 × …… = 5 × …… = d 120 Example: 17 × 2 = 34, hence 34 is a multiple of the number 2 10 × ……, then the factors of the number 120 are …………… 54 5452 62Mathematics for Primary 53Stage-Year 4 55 Shorouk Press 53 n1 Drill 4: Drill2: 3: Drill 3: table below contains numbers a Complete Complete the following table. from 0 to 49. aThe Complete the following table. a the following table. 0 0 1 1 22 2 3 3 0 3 44 5 4 5 6 65 7 7 868 9 971010 8 55 1 × ×3 03 5 512 10 011 13 14 15 16 17 18 20 6 3 0 f … 21 22 23 24 25 26 27 28 9 19 29 0 11 137 3 44 439 22 2 3338 55 5 66 6 30 31 32 33consecutive 34 35 0036 Opposite aset set b b Opposite Opposite isis ofof consecutive b is aa set of consecutive numbers arranged in atable. table. numbers arranged in43 numbers arranged aa table. 7 88 847 1011 10 111112 121213 1313 99 910 40 41 42 in 44 45 7746 48 49 Complete colouring using the Complete colouring using the Complete colouring using the 141415 151516 161617 171718 181819 191920 2020 14 a same Put apattern. yellow point in the cells having a multiple of the number 2. same pattern. same pattern. 212122 222223 23 2424number 252526 262627 2727 24 25 Put a red point in the cells having a 21 multiple of23the 3. Put a blue point in the cells having a28 multiple the number 5.34 28292930of 3031 3132 32333334 Complete. The numbers in the cells having yellow and red cb Complete. points are …………………………………………………………… Complete. c c The Complete. numbers written in the coloured squares are 0, 3, 6, …… each of these numbers isthe acoloured multiple ofsquares …… and the The numbers written colouredsquares are…… 10, …… The numbers written ininthe are 0,0,5,5,at 10, …… and they are the results of multiplication by …… same time and isresults also considered a multiple of …… andthey they are the results multiplication …… and are the ofofmultiplication byby…… c Complete. The numbers in the multiples cells having yellow points These numbers are called of the number 3 only are …………………………………………………………………… These numbersare arecalled calledthe themultiples multiplesofofthe thenumber number5 5 These numbers each of these numbers is a multiple of …… and it is not a multiple of …… or …… Generally: Generally: Generally: d Complete. The numbers the cells having yellow and blue numberisis ismultiplied multiplied by5,in 5,then then theproduct productis isa aamultiple multiple ofthe the If IfIfa aanumber byby the ofof number multiplied 3, then the product is multiple points are …………………………………………………………… number5 35 thenumber number each of these numbers is a multiple of …… and …… at the same time also considered aa multiple …… Example: ×5 = 5=is = 160, hence 160 is amultiple multiple thenumber number Example: 3232 160, hence ofof the Example: 21 ××and 3 63, hence 63160 is aismultiple of of the number 3 55 e Complete. The numbers in the cells having blue points only are ……………………………………………………………………… Note: Forthe themultiples multiplesofofthe thenumber number5,5,the theunits unitsdigit digitofofeach eachofof Note: For c Complete. d each of these isor5a 5of multiple of …… 30 and= is…… not ×a 3 these numbers is0 0or these numbers The number 30numbers is a is multiple 3 because multiple of …… The number 24 isora …… multiple of … because 24 = …… × 3 Complete. c c Complete. …,then thenthe thenumber number……isisa amultiple multipleofofthe thenumber number5 5 1717× ×5 5= =…, …,then thenthe thenumber number……isisa amultiple multipleofofthe thenumber number5 5 4242× ×5 5= =…, 56 53 54 Shorouk Press First Term 55 53 55 Exercise 1 Drill 2: Factors 1the following aLesson Complete3 table.and Prime Numbers Multiples Lesson 1 Multiples 1 Underline each number the of 1 Underline each number of of the following following that that is is a a multiple multiple of the the number 0 2: 5 ,, 64 10 number 2: 1 2 17 173 ,, 5 54 ,, 26 26 4 ,, 713 13 8,, 2 2 9,, 20 20 × 3 0 3 of the Number First: Factors 2 Underline each number of the following that is of 2Drill Underline number following that is a aofmultiple multiple of the theof We know1: thateach we can writeofa the number in the form the product number 3: 4 ,, 3 3: numbers. 4 ,, 15 15 ,, 21 21 3 ,, 10 10 ,, 12 12 ,, 22 22 a number Complete the following table. two, or more, 0 1 2 3 4 5 6 8 9 10 b Opposite is a set of consecutive •3 With respect to the number 6, we can write 0 1 2 3 4 5 6 7 that 8 is 10 Underline each number of the following multiple 3 Underline each number of the following that is9ita aas: multiple of of the the × 2 numbers arranged in a table. 7 8 9 10 11 12 13 6 = 1 × 6 or 6 = 2 × 3, then the numbers 1, 2, 3 and 6 are number ,, 15 number 5: 5:0 2 23 23 15 ,, 40 40 ,, 51 51 ,, 5 5 ,, 8 8 ,, 20 20 4using Complete colouring the called the factors of the number 6.14 15 16 17 18 19 20 same pattern. the of the 3 between 10 20. With respect theofnumber 35, we21 can write it24 as:and 4b Write all theismultiples multiples of the number number 3 between 10 and 20. 27 0 1 2 3 •4 4 Write 5 6all 22 23 25 26 Opposite atoset consecutive 0 1 2 3 4 5 6 35 = 1 × 35 or 35 = 5 × 7, then the numbers 1, 5, 7 and 35 numbers arranged in a table. 7 8 9 10 11 12 13 5 all the multiples number between 44. 7 8 14 9 and 10 11 are called factorsof ofthe thethe number5 5 Write Write all the multiples of the number 535. between 14 and 44. 12 13 Completethe colouring using c Complete. 4 15 16 17 18 19 20 Complete. Withwritten respect to the number 12, can as:19 20 14we15 16 176,it18 same pattern. The numbers in of the coloured squares are 0,write 3, …… 6 Write all the multiples the number 2 that are less than 10. 6 = Write all the12 multiples of theornumber are less than 10. 12 × ……, 2 × …… 12 = 32×that ……, and1they are the =results of multiplication by ……then the factors of the 12 are ………………………… c number Complete. quares are 0, 7 2, 4, …… Write all the of number 3 are than 20. 7 Write all the multiples multiples ofinthe the number 3 that that are less less than 20. The numbers written the coloured squares are 0, 2, These numbers are called the multiples of the number 3 Note: The process of writing the number in the form of the4, …… on by …… and they are of numbers multiplication by …… of the tworesults orof more called factorization 8 all the that are than 8 Write Writeproduct all the the multiples multiples of the number number 5 5 is that are less less than 30. 30. ples of the number 2 of the number into factors. These numbers are called the multiples of the number 2 Generally: 9 9 Complete. Complete. If 2, a12 number is multiplied by 3,number then the12 product is a multiple of Drill 3 × …… hence the is a multiple of …… e numbers is 0, 4,= 61: 12 = 3 × …… hence the number 12 is a multiple of …… Note: 1factorizing The unitseach digitthe ofthe each of 3these numbers is 0, 2, 4, 6 number Complete following numbers into factors and also alsoofconsidered considered a multiple multiple of …… …… and a of or 8. and write factors of each. 28 = × hence the number 28 is of …… mbers that you studied 28 =7 72the × …… …… hence the number 28 numbers is a a multiple multiple ofyou …… Multiples of 2 are the even that studied Example: 21 × 3 = 63, hence 63 is a multiple of the number 3 a and also considered a multiple multiple ofof…… …… a 18 = 1 × before. … = 2and × …also = 3 considered × …, then the factorsof the number 45 5 …… 45 =are 5× ×……… …… hence hence the the number number 45 45 is is a a multiple multiple of of …… …… 18= c Complete. and also considered a of …… a=multiple multiple of then …… the b Generally: 42number = 1 × …… =and 2 multiple ×also ……considered =of3 3× …… 6 × 30 ……, The 30 is a because = …… ×3 product is a multiple of of the number 42by are …………… Iffactors anumber number multiplied then the product is a multiple of The 24is is a multiple of2,numbers … because 245 =that …… × less 3 10 2 and are 2 10 Write Write the the multiples multiples of of the the two two numbers 2 and 5 that are less c than 24 =50. 1 × …… = 2 × …… =the 3 ×number …… = 24 × ……, then the than 50. factors of the number 24 are …………… 11 two 3 ltiple of the number 2 =the d Write 120 1 ×multiples …… = 2of …… = numbers 3 × …… 2 = and 4 × …… 5 ×less …… = 11 Write the multiples of×the the two numbers 2 and 3 that that=are are less Example: 17 × 2 = 34, hence 34 is a multiple of the number 2 than 10 ×30. ……, then the factors of the number 120 are …………… than 30. 57 56 52 54 62Mathematics for Primary 53Stage-Year 4 57 Shorouk Press 53 12 Join each number to its multiples. 12 Drill Drill 2:3: 3 example. 5 a 2 Complete the following table. Complete as in the 0 1 2 3 4 5 6 7 8 9 10 × 5 3 × 4 = 12, then 12 is a multiple of each of the two Example: 7 , 8 ,numbers 11 ,5 123, and 15 ,4 21 30 is divisible by each of 3 and 4. 0 and, 12 137 a a then number greater 20 that is a of multiple of the two a13 × 9 Write = ……, …… is the than multiple of each …… and …… numbers and 4consecutive and a multiple of 1 their 2 product 3 4 8. 5 6 b and Opposite a2set ofby …… is is divisible eachalso of …… and0 …… a number 20 that is8a multiple of the numbers arranged ingreater a is table. b 5b × 11Write = ……, then …… thethan multiple of …… 7 each 9of … 10 and 11 12 two 13 numbers 2 and 4 and not a multiple of their product 8. Complete colouringbyusing and …… is divisible eachthe of …… and …… 14 15 16 17 18 19 20 same pattern. c 3× 7 = ……, then …… is the multiple of each of …… and …… 14and Complete with the multiples the number as 24 the 25 example. 14 21…… 221023 26 27 …… is divisible by each ofof…… and Example: 50 < 57 < 60 28 29 30 31 32 33 34 a …… < 24 < …… b …… < 11 < …… Drill 3: …… 43 example. < …… d …… < 76 < …… c c Complete. Complete as in<the e < 69 written < …… in the coloured f …… < 95 are < …… The…… numbers squares 0, 5, 10, …… and they arenot thedivisible results by of multiplication by …… Example: 15 is 2 because when we divide 15 ÷ 2, 15 Complete with the multiples of the number 5 as the example. 15 the remainder is 1, hence 15 is not a multiple of the Example: 20 < 23 < 25 These numbers number 2. are called the multiples of the number 5 a …… < 17 < …… b …… < 8 < …… c …… < 32 < …… d …… < 66 < …… a Generally: 35eis not divisible by 3 because when we divide ÷ ……, the …… < 81 < …… by 5, then fthe …… < 94 <35 …… Ifremainder a number is multiplied product is a multiple of the is ……, hence 35 is not a multiple of …… number 5 b16 notnumber divisible 8 because when divide of …… 8, the 1628If isthe of by pupils in a class is awe multiple the÷two remainder is ……, hence 28 is …………… of30 8. and 40. How numbers32 2× and that is included between Example: 5 =3 160, hence 160 is a multiple of the number 5 many pupils are there in the class? c 72 is …………… by 9 because when we divide …… ÷ ……, the remainder is ……, hence is …………… of 9. Note: For the multiples of the 72 number 5, the units digit of each of 17 An alarm clock rings regularly every two hours, while another 17 these numbers is 0 or 5 one rings every 3 hours. If the two alarms ring together at 12 at what time will they ring together after that? c o’clock, Complete. 17 × 5 = …, then the number … is a multiple of the number 5 42 × 5 = …, then the number … is a multiple of the number 5 58Shorouk Press First Term 57 59 55 Drill Drill2:2: Divisibility Divisibility Lesson 2 2thethe aLesson a Complete Complete following following table. table. 0Meaning 0Meaning 34Divisibility 45 56 67 78 89 910 10 1 1 2 2of 3 of First: Divisibility First: × 3×The 3The Alaa and Yasmine a bag of sweets to distribute it equally Alaa and baught a bag of sweets to distribute it equally 0Yasmine 0 3 3baught among them. Complete. among them. Complete. • • If the bag contains 5 pieces of sweets, then every oneone will will taketake If the bag contains 5 pieces of sweets, then every 2 pieces, and …… piece willwill be be left.left. 2 pieces, and …… piece b b Opposite Opposite is is a set a set of of consecutive consecutive 0 01 12 23 34 45 56 6 • • If the bag contains 6 pieces of sweets, then every oneone will will taketake If the bag contains 6 pieces of sweets, then every numbers numbers arranged arranged in a in table. a table. 7 78 89 910 10 11 11 12 12 13 13 …… pieces, and nothing willwill be be leftleft in the bag. …… pieces, and nothing in the bag. Complete Complete colouring colouring using using thethe 14 15 15 16 16 17 17 18 18 19 i.e.i.e.When dividing 5 ÷5 2, thethe quotient is 2is and the remainder is 19 120 When dividing ÷ 2, quotient 214 and the remainder is 120 same same pattern. pattern. When dividing 6 ÷6 2, thethe quotient is 3is and remainder is zero When dividing ÷ 2, quotient 321 and the remainder is zero 21 22the 23 24 25 25 26 27 27 22 23 24 26 It is said that: thethe first case, thethe number 5 is5not divisible by 2. It is said that: in in first case, number is not divisible by 2. in in thethe second case, thethe number 6 is6divisible by 2. second case, number is divisible by 2. c c Complete. Complete. Generally: The number iscoloured divisibe by by another, Generally: The number that is divisibe another, if3,the The The numbers numbers written written in the inthat the coloured squares squares are are 0, if3, 0,the 6, …… 6, …… remainder ofofthe division operation is zero. remainder ofmultiplication division operation is zero. and and they they areare the the results results ofthe multiplication by by …… …… Drill 1:1:numbers Drill These These numbers areare called called thethe multiples multiples of the of the number number 3 3 Complete. Complete. a a In In dividing 7 ÷7 3, thethe quotient is …… andand thethe remainder is is dividing ÷ 3, quotient is …… remainder ……, hence 7 is by by 3. 3. ……, hence 7 …………… is …………… Generally: Generally: b b In In dividing 2020 ÷ 4, thethe quotient is …… andand thethe remainder is is dividing ÷ 4, quotient is …… remainder If aIf number a number is multiplied is multiplied by by 3, then 3, then thethe product product is aismultiple a multiple of of ……, hence 2020 is …………… by by 4. 4. ……, hence is …………… thethe number number 3 3 Second: and divisibilty Second:Multiples Multiples and divisibilty Example: Example: 2121 × 3× =3 63, = 63, hence hence 63 63 is aismultiple a multiple of the of the number number 3 3 We know that 3535 is a of the number 5, because if we We know that is multiple a multiple of the number 5, because if we multilpy 7 by 5 the product willwill be be 35 35 (5 ×(57×=735). To To express thisthis multilpy 7 by 5 the product = 35). express c c Complete. Complete. meaning in in another way that 35 35 is considered a multiple of the meaning another way that is considered a multiple of the The The number number 3030 is a is multiple a multiple of of 3 3because because 30 30 = …… = …… × 3× 3 number 5 because if we divide 35 35 ÷ 5÷the quotient willwill be be a whole number 5 because if we divide 5 the quotient a whole The The number number 2424 is a is multiple a multiple of of … …because because 24 24 = …… = …… × 3× 3 number 7 and thethe remainder willwill be be zero. So,So, it isitsaid thatthat number 7 and remainder zero. is said multiples of of thethe number 5 are divisible by by 5 and multiples of the multiples number 5 are divisible 5 and multiples of the number 7 are divisible by by 7. 7. number 7 are divisible Generally: AllAll multiples of of a number areare divisible by this number. Generally: multiples a number divisible by this number. 58 58 54 60 54 60 Mathematics for Primary Stage-Year 4 Shorouk Press e e 3 0 7o . . Drill2:2: Drill Completeasasininthe theexample. example. Complete Example: 3 3× ×4 4= =12, 12,then then1212isisa amultiple multipleofofeach eachofofthe thetwo two Example: numbers3 3and and4 4and and1212isisdivisible divisiblebybyeach eachofof3 3and and4.4. numbers ……,then then…… ……isisthe themultiple multipleofofeach eachofof…… ……and and…… …… a a 7 7× ×9 9= =……, and…… ……isisdivisible divisiblebybyeach eachofof…… ……and and…… …… and ……,then then…… ……isisthe themultiple multipleofofeach eachofof……and and…… …… b b 5 5× ×1111= =……, and…… ……isisdivisible divisiblebybyeach eachofof…… ……and and…… …… and ……,then then…… ……isisthe themultiple multipleofofeach eachofof…… ……and and…… …… c c 3 3× ×7 7= =……, and…… ……isisdivisible divisiblebybyeach eachofof…… ……and and…… …… and Drill3:3: Drill Completeasasininthe theexample. example. Complete Example: 1515isisnot notdivisible divisiblebyby2 2because becausewhen whenwe wedivide divide1515÷ ÷2,2, Example: theremainder remainderisis1,1,hence hence1515isisnot nota amultiple multipleofofthe the the number2.2. number notdivisible divisiblebyby3 3because becausewhen whenwe wedivide divide3535÷ ÷……, ……,the the a a 3535isisnot remainderisis……, ……,hence hence3535isisnot nota amultiple multipleofof…… …… remainder notdivisible divisiblebyby8 8because becausewhen whenwe wedivide divide…… ……÷ ÷8,8,the the b b 2828isisnot remainderisis……, ……,hence hence2828isis…………… ……………ofof8.8. remainder ……………byby9 9because becausewhen whenwe wedivide divide…… ……÷ ÷……, ……, c c 7272isis…………… theremainder remainderisis……, ……,hence hence7272isis…………… ……………ofof9.9. the . Shorouk Press First Term 59 59 Generally: Drill Drill 2:2: Divisibility 2thethe A number isfollowing divisible bytable. 2,table. if its units digit is 0 or any other even aLesson a1Complete Complete following number. 0 0 1 1 2 2 3 of 34Divisibility 45 56 67 78 89 910 10 First: × number 3The Meaning 2×3 A is divisible by 5, if its units digit is 0 or 5. Alaa and 0Yasmine 0 3 3 baught a bag of sweets to distribute it equally 3 A number is divisible by 3, if the sum of its digits is divisible by 3. among them. Complete. • If the bag contains 5 pieces of sweets, then every one will take 2 pieces, and …… piece will be left. b b Opposite Opposite is is a set a set of of consecutive consecutive 0 01 12 23 34 45 56 6 • If the bag contains 6Exercise pieces of sweets, every one will take 2 78then numbers numbers arranged arranged in a in table. a table. 7 11 11 12 12 13 13 89 910 10 …… pieces, and nothing will be left in the bag. Complete Complete colouring colouring using using thethe 14214 15 16 17 17 18 18 19 19 20 When dividing 5 ÷ 2, the quotient is and15 the16 remainder is 120 1i.e. Complete. same same pattern. pattern. 6 ÷ 2, the is and the remainder is zero aWhen35dividing ÷ 6 = ……… andquotient the remainder ……… 21321 22is22 23 24 25 25 26 26 27 27 23 24 It isbsaid that: in the first case, is not divisible by 2. A number is divisible bythe 2 if number its units 5digit is …………… in the second case, number is …………… divisible by 2. cComplete. A number is divisible by 5 ifthe its units digit6 is c c Complete. dThe 34 ÷ 3written = written ……… and the remainder is ………, 34…… is Generally: The number that is divisibe by another, if3,the The numbers numbers in the in the coloured coloured squares squares are are 0, 3, 0,then 6, …… 6, …………… by 3.ofofmultiplication remainder division operation and and they they areare the the results results ofthe multiplication by by …… ……is zero. 1:the 2Drill Circle numbers that arethe divisible by 2. These These numbers numbers areare called called the multiples multiples of the of the number number 3 3 Complete. 15 , 18 , 102 , 5224 , 6143 a In dividing 7 ÷ 3, the quotient is …… and the remainder is ……, the hence 7 is …………… by 3. by 5. 3Generally: Circle numbers that are divisible Generally: b 125 In dividing 20 ÷ 4, the quotient is …… and the remainder is , 3123 , multiplied 1460 , by 2327 , 4265 If aIf number a number is multiplied is by 3, then 3, then thethe product product is aismultiple a multiple of of ……, hence 20 is …………… by 4. thethe number number 3 3 4 Circle the numbers that are divisible by 3. Second: Multiples and divisibilty 33 , 1256 410 , hence 1278 Example: Example: 2121 ×, 3×73 =3 63, = 63, hence 63 63 is aismultiple a multiple of the of the number number 3 3 We know that 35 is a multiple of the number 5, because if we multilpy 7three by 5 numbers the product 35 (5 ×by7 2= and 35).5. To express this Write thatwill arebe divisible c5c Complete. Complete. meaning in another way that 35 is considered a multiple of the The The number number 3030 is a is multiple a multiple of of 3 3because because 30 30 = …… = …… × 3× 3 number 5 because if we divide 35 ÷ 5 the quotient will be a whole 6 The Write three 24 numbers are by 3 and The number number 24 is a is multiple a that multiple of divisible of … …because because 24 24 =5.…… = …… × 3× 3 number 7 and the remainder will be zero. So, it is said that of thenumbers number that 5 are divisible byby5 2, and multiples of the 7multiples Write three are divisible 3 and 5. number 7 are divisible by 7. Generally: All multiples of a number are divisible by this number. 60 58 54 54 60 Mathematics for Primary Stage-Year 4 Shorouk Press 61 Drill 2: Lesson 3 Factors and Prime Numbers Lesson Complete as3 in the example. sson 3 Factors and Prime Numbers Example: 3 × 4 = 12, then 12 is a multiple of each of the two First: Factors of the Number numbers 3 and 4 and 12 is divisible by each of 3 and 4. st: Factors of the Number We know that we can write a number in the form of the product of eknow that we can athen number of the numbers. atwo, 7 ×or 9more, = write ……, ……inisthe theform multiple of product each of of …… and …… , or more, numbers. …… is divisible each of andwrite ……it as: • and With respect to the by number 6, …… we can eWith respect to the number 6, we can write it as: b 5 6× =111 =× ……, the the multiple of each and …… 3 6 or then 6 = 2…… × 3, is then numbers 1, 2,of3 … and 6 are 6 = 1 × 6 or 6 …… = 2 the ×is3,factors then the numbers 2, 3and and…… 6 are and divisible each of 1, …… called ofby the number 6. 0 called the of……, the number 6. is the multiple of each of …… and …… c• factors 3 With × 7 =respect then …… to the number 35, we can write it as: o 7With respect and …… is divisible by each of …… and …… 1, 5, 7 and 35 to = the number itthe as: 35 1× 35 or 35, 35 we = 5 can × 7,write then numbers . 35 = 1 × 35 are or 35 = 5 the × 7,factors then the 1, 5, called of numbers the number 35.7 and 35 . Drill 3: of the number 35. are called the factors Complete. With respect to the number 12, we can write it as: Complete as in the example. mplete. With to 12 the=number it as: 12 = respect 1 × ……, 2 × ……12,orwe12can = 3write × ……, then the factors of = 1 × ……, = 2 × …… or………………………… 12 = 3 × ……, then the factors of the12number 12 are Example: 15 is not divisible by 2 because when we divide 15 ÷ 2, number 12 are ………………………… theprocess remainder is 1, hence 15 is not a multiple Note: The of writing the number in the form of of thethe te: The processproduct ofnumber writing the formisofcalled the factorization 2. number of the two or moreinnumbers product of two numbers is called factorization of or themore number into factors. of the factors. a number 35 is notinto divisible by 3 because when we divide 35 ÷ ……, the Drill 1: is ……, hence 35 is not a multiple of …… remainder rill 1: Complete factorizing each of the following numbers into factors b 28 is not divisible 8 because when we divide …… ÷ 8, the mplete factorizing of the by following and writeeach the factors of each. numbers into factors remainder is ……, hence 28 is …………… of 8. write the factors of each. a 18 = 1 × … = 2 × … = 3 × …, then the factors of the number c 9 because when …… ÷ ……, 18 = 1 × …72 =182isare ×…………… ………… = 3 × …,bythen the factors of we the divide number the remainder is ……, hence 72 is …………… of 9. 18 are ……… b 42 = 1 × …… = 2 × …… = 3 × …… = 6 × ……, then the 42 = 1 × ……factors = 2 × of …… 3 × ……42= are 6 × …………… ……, then the the=number factors of the number 42 are …………… c 24 = 1 × …… = 2 × …… = 3 × …… = 4 × ……, then the 24 = 1 × ……factors = 2 × of …… 3 × ……24= are 4 × …………… ……, then the the=number factors of the number 24 are …………… d 120 = 1 × …… = 2 × …… = 3 × …… = 4 × …… = 5 × …… = .120 = 1 × …… = 2 × …… = 3 × …… = 4 × …… = 5 × …… = 10 × ……, then the factors of the number 120 are …………… 10 × ……, 62 then the factors of the number 120 are …………… 61 59 Shorouk Press First Term Second: Drill Drill2:2: Prime Numbers Divisibility Lesson 2thethefollowing a a Complete Complete following table. table. Drill 2: 0 0Meaning 1 2each 2 3 of 3 4Divisibility 4 5numbers: 5 6 6 7 748, 879, 910 10 1 of First: The Find of the , 11 , 15 , 17. ×the × 3 3factors Alaa and the Yasmine Complete 0 0solution. 3 3 baught a bag of sweets to distribute it equally aamong 4 = 1them. × … =Complete. 2 × …, then the factors of the number 4 are …… • If the bag contains 5 pieces of sweets, then every one will take b 7 = 1 × …, then the factors of the number 7 are …… 2 pieces, and …… piece will be left.0 01 12 23 34 45 56 6 bcb Opposite Opposite a=set a2set of consecutive consecutive = 1 bag × is …is ×of…, the of factors of the number • 10 If the contains 6then pieces sweets, then every 10 oneare will…take numbers numbers arranged arranged in in a table. a table. 7 78 89 910 10 11 11 12 12 13 13 …… pieces, and nothing will be left number in the bag. d Complete 11 = 1 × ……, then the factors of the 11 are ………… Complete colouring colouring using using thethe 15 15 16 17 17 18 18 19 19 20120 i.e. When dividing 5 ÷ 2, the quotient is14of 214 and the16 remainder e same 15 =1 × … = 3 × …, then the factors the number 15 are is … same pattern. pattern. When dividing 6 ÷ 2, the quotient is 321 and the23 remainder is 22 22 23 25……… 26 26 27zero 27 24 25 f 17 = 1 × ……, then the factors of the21 number 1724 are It is said that: in the first case, the number 5 is not divisible by 2. in the second case, the number 6 is divisible by 2. cFrom c Complete. Complete. the above, the numbers 4, 10 and 15 have more than two Generally: The number that is17 divisibe by are another, if3,the The The numbers numbers written written in 7, in the11 the coloured coloured squares squares are 0,factors 3, 0, 6, …… 6,(one …… factors while the numbers and have only two remainder the division and they they are are the the results results ofofof multiplication multiplication bynumbers. by …… ……is zero. andand the number) and they are called Primeoperation Drill 1: These These numbers numbers areare called called thethe multiples multiples of the of the number number 3 3 Generally: Complete. onlyquotient two factors is called a prime number. aTheInnumber dividingthat 7 ÷has 3, the is …… and the remainder is ……, hence 7 is …………… by 3. Generally: Generally: i.e. The prime number divisible by is itself and the whole one. is b In dividing 20 ÷ 4,isthe quotient …… and the remainder If Ifa a number number is is multiplied multiplied byby 3, 3, then then thethe product product is aismultiple a multiple of of ……, hence 20 is …………… by 4. number number 3 3 Note: The whole one is notthe athe prime number. Second: Multiples and divisibilty Example: Example: 21 ×3 ×= 3 63, = 63, hence hence 6363 is a is multiple a multiple of the of the number number 3 3 Drill 3: 21 We know that 35 is a multiple of the number 5, because if we Discuss, theproduct following prime this multilpy which 7 by 5ofthe willnumbers be 35 (5is×considered 7 = 35). Toaexpress cnumber c Complete. Complete. and is not: 27, 5, 13 and 19 ,a then complete. meaning in which another way that 3522, is considered multiple of the The The number number 30 30 is is a multiple a multiple of of 3 3 because because 30 30 = …… = …… × 3× 3 anumber With respect to 27: 5 because if we divide 35 ÷ 5 the quotient will be a whole The number 24 iswrite is a multiple a 27 multiple of … …because because 24 24 = …… = …… ×has 3× 3 ItThe is number possible to24 = 1will × of …… =3 ×So, ……, number 7 and the remainder be zero. it isthen said27 that other factors 1 and 27.divisible So, it is by not5considered a ……… multiples of the than number 5 are and multiples of the number 7 are divisible by 7. Generally: All multiples of a number are divisible by this number. 62 58 54 54 60 Mathematics for Primary Stage-Year 4 63 Shorouk Press b With respect to the number 5: Drill Drill 2:2: It is impossible to write it in the form of the product of two Complete the example. Complete asas in in the example. numbers except in the form of 5 = 1 × … or 5 = 5 × …, then the factors of the number 5 are only … and … So, it is a ……… Example: 3 × 34 ×= 4= 12, then a multiple each the two Example: 12, then 1212 is is a multiple of of each of of the two c With respect to the 22: numbers 3 number and 4 and divisible each 3 and numbers 3 and 4 and 1212 is is divisible byby each of of 3 and 4. 4. It is possible to write 22 = 1 × …… = 2 × ……, then the number …………… because itmultiple has …………… 79 ×is= 9a= ……, then …… the multiple each …… and …… a a 722 × ……, then …… is is the of of each of of …… and …… and …… divisible by each …… and …… …… is is divisible each of of …… and …… d and With respect to the by number 13: 5is11 × impossible 11 ……, then …… the multiple each and b b 5It× == ……, then …… is is the multiple of of each of of …… and …… to find two numbers, the product which is…… 13 and …… is divisible each …… and …… and …… is and divisible byby each of of …… and …… except … …, then …………… 37 ×= 7respect = ……, …… the multiple each …… and …… cec 3With × ……, then …… is is the multiple of of each of of …… and …… tothen 19: and …… divisible each …… and …… and …… is is divisible byby each of of …… and …… ………………………………………………………………………… ………………………………………………………………………… Drill Drill 3:3: ………………………………………………………………………… Complete the example. Complete asas in in the example. Third: Factorizing the Number (non-prime) to its Prime Factors Example: not divisible 2tobecause when divide ÷ 2, Example: 1515 is is not divisible byby 2 because when wewe divide 1515 ÷ 2, We saw that factorizing a number its prime factors, means writing the remainder 1, hence a multiple the remainder 1, hence 1515 is is not a multiple of of the this numberthe in the form ofisais product of two ornot more numbers. number number 2. 2. Example: For example:Factorize the number 315 to its prime Factors . Solution To a number 28 into factors, itdivide is possible to write 35 is not divisible 3like because when ÷ ……, the aaa 35 isfactorize not divisible byby 3 because when wewe divide 3535 ÷ ……, the divide the bynot the 28 = 4 ×we 7. But 4 is notnumber a35 prime number, because it has3 more remainder ……, hence 35 aprime multiple …… remainder is is ……, hence is is not a multiple of of …… 315 than two factors. So, factorize the number into its ÷prime numbers 2,3,5,7,..... according 105 28 not divisible by 8 because when divide …… ÷38, the b b 28 is is not divisible by 8 to because when wewe divide …… 8, the factors, we write 28 = 2 × 2 × 7, because each of 2, 2 and toisthe divisibility of28 this number byof of remainder is ……, hence …………… remainder ……, hence 28 is is …………… 8. 8. 35 5 7 is a prime factor. these prime .when 7÷ ……, …………… 9 because when divide …… ÷7……, c c 7272 is is …………… byby 9 numbers because wewe divide …… b Also, to factorize the number 24 to its prime factors, we write the remainder ……, hence …………… the remainder is is ……, hence 7272 is is …………… of of 9. 9.1 first 24 = 3 × 8. But 8 is not a prime number. So, we complete 315 = 3 × 3 × 5 × 7 the factorization, then 24 = 3 × 2 × 2 × 2. Drill 4: Factorize each of the following numbers to its prime factors. 15 , 12 , 9 , 26 and 36 64 Shorouk Press First Term 63 59 59 Drill Drill2:2: Exercise 2 Divisibility Lesson 2 a a Complete Complete thethe following following table. table. 1 Find the factors of each of the following numbers. 00 2 3 of 3 4Divisibility 4 5 5 6 6 7 78 89 910 10 1 First: 14× 38 , Meaning 261,2 75 × 3 ,3The Alaa and Yasmine 0 0 3 3 baught a bag of sweets to distribute it equally them. Complete. 2among Complete. • aIf the bag contains pieces of sweets, everyand one will take A prime number 5has two factors that then are …… …… 2 pieces, and …… piece will=be 0 01then 12 the 23 factors 34 45 of56the6 b 16 =is1is 2 × …… 4 ×left. ……, b b Opposite Opposite a× set a…… set of = of consecutive consecutive • If the bag contains 6 pieces of sweets, then every one will take number 16 arein………………………… numbers numbers arranged arranged in a table. a table. 7 78 89 910 10 11 11 12 12 13 13 …… pieces, and nothing will benumber left in the bag. ……………… c 1 is not considered a prime because Complete Complete colouring colouring using using thethe 15 15 16 16 17 17 18 18 19 19 20 i.e. dWhen dividing 5 ÷ 2, the quotient is14214 and the remainder is 120 3pattern. ispattern. considered a factor of the numbers ……… and ……… same same When dividing 6 ÷ 2, the quotient is21321 and the23 remainder is 22 22 23 24 25 25 26 26 27zero 27 24 said that: in the the following first case,isthe number 5 is not divisible by 2. 3It isState which of a prime number. second 2Complete. , 7 , 25 , in 29the , 34 , 57 case, the number 6 is divisible by 2. c c Complete. Generally: The number that is divisibe by are another, if3,the The The numbers numbers written written in in thethe coloured coloured squares squares are 0, 3, 0, 6, …… 6, …… 4 and Factorise each of the following numbers its…… prime factors. remainder the division operation is zero. and they they are are the the results results ofofof multiplication multiplication bytoby …… 12 , 18 , 23 , 36 Drill 1:numbers These These numbers areare called called thethe multiples multiples of the of the number number 3 3 Complete. 5 Find the number whose prime numbers are 2, 2 and 3. a In dividing 7 ÷ 3, the quotient is …… and the remainder is ……,the hence 7 is whose …………… 3. 6Generally: Find number primeby numbers are 2, 5 and 7. Generally: b In dividing 20 ÷ 4, the quotient is …… and the remainder is If Ifa a number number is is multiplied multiplied byby 3, 3, then then thethe product product is aismultiple a multiple of of ……, hence 20 is …………… by 4. thethe number number 3 3 Second: Multiples and divisibilty Example: Example: 2121 ×3 ×= 3 63, = 63, hence hence 6363 is a is multiple a multiple of the of the number number 3 3 We know that 35 is a multiple of the number 5, because if we multilpy 7 by 5 the product will be 35 (5 × 7 = 35). To express this c c Complete. Complete. meaning in another way that 35 is considered a multiple of the The The number number 3030 is is a multiple a multiple of of 3 3 because because 30 30 = …… = …… × 3× 3 number 5 because if we divide 35 ÷ 5 the quotient will be a whole The The number number 2424 is is a multiple a multiple of of … …because because 24 24 = …… = …… × 3× 3 number 7 and the remainder will be zero. So, it is said that multiples of the number 5 are divisible by 5 and multiples of the number 7 are divisible by 7. Generally: All multiples of a number are divisible by this number. 64 58 54 54 60 Mathematics for Primary Stage-Year 4 (2015 - 2016) Shorouk Press 65 Common Factors for Two or Common Factors for Two or Drill 2: Common Factors for TwoLesson or Lesson 4 more Numbers and Highest 4 on 4 Lesson Complete example. 4in the more as Numbers and Highest more Numbers and Highest Common Factor (H.C.F.) Common Factor (H.C.F.) Common Factor Example: 3 × 4 = 12, then 12 is a multiple(H.C.F.) of each of the two Drill 1: numbers 3 and 4 and 12 is divisible by each of 3 and 4. 1: Drill 1: Complete. te. Complete. a 7 × 9of=the ……, then …… is the …… …… Factors number 303 are 16multiple ,, 210 , ,3 … ,of5,each ,… 6 , of10 , …and , … of the number 30 are 1 , 2 , , 5 , Factors the 30 are 11of ,, …… 22 ,, 34and ,, 55for ,, 68 ,, Two 10 ,, … and of …… isnumber divisible eachFactors …… Common Factors of the number 40by are 10 ,, … …or … of the number 40 are 1 , 2 , 4 , 5 , 8 , 10 , … , … Factors of the number 40 are 1 , 2 , 4 , 5 , 8 , 10 , … , … b 5 × 11 = ……, then …… is the multiple of each of … and …… Lesson 4 Numbers that are factors Numbers of the number 30 and at the same time more and Highest rs that are factorsthat of the number 30 andnumber at the same time Numbers are factors of the 30 and at the and …… is divisible by each of …… and …… factors 40 of the number 40 are 1, , …… …… , …… , …… same time of the number are 1 , …… , …… Common (H.C.F.) factors of number 40 are ,Factor …… , …… , for …… c 3 ×numbers 7 =the ……, then …… is1the multiple of each of …… and …… These are called common factors the two numbers. numbersThese are called common factors for the two numbers. numbers are called factors for the two numbers. ……ofisthese divisible bycommon each of …… and …… Theand highest common factors is …… hest of The these common factors is …… of these common factorscommon is …… factor for the two Drill So,10ithighest is1: saidhighest that 10 is the highest said that is the common factor for the factor two So, it is said that 10 is the highest common for the two Drill 3: Complete. numbers 30 and 40 andas is H.C.F. symbolized as H.C.F. s 30 and 40 and is symbolized numbersof30 and 40example. and symbolized Complete as innumber the Factors the 30isare 1 , 2 , as 3 ,H.C.F. 5 , 6 , 10 , … , … Factors of the number 40 are 1 , 2 , 4 , 5 , 8 , 10 , … , … Generally: ally: Generally: Example: 15are is not divisible by 2 because when 15 ÷ 2, Numbers that factors of the number 30aand at we the divide same is time The highest common factor (H.C.F.) for set of numbers the ighest common factor (H.C.F.) for a set of numbers is the The highest common factor set of numbers the the remainder isall 1, 15 isa not multiple ofisthe factors of the number 40that are 1(H.C.F.) ,hence …… ,for…… , a …… highest number the numbers are divisible by. highest numberhighest that allnumber the numbers are divisible by. all the numbers arefor divisible number 2. thatcommon These numbers are called factors the twoby. numbers. Example (1) : Find the H. C. F for the numbers 30 , 40 highest Drill 2: of these common factors is …… 2: The Solution Drill So, it the isis2: said 10the isby the highest common factor the two 35 not that divisible 340 because when 35 ÷for ……, the Find H.C.F. for numbers 30 and 40we bydivide factorizing them to e H.C.F.a for the numbers 30 and by factorizing them to 30H.C.F. 2andfor 40 2 30 andas40H.C.F. Find the the numbers by factorizing them to numbers 30 40 and is symbolized is ……, hence 35 is not a multiple of …… theirremainder prime complete. factors. Then, complete. me factors. Then, 15 factors. 3 20 2 their prime Then, complete. 30 =28 is2not × 3divisible × …… because when we divide …… ÷ 8, the 2 × 3 ×b …… 5 53 × …… by 810 2 30 = 2 × Generally: 30 = 2 × 3 × 5 40 = 2 × 2 × 2 × …… is ……, hence 28 is …………… of 8. 2 × 2 ×402 = ×remainder …… 12 common 5 (H.C.F.) 540 = 2 × 21 × × 2 × ……factor The highest for a=set numbers 40 2 ×of × 5 × 2 is×the 2 H.C.F. for the numbers 30 and …… = …… or the numbers 30 and 40 = 2 × …… = …… c 72 is …………… by 9 because when we divide …… ÷ ……, 1all the 140 = H.C.F. for the numbers 30 and 2 × …… highest number that numbers divisible H.C.F. = are 2=×…… 5 = 10 by. the remainder is ……, hence 72 is …………… of 9. Example: Find the H.C.F. for the numbers 9 , 12 and 15. e: Find the H.C.F.Find for the , 12numbers and 15. Example: thenumbers H.C.F. for9 the 9 , 12 and 15. Drill 2: Complete the solution. te the solution. Find the H.C.F. for the numbers 30 and 40 by factorizing them to Complete the solution. 9 =prime 3 ×factors. …… Then, complete. their 3 × …… 9 = 3 × …… 12 ×==…… × …… 30 23 ×× 3…… × …… 3 × …… 12 = 3 × …… × …… 15 == 23 ×× 2…… 40 × 2 × …… 3 × …… 15 = 3 × H.C.F. …… for the numbers 9 , 12 and 15 = ……… H.C.F. numbers ,3012and 40 15 = 2= × …… = …… H.C.F. for for thethe numbers and ……… H.C.F. for9the numbers 9 , 12 and 15 = ……… 66 65 59 Shorouk Press 66 Example: Find the H.C.F. for the numbers 9 , 12 and 15. First Term Complete the solution. 9 = 3 × …… Exercise 4 Drill Drill2:2: Divisibility Lesson 2thethefollowing a a Complete Complete following table. table. 1 Find three common factors for 8 and 16. 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 78 89 910 10 First: ×× 3 3The Meaning of Divisibility andthree Yasmine a bag 0 0 3common 3 baught 2Alaa Find factors for of 12sweets and 28.to distribute it equally among them. Complete. If the bag contains pieces of sweets, one will take 3• Facorize each of the5two numbers 6 and then 15 to every their prime 2 pieces, and …… piece will left.0 01 12 23 34 45 56 6 factors, then H.C.F. forbe them. b b Opposite Opposite is is a set afind set ofthe of consecutive consecutive • If the bag contains 6 pieces of sweets, then every one will take numbers numbers arranged arranged in in a table. a table. 7 78 89 910 10 11 11 12 12 13 13 …… pieces, and nothing willasbe left in the bag. 4 Complete Complete the following table the example. Complete colouring colouring using using thethe 15 15 16 17 17 18 18 19 19 20 i.e. When dividing 5 ÷ 2, the quotient is14214 and the16 remainder is 120 same same pattern. pattern. When Division dividing 6 ÷ Quotient 2, the quotient is21321 and the23 remainder is Remainder Divisibility 22 22 23 24 25 25 26 26 27zero 27 24 operation It is said that: in the first case, the number 5 is not divisible by 2. Example 65 ÷ 4 16 1 65 is not divisible by 4 in the second case, the number 6 is divisible by 2. c c Complete. Complete. 57 ÷ 7 Generally: The number that is divisibe by are another, if3,the The The numbers numbers in in thethe coloured coloured squares squares are 0, 3, 0, 6, …… 6, …… 21 ÷ written 3 written remainder the division operation and and they they are are the the results results ofofof multiplication multiplication by by …… ……is zero. 75 ÷ 9 Drill 1:numbers These These numbers areare called called thethe multiples multiples of the of the number number 3 3 5Complete. a Find all the factors for each of the numbers 16 and 20. a bIn dividing ÷ 3, the factors quotientforisthe …… and the16remainder Find the7common numbers and 20. is hence 7 is …………… by 3. 16 and 20. c……, Find the H.C.F. for the numbers Generally: Generally: b In dividing 20 ÷ 4, the quotient is …… and the remainder is If Ifa a number number is is multiplied multiplied byby 3, 3, then then thethe product product is aismultiple a multiple of of ……,the hence 20for is …………… by 4. 6 Find H.C.F. eachthe ofthe the following sets of numbers. number number 3 3 a 20 and 30 b 35 and 49 Second: Multiples and divisibilty c 12 21 and 40 of and Example: Example: 21 × 16 3 ×= 3 63, = 63, hence hence 6363 is d a is multiple a24, multiple the of56 the number number 3 3 Weeknow 35 is21a multiple of the 5,8because if we 15,that 18 and f number 6, 7 and multilpy 7 by 5 the product will be 35 (5 × 7 = 35). To express this c c Complete. Complete. in another waynumbers that 35 is is 7, considered multiple of the 7meaning If the H.C.F. for two then whataare the two The The number number 3030 is is a multiple a multiple of of 3 3 because because 30 30 = …… = …… × 3× 3 number 5 because if we possible divide 35answers. ÷ 5 the quotient will be a whole numbers? Give three The The number number 2424 is is a multiple a multiple of of … …because because 24 24 = …… = …… × 3× 3 number 7 and the remainder will be zero. So, it is said that multiples of the number 5 are divisible by 5 and multiples of the number 7 are divisible by 7. Generally: All multiples of a number are divisible by this number. 66 58 54 54 60 67 Mathematics for Primary Stage-Year 4 Shorouk Press Drill 2: Common or 5 Common MultiplesMultiples for Two for or Two Lesson Lesson 5 son 5Complete as inNumbers the example. more Numbers and Lowest more and Lowest (L.C.M.) Common Multiples Example: 3 × 4 Common = 12, then 12 isMultiples a (L.C.M.) multiple of each of the two numbers 3 and 4 and 12 is divisible by each of 3 and 4. know thatnumbers each of the numbers 18, … is for a multiple for now thatWe each of the 6, 12, 18, … 6, is a12, multiple numbers and 3. that So, iteach is said that each of these numbersboth 2 and 3. So, it2 is said of these numbers is numbers is a 7 × 9 = ……, then …… is the multiple of each of …… and …… common for the numbers 2 and 3. mmon amultiple formultiple the numbers 2 and 3. and …… is divisible by each of …… and …… theisnumber 15 for is aboth multiple for both numbers 3 and 5. arly, the Similarly, number 15 a multiple numbers 3 and 5. b 5 × 11 = ……, then …… is the multiple of each of … and …… So, it is a common multiple for the numbers and45, 5. Also 30, 45, is a common multiple for the numbers 3 and 5. Also330, and …… is divisible by each of …… and …… 60, … are common multiples for the numbers 3 and 5. … are common multiples for the numbers 3 and 5. c 3 × 7 = ……, then …… is the multiple of each of …… and …… and …… is divisible by each of …… and …… ll 1: Drill 1: reach70. the number 70. Completeatill Complete you reach till theyou number Drill 3: multiples 5 (up to …………, 70) are 0, 70 5, …………, 70 he multiplesThe of the numberof5the (upnumber to 70) are 0, 5, Complete as in the example. multiples 7 (up to …………, 70) are 0, 70 7, …………, 70 he multiplesThe of the numberof7the (upnumber to 70) are 0, 7, common multiples for the numbers 5 and 7. UnderlinebtheUnderline common the multiples for the numbers 5 and 7. Example: 15 is not divisible by 2 because when we divide 15 ÷ 2, c Are all these common multiples for the product Are all these common multiples alsomultiples multiplesalso for the product the remainder is 1, hence 15 is not a multiple of the of 5 × 7 (i.e. multiples for35)? the number 35)? f 5 × 7 (i.e. multiples for the number number 2. ll 2: Drill 2: aatill35 is reach not divisible by 3 because when24. we divide 35 ÷ ……, the Complete till reach the number Complete you theyou number 24. remainder is ……, hence 35 are is2 not The multiples of2the number (up tomultiple 24) are of 0, …… 2, …………, 24 he multiples of the number (up to 24) 0, a2, …………, 24 The multiples of4the 4 (up to …………, 24) are 0, 24 4, …………, b 28 notnumber divisible by because when we divide …… ÷ 8, the 24 he multiples ofisthe (up8number to 24) are 0, 4, Underline the common multiples for the numbers remainder ……, hence 28numbers is …………… of Underlinebthe common is multiples for the 2 and 4. 8. 2 and 4. Are these common multiples also multiples for the÷ product Are all these common multiples multiples for the product cc 72 is all …………… by also 9 because when we divide …… ……, of 2remainder × 4 (i.e. multiples for the number 8)? f 2 × 4 (i.e. the multiples for the number 8)? is ……, hence 72 is …………… of 9. ll 3: Drill 3: reach60. the number 60. Completeatill Complete you reach till theyou number multiples 2 (up to …………… 60) are 0, 2, …………… he multiplesThe of the numberof2the (upnumber to 60) are 0, 2, multiples 3 (up to …………… 60) are 0, 3, …………… he multiplesThe of the numberof3the (upnumber to 60) are 0, 3, multiples 5 (up to …………… 60) are 0, 5, …………… he multiplesThe of the numberof5the (upnumber to 60) are 0, 5, btheUnderline common multiples for the Underlineb common the multiples for the numbers 2, 3numbers and 5. 2, 3 and 5. 68Shorouk Press First Term 67 59 c What is the smallest common multiple (other than zero) for the Drill Drill 2:2: 2, 3 and 5? (This number is called the lowest numbers Divisibility Lesson 2thethefollowing a a Complete Complete following table. table. common multiple for the numbers 2, 3 and 5) 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 78 89 910 10 First: ×× 3 3The Meaning of Divisibility Theand lowest common multiple for a set of numbers is the Alaa Yasmine 0 0 3 3 baught a bag of sweets to distribute it equally smallest number (other than zero) that is divisible by each of among them. Complete. then5 itpieces is a of multiple each of one these • these If thenumbers, bag contains sweets,for then every will take numbers individually is will abbriviated 2 pieces, and …… and piece be left. as L.C.M. b b Opposite Opposite is is a set a set of of consecutive consecutive 0 01 12 23 34 45 56 6 • If the bag contains 6 pieces of sweets, then every one will take numbers numbers arranged arranged in in a table. a table. 7 78 89 910 10 11 11 12 12 13 13 …… pieces, and nothing will be left in the bag. Complete Complete colouring colouring using using thethe Example: the L.C.M. for quotient 4 , 12 and 15. 15 15 16 17 17 18 18 19 19 20 i.e. When Find dividing 5 ÷ 2, the is14214 and the16 remainder is 120 same same pattern. pattern. Complete thedividing solution. When 6 ÷ 2, the quotient is21321 and the23 remainder is 22 22 23 24 25 25 26 26 27zero 27 24 Multiples for the number 4 are 0, 4, 8, ……………………………… It is said that: in the first case, the number 5 is not divisible by 2. Multiples for the number 12 are 0, 12, ……………………………… in the second case, the number 6 is divisible by 2. c c Complete. Complete. Multiples for the number 15 are 0, 15, ……………………………… Generally: The number that is divisibe by are another, if3,the The The numbers numbers written written in in thethe coloured coloured squares squares are 0, 3, 0, 6, …… 6, …… The lowest common multiple for the numbers 4 , 12 and 15 remainder the division operation and and they they are are the the results results ofofof multiplication multiplication by by …… ……is zero. (other than zero) is …… Then, the1: L.C.M. for the numbers 4 , 12 and 15 is ……… Drill These These numbers numbers areare called called thethe multiples multiples of the of the number number 3 3 Complete. Another solution 7using factors. a In dividing ÷ 3, factorization the quotient to is the ……prime and the remainder is 4 hence = 2 7×is …………… 2 ……, by 3. Generally: Generally: = 220 ×÷ 4,2the×quotient 3 b In 12 dividing is …… and the remainder is If Ifa a number number is is multiplied multiplied byby 3, 3, then then thethe product product is aismultiple a multiple of of 15 hence = 3 ×by 4. 5 ……, 20 is …………… thethe number number 3 3 L.C.M. 2 × and 2 divisibilty × 3 × 5 = 60 Second: Multiples Example: Example: 2121 ×3 ×= 3 63, = 63, hence hence 6363 is a is multiple a multiple of the of the number number 3 3 We know that 35 is a multiple of the number 5, because if we Then, L.C.M. 4 ,be1235and 60.To express this multilpy 7 byfor 5 the numbers product will (5 × 15 7 =is35). c c Complete. Complete. meaning in another way that 35 is considered a multiple of the The The number number 3030 is is a multiple a multiple of of 3 3 because because 30 30 = …… = …… × 3× 3 number 5 because if we divide 35 ÷ 5 the quotient will be a whole The The number number 2424 is is a multiple a multiple of of … …because because 24 24 = …… = …… × 3× 3 number 7 and the remainder will be zero. So, it is said that multiples of the number 5 are divisible by 5 and multiples of the number 7 are divisible by 7. Generally: All multiples of a number are divisible by this number. 68 58 54 54 60 Mathematics for Primary Stage-Year 4 69 Shorouk Press Drill2:2: Drill Exercise 5 Complete the example. Complete asas in in the example. 11 Write three multiples for the number 7. Example: 3 × 34 ×= 4= 12, then a multiple each the two Example: 12, then 1212 is is a multiple of of each of of the two 2 Write three common multiples for the numbers 6 and 10. 2 numbers 3 and 4 and divisible each 3 and numbers 3 and 4 and 1212 is is divisible byby each of of 3 and 4. 4. 3 Write three common multiples for the numbers 2, 7 and 10. 3 79 ×= 9= ……, then …… the multiple each …… and …… aa7 × ……, then …… is is the multiple of of each of of …… and …… 4 and Find all the common between 50 and 100 for the and …… divisible by each …… and …… …… is is divisible bymultiples each of of …… and …… 5 11 × 11 ……, then …… the multiple each and …… b b 5numbers: × == ……, then …… is is the multiple of of each of of …… and …… aand 3 …… andis5is b by 4each and c…… 2, 7 and 8 divisible of …… and …… and …… divisible by each of6 …… and 37 ×= 7= ……, then …… the multiple each …… and …… cc3 × ……, then …… is is the multiple of of each of of …… and …… 5 and a Write the multiples for the number 3 up to 63. and …… divisible each …… and …… …… is is divisible byby each of of …… and …… b Write the multiples for the number 7 up to 63. c Write all the common multiples for the numbers 3 and 7 Drill 3: Drill 3: up to 63. Complete the example. Complete asas in in the example. d Write the L.C.M. for the numbers 3 and 7. not divisible by 2number because when we divide ÷ 2, Example: 1515 is is not divisible 2 because divide 1515 ÷ 2, a Write the multiples forbythe 2when up towe 60. 66Example: the remainder is hence not a 30. multiple the the remainder 1, 1, hence 1515 is is atomultiple of of the b Write the multiplesisfor the number 3not up number number 2. 2. c Write the multiples for the number 5 up to 30. d Write all the common multiples for the numbers 2, 3 and 5 todivisible 30. is not divisible 3 because when divide ÷ ……, the a a 3535 isup not byby 3 because when wewe divide 3535 ÷ ……, the eremainder Write the L.C.M. for the numbers 3 and ……, hence is not a 2, multiple of …… remainder is is ……, hence 3535 is not a multiple of 5. …… b 28 is not divisible 8 because when …… ÷factors. 8, the b7 isFactorize not divisible byby because when wewe divide …… ÷ 8, the a28 each of8 the numbers 8 and 18divide to its prime ……, hence …………… of remainder is is ……, hence 2828 is is …………… 8. 8. bremainder Find the L.C.M. for the numbers 8 andof18. …………… 9 because when divide …… ÷ ……, c c 7272 is is …………… byby 9 because when wewe divide …… ÷ ……, 8 Find the L.C.M. for each of the following sets of numbers. the remainder ……, hence …………… the remainder is is ……, hence 7272 is is …………… of of 9. 9. a 2, 3 and 4 b 3, 4 and 5 c 2, 6 and 7 d 3, 6 and 7 9 If you know that the lowest common multiple for two numbers is 24, what are the two numbers (give more than one answer). 10 Find the L.C.M. for the numbers (5 × 7 × 13) and (2 × 5 × 11). 11 Find the L.C.M. for the numbers (2 × 3 × 5 × 7) and (3 × 3 × 7). 70Shorouk Press First Term 69 59 59 b c d e Write the multiples for the number 3 up to 30. Write the multiples for the number 5 up to 30. Write all the common multiples for the numbers 2, 3 and 5 up to 30. Write the L.C.M. for the numbers 2, 3 and 5. Drill Drill 2: Factorize each ofExercise the numbers 8 5 and 18 to its prime factors. 7 a 2: 7 Divisibility Lesson 2 a a Complete thethe following following table. table. b Complete Find the L.C.M. for the numbers 8 and 18. 1 Write three multiples for the number 7. 0L.C.M. 0Meaning 23 3 4Divisibility 4 5the 5 6following 6 7 78 sets 89 9of 10 1 1 2for 10numbers. of 8 Find each of 8First: ×× 3 the 3The a bag of sweets to distribute equally 2Alaa Write common a and 2, three 3Yasmine 43 bbaught 3,multiples 4 and 5 for c the 2,numbers 6 and 7 6dand3,10. 6it and 7 0and 03 among them. Complete. 3 three multiples for themultiple numbers 7 and 10. 9 If you know that the lowest common for2, two numbers 9• Write If the bagcommon contains 5 pieces of sweets, then every one will take is 224, what are the two numbers (give more than one answer). pieces, and ……multiples piece willbetween be left. 01 and 12 100 23 for 34 the 45 56 6 all the common b4b Find Opposite Opposite is is a set a set of of consecutive consecutive 0 50 If the contains 6 pieces of(5 sweets, then every one will take 10 Find thebag L.C.M. for in the × 77 ×713) (210 ×11 511 ×1211). 10• numbers: numbers numbers arranged arranged in a numbers table. a table. 8 8and 9 910 13 13 12 …… pieces, and nothing will6 be left inc the2,bag. a 3 and 5 b 4 and 7 and 8 Complete colouring colouring using using thethe 15 16 17 17 18×18 19 20 11 Find the dividing L.C.M. for (2 ×is14 3 2×14 5 ×15 7) and (3 3 ×19 7).120 11i.e.Complete When 5 ÷the 2, numbers the quotient and the16 remainder is same same pattern. pattern. Writedividing the multiples number 3 and up tothe 63.remainder is zero 6 ÷ 2, for thethe quotient is213 22 22 23 23 24 24 25 25 26 26 27 27 21 705 a When b Write the multiples for the number 7 up to 63. It is said that: in the first case, the number 5 is not divisible by 2. c Write all the multiples for number the numbers 3 and 7 by 2. in common the second case, the 6 is divisible c c Complete. Complete. up to 63. Generally: The number that is divisibe by another, if3,the The The numbers numbers written written in in the the coloured coloured squares 0, 3, 0, 6, …… 6, …… d Write the L.C.M. for the numbers 3 squares and 7.areare remainder the division operation and and they they are are the the results results ofofof multiplication multiplication by by …… ……is zero. 6 a Write the multiples for the number 2 up to 60. Drill 1: the bThese These Writenumbers numbers multiples areare called for called the thenumber the multiples multiples 3 up of to the of 30. the number number 3 3 Complete. c Write the multiples for the number 5 up to 30. a In dividing 7 ÷ 3, the quotient is …… and the remainder is d Write all the common multiples for the numbers 2, 3 and 5 ……, hence 7 is …………… by 3. Generally: Generally: up to 30. b In dividing 20 ÷ 4, the quotient is …… and the remainder is If e Ifa a number Write number the is is multiplied L.C.M. multiplied forby the by 3,numbers 3, then then thethe 2, product 3product and is5.aismultiple a multiple of of ……, hence 20 is …………… by 4. thethe number number 3 3 7 a Factorize each of the numbers 8 and 18 to its prime factors. Second: divisibilty b FindMultiples the L.C.M.and for the numbers 8 and 18. Example: Example: 2121 ×3 ×= 3 63, = 63, hence hence 6363 is a is multiple a multiple of the of the number number 3 3 We know that 35 is a multiple of the number 5, because if we 8multilpy Find the L.C.M. each of thebefollowing sets of numbers. 7 by 5 thefor product will 35 (5 × 7 = 35). To express this c c Complete. Complete. a 2, 3 and 4 b 3, 4 and 5 c 2, 6 and 7 d 3, 6 of and meaning in another way that 35 is considered a multiple the7 The The number number 3030 is is a multiple a multiple of of 3 3 because because 30 30 = …… = …… × 3× 3 number 5 because if we divide 35 ÷ 5 the quotient will be a whole 9 The If The younumber know that lowest common multiple for24 number 2424 isthe is a multiple a multiple of of … …because because 24 =two …… = numbers …… × 3× 3 number 7 andare thethe remainder will be zero. So,than it is said that is 24, what two numbers (give more one answer). multiples of the number 5 are divisible by 5 and multiples of the 10number Find the L.C.M. for the (5 × 7 × 13) and (2 × 5 × 11). 7 are divisible bynumbers 7. All multiples of a number by(3this 11Generally: Find the L.C.M. for the numbers (2 × are 3 × 5divisible × 7) and × 3number. × 7). 70 58 70 54 54 60 Mathematics for Primary Stage-Year 4 Shorouk Press Unit 3 Activities Drill 2: Complete as in the example. Activity 1 Find: a 3 × the all numbers. Example: 4 common = 12, thenmultiple 12 is a of multiple of each of the two b numbers the common 3 andfactor 4 andof12allisnumbers. divisible by each of 3 and 4. 2 a Activity 7 × 9 = ……, then …… is the multiple of each of …… and …… First: Complete the by following and …… is divisible each of table. …… and …… b 5 × 11 = ……, then …… is the multiple of each of … and …… 1 2 3 4 5 6 7 8 9 10 11 12 and …… is divisible by each of …… and …… 2×74 6 then8 …… 10is the multiple of each of …… and …… c 3 = ……, and 3 …… 6 is9divisible 12 by each of …… and …… 4 Drill 3:8 12 5 10 Complete as in the example. 6 Example: 7 8 15 is not divisible by 2 because when we divide 15 ÷ 2, the remainder is 1, hence 15 is not a multiple of the number 2. 9 a 35 is not divisible by 3 because when we divide 35 ÷ ……, the 10 remainder is ……, hence 35 is not a multiple of …… 11 b 28 is not divisible by 8 because when we divide …… ÷ 8, the 12 remainder is ……, hence 28 is …………… of 8. c 72 is …………… by 9 because when we divide …… ÷ ……, Second: Using above, following. the remainder is the ……,table hence 72 is complete ……………the of 9. a The number 108 is divisible by …… and …… b The number …… is divisible by 11 and 12. c The number 54 is considered a common multiple for the two numbers …… and …… d Multiples of the number 12 that are less than 150 are ……… e The number 11 is considered one of the factors of the numbers …………… Shorouk Press First Term 59 71 Drill 2: General Exercises on Unit 3 Lesson 2 theDivisibility a Complete following table. 1 Join each number from group a with the suitable phrase from 1 2 of 3 Divisibility 4 5 6 7 8 9 10 First: The0Meaning group × 3b. Alaa Yasmine it equally a and15 24 a bag of sweets 28 to distribute39 0 3 baught among them. Complete. • If the bag contains 5 pieces of sweets, then every one will take 2 pieces, and …… piece will be left. 0 1 2 3 4 5 6 b Opposite is a set of consecutive • b If divisible the bag contains 6 pieces of sweets, then every one will take divisible divisible numbers arrangeddivisible in a table. 7 8 9 10 11 12 13 ……bypieces, and nothing will be left in13the bag. 7 by 3 by by 5 Complete colouring using the 14 15 16 17 18 i.e. When dividing 5 ÷ 2, the quotient is 2 and the remainder19 is 120 same pattern. When dividing 6 ÷ 2, the quotient is 321 and22the23remainder is zero 27 24 25 26 2 It Put (✔) for the correct statement and (✗) for the incorrect one is said that: in the first case, the number 5 is not divisible by 2. and correct theinwrong statement. the second case, the number 6 is divisible by 2. c a Complete. The number 63 is divisible by 6. ( ) Generally: The number that is divisibe by another, if the The numbers written in the coloured squares are 0, 3, 6, …… b The number 17 is a prime number. ( ) division they7are the resultsof multiplication c and 0 and areremainder multiples ofofthe number operation 7. by ……is zero. ( ) d The H.C.F. for the two numbers 8 and 24 is 4. ( ) Drill 1: e These The L.C.M. for the numbers 8 and 24ofisthe 8. number ( 3) numbers aretwo called the multiples Complete. a In dividing 7 ÷ 3, the quotient is …… and the remainder is 3 Complete. 7 isof…………… 3. a ……, The hence multiples the numberby 6 which are between 20 and Generally: b In40 dividing 20 ÷ 4, the quotient is …… and the remainder is are ……… If a number is multiplied by 3, then the product is a multiple of b ……, The hence factors20 of is the…………… number 35by are4.……… the number 3 Multiples and divisibilty 4 Second: Find: Example: 21 × 3 = 63, hence 63 is a multiple of the number 3 We that 35for is the a multiple of 24 theand number a know the H.C.F. numbers 36. 5, because if we multilpy by 5 the will be7 35 the7L.C.M. forproduct the numbers and(59.× 7 = 35). To express this c b Complete. meaning in another way that 35 is considered a multiple of the The number 30 is a multiple of 3 because 30 = …… × 3 number 5 because if we divide 35 ÷ 5 the quotient will be a whole The number 24 is a multiple of … because 24 = …… × 3 number 7 and the remainder will be zero. So, it is said that multiples of the number 5 are divisible by 5 and multiples of the number 7 are divisible by 7. Generally: All multiples of a number are divisible by this number. 58 72 54Mathematics for Primary Stage-Year 4 60 Shorouk Press e e 3 0 7o . . . The Length The Area Unit 4 Activities General Exercises on Unit 4 Lesson11 The TheLength Length Lesson Youknow know that centimetre (cm) and metre units used You that thethe centimetre (cm) and metre (m)(m) areare units used measuring length. forformeasuring length. The metre (m) = 100 centimetres (cm) The metre (m) = 100 centimetres (cm) Drill1:1: Drill Complete. Complete. The metre…… ……thethe centimetre a a The metre centimetre metres …… centimetres bb 3 3 metres == …… centimetres metres …… centimetres cc 4 4 metres == …… centimetres …… metres = 700 centimetres d d …… metres = 700 centimetres …… metres = 300 centimetres e e …… metres = 300 centimetres > or (< (< , >, or =) =) 1 cm1 cm The centimetre (cm) = 10 millimetres (mm) The centimetre (cm) = 10 millimetres (mm) Drill2:2: Drill complete. complete. centimetres = …… mm a a 3 3centimetres = …… mm cm …… mm bb 2 2 cm == …… mm …… mm c c …… cmcm == 4040 mm …… mm d d …… cmcm == 6060 mm …… 400 = …… mm e e …… mm == 400 cmcm = …… mm Arrange the units length ascendingly (cm , ,mmm) , mm) f f Arrange the units of of length ascendingly (cm , m …… …… , …… …… , ,…… , …… Drill3:3: Drill Choose the suitable unit measure each of the following. Choose the suitable unit to to measure each of the following. Thickness electric wire.(mm (mm , cm , m) a a Thickness of of anan electric wire. , cm , m) Length classroom. (mm , cm , m) b b Length of of thethe classroom. (mm , cm , m) Length playground. (mm , cm , m) c c Length of of thethe playground. (mm , cm , m) The height a lamppost. (mm , cm , m) d d The height of of a lamppost. (mm , cm , m) 74Mathematics for Primary Stage-Year 4 74 Shorouk Press Shorouk Press First Term Figure number Figure name Side length Sum of side lengths (Perimeter) 1 Square 1 cm 1 + 1 + 1 + 1 = 1 × 4 = 4 cm 2 ………… … cm … + … + … + … = … × … = … cm 4 ………… … cm … + … + … + … = … × … = … cm Lesson 1 The Length You3 know that the centimetre (m)= … are units + …metre +…+… ×… = …used cm ………… … cm (cm)…and for measuring length. The metre (m) = 100 centimetres (cm) From the previous we deduce that: Drill 1: Complete. perimeter of a square = side length × …… a The metre …… the centimetre (< , > or =) b 3 metres = …… centimetres Drill 7: c 4 metres = …… centimetres cm Use the relation between the perimeter of the square and its 1side d …… metres = 700 centimetres length to complete. e …… metres = 300 centimetres a Perimeter of a square of side length 9 cm = … × … = …… cm centimetre (cm)piece = 10 of millimetres (mm) b Perimeter The of a square-shaped land of side length 10 m = …………… = ……… Drill 2: c Perimeter of a square-shaped piece of paper of side length complete. 2 dm = …………… = …… dm = …… cm a 3 centimetres = …… mm b 2 cm = …… mm Drill 8: c …… cm = 40 mm Notice the following rectangles, then complete ( consider the unit d …… cm = 60 mm of length = 1 cm). e …… m = 400 cm = …… mm f Arrange the units of length ascendingly (cm , m , mm) …… , …… , …… Drill 3: Choose the suitable unit to measure each of the following. a Thickness of an electric wire. (mm , cm , m) b Length of the classroom. (mm , cm , m) c Length of the playground. (mm , cm , m) 2 1 d The height of a lamppost. (mm , 3cm , m) 4 76 74Mathematics for Primary Stage-Year 4 Shorouk Press Rectangle Length Width number Sum of side lengths (Perimeter) 1 5 4 5 + 5 + 4 + 4 = 5 × 2 + 4 × 2 = (5 + 4) × 2 =18 cm 2 4 ………… 4 + 4 + … + … = 4 × 2 + … × 2 = (4 + …) × 2 =… cm 3 ………… 2 … + … + 2 + 2 = … × 2 + 2 × 2 = (… + 2) × 2 =… cm 4 ………… ………… … + … + … + … = … × 2 + … × 2 = (… + …) × 2 =… cm From the previous we deduce that: The perimeter of a rectangle = (……… + width) × …… Drill 9: Complete. a The perimeter of a rectangle whose length is 7 cm and width 3 cm = (…… + ……) × …… = …… cm b The perimeter of a rectangle whose dimensions 6 m and 3 m = (…… + ……) × …… = …… metre Example: Calculate the perimeter of a rectangle of dimensions 3 dm and 50 cm. Solution: 3 dm = 30 cm, then the perimeter of the rectangle equals (30 + ……) × …… = …… cm Note: To calculate the perimeter of a figure whose dimensions are in different units, you have to make the dimensions in the same unit. Drill 10: The kilometre (km) = 1000 meters (m) Complete. a 3 km = …… m c 8 km = …… m = …… dm b d 9000 m = …… km 4 km = …… m = …… cm Drill 11: A rectangular-shaped piece of land with dimensions 3 km and 2 km, it is needed to be surrounded by a wire fence. The cost of one metre of wire fence equals 8 pounds what is the total cost of the fence? Solution: Perimeter of land = (… + …) × 2 = …… km = …… m Cost of fence = …… × …… = …… pounds Shorouk Press First Term 77 Lesson 1 1 Exercise 1 The Length Put (✔) for the correct statement and (✗) for the incorrect one and correct the wrong statement. a know The perimeter of the square sidemetre length(m) + 4. ) You that the centimetre (cm)=and are units( used The perimeter ) forbmeasuring length.of a rectangle = (length + width) + 2. ( c The decimetre > the metre. ( ) The metre (m) = 100 centimetres (cm) d The millimetre < the centimetre. ( ) e If 1: the dimensions of a rectangle are 3 cm and 5 cm, then Drill half its perimeter equals 8 cm. ( ) Complete. a b c 3d e The metre …… the centimetre (< , > or =) Arrange the units of length in ascending order. 3 metres = …… centimetres centimetre , decimetre , millimetre , kilometre , metre 4 metres = …… centimetres 1 cm …… metres = 700unit centimetres Choose the suitable to measure each of the following. = 300 centimetres a …… Themetres distance between Cairo and Alexandria. (mm, dm, km) b The height of a building. (mm, dm, m) The centimetre (cm) = 10 millimetres (mm) c The height of a man. (km, cm, mm) Drill 2:length of an ant. d The (km, mm, m) complete. 4 a Choose the closest answer. 3 centimetres = …… mm The=length of a taxi = ……… (2 km, 20 m, 200 cm) b a 2 cm …… mm Thecm length my pen = ……… ( 12 km, 15 dm, 15 cm) c b …… = 40ofmm Thecm height my brother = ……… (3 m, 160 cm, 160 mm) d c …… = 60ofmm My m mother a piece e d …… = 400bought cm = …… mmof cloth of length = ……… (3 km, f Arrange the units of length ascendingly (cm3 ,m,m3, cm, mm)3 mm) e …… In my house, there is a squared room of side length = …… , …… , …… (5 m, 5 cm, 5 mm, 5 km) 2 Drill 3: the the suitable unit toofmeasure each of the following. 5 Choose Calculate perimeter each of the following. a a Thickness electric A squareofofan side lengthwire. 3 dm. (mm , cm , m) b b Length of the classroom. cmwidth , m)5 cm. A rectangle whose length is 12(mm cm ,and c c Length of the playground. , cm , m) A rectangle whose length is 3 (mm dm and width 25 cm. d d The height of a lamppost. , m) A rectangle whose dimensions(mm are ,2 cm m and 150 cm. 78 74Mathematics for Primary Stage-Year 4 Shorouk Press 6 Calculate, in centimetres, the side length of a square whose perimeter is 4 dm. 7 The perimeter of a rectangle is 86 cm, and its length is 23 cm. Find its width: a in centimetres. b indecimetres. 8 The sum of the perimeters of two squares is 100 dm. If the side length of one of them is 8 dm, find the side length of the other square. a in decimetres b in centimetres 9 It is wanted to make a frame to a rectangle-shaped picture whose dimensions are 400 cm and 500 cm. If the cost of one metre of the frame is 3 pounds, what is the cost of the frame? 1 10 The width of a rectangle-shaped piece of land equals 3 of its length. Calculate its perimeter if its width equals 15 metres. 11 Calculate the perimeter of each of the following. a A rectangle-shaped room whose dimensions are 4 m and 3 m. b A rectangle-shaped picture frame whose dimensions are 5 dm and 20 cm. c A rectangle-shaped bed sheet whose dimensions are 2 m and 150 cm. d A rectangle-shaped room door whose length is 18 dm, and width 1 metre. e A square-shaped window of side length 15 dm. 12 Notice the drawn figure, imagine that you cut the red part, calculate the perimeter of the remaining part (consider that the side length of the small square is 1m). 13 The figure represents a rectangular piece of land, its dimensions are 70 m and 50 m and a squared playground, its side is 30 m long is constructed inside it. If the shaded part is surrounded by a wire from inside and outside, find the length of the wire in each case. Shorouk Press First Term 79 Lesson Lesson21 The TheArea Length You know that the centimetre (cm) and metre (m) are units used Preface forAreas measuring of the length. figures like squares, rectangles, triangles, … etc, are measured by units In this lesson, you will The metre (m)of = area, 100 centimetres (cm) know some of these units. Drill 1: Complete. Drill 1: a The …… the centimetre (<into , > equal or =)parts, Notice the metre following figures, each figure is divided b 3of metres units area.= …… centimetres c 4 metres = …… centimetres 1 cm d …… metres = 700 centimetres e …… metres = 300 centimetres The centimetre (cm) = 10 millimetres (mm) Drill 2: complete. Figure 1 Figure 2 Figure 3 a 3 centimetres = …… Complete the following table:mm b 2 cm = …… mm Number of equal parts (area of figure) cFigure ……number cm = 40 mm d ……1cm = 60 mm …………… e ……2m = 400 cm = …… mm …………… f Arrange the units of length ascendingly 3 …………… (cm , m , mm) …… , …… , …… Question Can you determine, which of the previous figures is Drill 3:greater in area? why? Choose the suitable unit to measure each of the following. Toacompare the of areas of somewire. figures, you, have Thickness an electric (mm cm , tom)calculate the area each using same unit. So, (mm we are in need b of Length of thethe classroom. , cm , m) of standard units, One of these is the square centimetre c Length of the units playground. (mm , cm , m) and its 2 symbol is cm . Then, what is the square d The height of a lamppost. (mmcentimetre? , cm , m) 80 74Mathematics for Primary Stage-Year 4 (2015 - 2016) Shorouk Press Drill 2: Notice the shaded figure opposite to recognize the square centimetre cm2, then complete. cm2 is the area of a square of side length …… Drill 3: Notice the following squares and count the square centimetres which form each square (number of small squares), then complete as the example. cm2 1 2 3 Square Number of small Side length of number squares (cm2) square Example 1 4 cm2 2 cm Notes 4=2×2 2 3 Given that the area of the square = Number of the small squares (cm2), then complete: a Area of square 1 = 4 cm2 = 2 cm × 2 cm b Area of square 2 = … cm2 = … cm × … cm c Area of square 3 = ……… = … cm × … cm From the previous, we deduce that: Area of the square = side length × …… Shorouk Press First Term 81 Drill 4: Lesson 1 relations, The Length Using the previous complete. a Area of square of side length 9 cm = …… × …… = …… cm2 b Area of square of side length 2 cm = …… × …… = ……… c You Perimeter of a square is 24 cm know that the centimetre (cm) and metre (m) are units used length of the square = …… ÷ 4 = …… cm (Why?) forSide measuring length. Area of the square = …… × …… = …………… The metre (m) = 100 centimetres (cm) Drill Drill5:1: Notice the following rectangles and calculate the number of square Complete. centimetres (small…… squares) in each figure, then (< complete. a The metre the centimetre , > or =) b c d e 3 metres = …… centimetres 4 metres = …… centimetres …… metres = 700 centimetres …… metres = 300 centimetres cm 2 1 cm The centimetre (cm) = 10 millimetres (mm) Drill 2: complete. a 3 centimetres = …… mm b 2 cm = …… mm 1 cm = 40 mm 2 3 c …… d …… cm = 60 mm of square e Rectangle …… m Number = 400 cm = …… mm Rectangle Rectangle length × width centimetres f number Arrange the units of length ascendingly length width (cm , m , mm) (area) …… , …… , …… Example 1 Drill 3: 6 cm2 3 cm 2 cm 3 cmx × 2 cm = 6 cm2 …… × …… = …… 2 the suitable ……unit to measure …… ……of the Choose each following. a Thickness of …… an electric wire. , cm ,…… m) × …… = …… 3 …… (mm…… b Length of the classroom. (mm , cm , m) c Length of the we playground. From the previous, deduce that: (mm , cm , m) d The height of a lamppost. (mm , cm , m) Area of the rectangle = ……… × ……… 82 74Mathematics for Primary Stage-Year 4 Shorouk Press Drill 6: Use the previous relation between the area of the rectangle and its dimensions, then complete. a Area of rectangle whose length is 9 cm and width 6 cm equals …… cm × …… cm = …… cm2. b Area of rectangle whose dimensions are 3 cm and 8 cm equals …… × …… = …………… c The perimeter of a rectangle is 18 cm and its width 3 cm 1 length + width = 2 perimeter = …… cm We know that width = 3 cm, then length = … – … = …… cm Then, area of rectangle = …… × …… = …………… d The length of a rectangle is 12 cm, which is twice its width. 1 width of rectangle = 2 length = …… cm Then, area of the rectangle = …… × …… = …… cm Drill 7: The figure opposite represents a rectangle whose dimensions are 10 cm and 6 cm with a square of side length 5 cm inside it. Calculate: 1 the area of the shaded part. 2 the perimeter of the shaded part. 6 cm 5 cm 10 cm Drill 8: We knew that the square centimetre (cm2) is the area of a square of side length 1 cm. Use the same pattern to write mathematical statements to show the meaning of the following units of area. a the square metre (m2) is the area of a square of side length ……… (m2 = 1 m × 1 m) b The square kilometre (km2) is the area of …… whose side length …… (km2 = ……… × ………) c The square decimetre (dm2) is …… (dm2 = ……… × ………) Shorouk Press First Term 83 Drill 9: Lesson 1 youThe Use the relations got in Length the previous drill, and complete. a m2 = 1 m × 1 m = 100 cm × 100 cm = 10 000 cm2 b km2 = …… km × …… km = …… m × …… m = …… m2 2 c You dmknow = …… …… dm = …… …… cm …… cm2used thatdm the× centimetre (cm) cm and×metre (m)=are units From the previous, we deduce that: for measuring length. The square decimetre = 100 cm2 The metre (m) = 100 centimetres (cm) The square metre = 100 dm2 = 10 000 cm2 Drill 1: the square kilometre = 1 000 000 m2 Complete. a The metre …… the centimetre (< , > or =) Drill 10: b 3 metres = …… centimetres Choose the suitable unit to measure each of the following. 4 metres …… a c Area of the =floor of centimetres the room. (km2 , dm2 , cm21, cmm2) ……ofmetres = 700 centimetres b d Area the agricultural land in Egypt. (km2 , dm2 , cm2 , m2) ……ofmetres = 300ofcentimetres c e Area the surface a book page. (km2 , cm2 , m2) d Area of the playground of your school. (km2 , cm2 , m2 , dm2) The centimetre (cm) = 10 millimetres (mm) e Area of the eastern desert. (km2 , cm2 , dm2) Drill 2: complete. Drill 11: a 3 the centimetres = …… mm Choose closest answer. 2 cm …… a b Area of =the flatmm which I live in is …… c …… cm = 40 mm (75 km2 , 75 cm2 , 75 m2 , 75 dm2) ……ofcm 60 mm in our school is …… b d Area the=classroom e …… m = 400 cm = …… mm (24 m2 , 24 cm2 , 24 km2) the units4 of length ascendingly (cm , m , to mm) c f A Arrange pupil in Primary used his geometric instruments draw a …… , …… , …… rectangle whose area is …… (12 m2 , 12 dm2 , 12 cm2) Drill 3: d Area of the tile used in tilling our house is …… Choose the suitable unit to measure each of the following. (25 dm2 , 25 cm2 , 25 m2) a Thickness of an electric wire. (mm , cm , m) b Length of the classroom. (mm , cm , m) c Length of the playground. (mm , cm , m) d The height of a lamppost. (mm , cm , m) 84 74Mathematics for Primary Stage-Year 4 Shorouk Press Exercise 2 1 Put (✔) for the correct statement and (✗) for the incorrect one and correct the wrong statement. a The square metre (m2) is a unit of measurement used to measure the perimeters of figures. ( ) b The decimeter (dm) is a unit of measurement used to measure the areas of the figures. ( ) c The millimetres (mm) is a unit of measurement used to measure the lengths of the things. ( ) d Area of square = side length × 4 ( ) e Area of rectangle whose length is 2 dm and width 5 cm is 100 cm2. ( ) f Area of a square-shaped piece of land of side length 3 km is 9 million m2. ( ) 2 Complete. 3 a 3 cm = …… mm b 5 dm = …… cm c 2 km = …… m d 2 m = …… cm e 50 mm = …… cm f 850 cm = …… dm g 4 200 mm = …… dm h 8 000 cm = …… m i 6 000 m = …… km j 3 km = …… m b 7 m2 = …… cm2 Complete. a c e Shorouk Press 3 m2 = …… dm2 1 2 km2 = …… m2 90 000 cm2 = …… m2 2 2 m2 = dm ........ d 27 2 700 =dm …… m2 f 6 000 000 m2 = …… km2 First Term 85 4 Complete using a suitable sign <, >, or = in each Lesson a 3 km 1 c The 300 m 5 000 mm Length b 8 dm 5 metres d 7 km . 80 cm 75 000 cm e Area of square of side length 8 cm Area of rectangle You know that the centimetre (cm) and metre whose dimensions are 9 cm and 8 cm. (m) are units used for measuring length. f Area of rectangle whose dimensions are 3 dm and 7 cm The metre (m)length = 100half centimetres Area of square of side a metre. (cm) Drill 1: The figure opposite is a rectangle Complete. whose dimensions are 9 cm and 6 cm. a The metre …… the centimetre (< , > or =) 4 cm A square of side length 4 cm is cut b 3 metres = …… centimetres 3 cm 2 cm from it. Calculate: c 4 metres = …… centimetres 1 cm themetres area of=the remaining part by two different methods. d a …… 700 centimetres e b …… = 300 centimetres themetres perimeter of the remaining part. 6 cm 5 9 cm The centimetre (cm) = 10 millimetres (mm) 20 cmtimes its width. If its If its The length of a rectangle is three its width. 2 Drill 2: is 64 cm, find its area in cm . perimeter complete. 3 centimetres mm 7 a The perimeter of =a …… square is 28 cm, find its area. b 2 cm = …… mm cm of = 40 8 c If …… the sum themm perimeters of two squares is 48 cm, and the d side …… cm =of60 mm length one of them is 7 cm. Find: e a …… = 400 cm of = the ……second mm square. them side length f b Arrange the length ascendingly (cm , m , mm) the sum ofunits their of areas. …… , …… , …… 9 Drill A rectangle-shaped hall whose dimensions are 8 m and 6 m. 3: How many tiles areunit needed to tile this hall, that the side Choose the suitable to measure each of given the following. of the of required square-shaped is 20 cm? a length Thickness an electric wire. (mmtiles , cm , m) 6 b c d Length of the classroom. Length of the playground. The height of a lamppost. 86 74Mathematics for Primary Stage-Year 4 (mm , cm , m) (mm , cm , m) (mm , cm , m) Shorouk Press Unit 4 Activities Activity 1 1 cm In the figure opposite, 15 dots are arranged in the form of a lattice such 1 cm that the horizontal and vertical distances between every two adjacent dots, vertically or horizontally, are equal. Consider that the distance between every two adjacent points is 1 cm, then answer the following questions. a How many squares can be drawn such that the vertices of each coinside with these dots, and its area equals: i 1 cm2 ii 2 cm2 iii 4 cm2 b How many rectangles can be drawn such that the vertices of each coinside with these dots, and its perimeter equals: i 6 cm ii 8 cm iii 10 cm Activity 2 Notice and deduce. a Find the area of the coloured part and also its perimeter (consider that the side length of the small square is 1 cm). b If the previous figure is drawn three times, you will get the figure below. What is the area of this new figure? What is its perimeter? c If you imagine that we drew the original figure 20 times using the same previous way (on a large paper), what is the area of the resulted figure? What is its perimeter? Shorouk Press First Term 87 General Exercises on Unit 4 Lesson 1 The Length 1 Complete using a suitable sign <, >, or = in each . a 6 metres 650 cm b 10 dm 1 metre You that the25 centimetre metre (m)6are 1 2 2 c know km 000 m2 (cm) d and 81dm 400units cm2 used 2 for measuring length. 2 Choose the suitable unit(m) of measurement for each The metre = 100 centimetres (cm)of the following life situations. Drill 1: a Measuring the heights of the pupils. Complete. (square…… centimetre , millimetre , centimetre a The metre the centimetre (< , > ,orkilometre) =) Calculating areas of the walls in a house. b b 3 metres = …… centimetres (m , cm2 , km2 , m2) c 4 metres = …… centimetres 1 cm d c …… metres =the 700 centimetres Calculating perimeter of a piece of land allocated for e …… metres = 300 building a new citycentimetres in facing the problem of over-population. 2 (m , km , km , cm2) The centimetre (cm) = 10 millimetres (mm) d Calculating the distance between the earth and the moon. Drill 2: (cm , m , km , km ) 2 3 complete. Complete. a 3 centimetres = …… mm The=condition b a 2 cm …… mmof congruency of two squares is …… c b …… cmof=rectangle 40 mm = ………………………… and perimeter Area d …… cm = 60 mm of square = ………………………… e c …… m= 400 cm = of …… mm If the dimensions a rectangle are 8 cm and 5 cm, then f Arrange the units of length ascendingly (cm , m , mm) its area = ………………………… …… , …… , …… d If the perimeter of a square = 24 cm, then its area = ……… Drill 3: the suitable to measure each the40 following. 4 Choose The dimensions of unit a rectangle are 90 cmof and cm. If the a area Thickness of an electric wire. (mmof, acm , m) find the of the rectangle equals the area square b perimeter Length of (mm , cm , m) of the the classroom. square in decimeters. c Length of the playground. (mm , cm , m) d The height of a lamppost. (mm , cm , m) 88 74Mathematics for Primary Stage-Year 4 Shorouk Press GeneralExercises Exercises General Exercise11 Exercise Findthe theresult resultofofthe thefollowing. following. 1 1 Find 587692 692+ +401 401203 203= =…………… …………… a a 587 806735 735– –8 8805 805524 524= =…………… …………… b b 9 9806 867 000000 000 cc 3535867 d d 9 9000 954 278456 456 + + 8 8954 – –278 ………… …………… ………… …………… Completeusing usinga asuitable suitablesign sign<,<,>,>,oror= =inineach each . . 2 2 Complete a a 3 3× ×1515 9090÷ ÷2 2 b b 4 4× ×1313 3 3× ×1717 Measureofofthe theacute acuteangle angle Measure Measureofofthe theright rightangle. angle. c c Measure Measureofofthe thestraight straightangle angle Measureofofthe theobtuse obtuse d d Measure Measure angle. angle. Areaofofthe therectangle rectanglewhose whosedimensions dimensionsare are4 4cm cmand and e e Area cm Areaofofthe thesquare squareofofside sidelength length8 8cm. cm. 1515cm Area Joineach eachfigure figuretotothe thesuitable suitablename. name. 3 3 a a Join Rhombus Rhombus Trapezium Parallelogram Parallelogram Rectangle Rectangle Square Square Trapezium Findthe theH.C.F. H.C.F.and andL.C.M. L.C.M.forforthe thenumbers numbers6 6and and8.8. b b Find Drawthe thetriangle triangleABC ABCininwhich whichBC BC= =4 4cm, cm,m(∠B) m(∠B)= =70˚ 70˚and and 4 4 Draw m(∠C)= =50˚, 50˚,then thenanswer. answer. m(∠C) Withoutusing usingthe theprotractor, protractor,calculate calculatem(∠A). m(∠A). a a Without Whatisisthe thetype typeofof∆ABC ∆ABCwith withrespect respecttotothe themeasures measuresofof b b What angles. itsitsangles. Heshamhas hasLELE2020000, 000,hehebought boughta abedroom bedroomsuite suiteforforLELE8 8750 750 5 5 Hesham anda areception receptionsuite suiteforforLELE6 6250. 250.Find Findthe theremainder. remainder. and Shorouk Press First Term 89 89 Exercise Exercise2 2 1 1 Put ( () for thethe correct statement and ( )( for thethe incorrect oneone Put ) for correct statement and ) for incorrect and correct thethe wrong statement. and correct wrong statement. a a 549 467 + one hundred thousand = 559 467467 ( ( ) ) 549 467 + one hundred thousand = 559 bb 8 8 256 344 – three thousand = 8= 256 044044 ( ( ) ) 256 344 – three thousand 8 256 c c 906 ÷3 ( ( ) ) 906 ÷= 3 302 = 302 d d 6565 ×8 ( ( ) ) ×= 8 800 = 800 e e The sum of of measures of of angles of of a triangle = 180˚( The sum measures angles a triangle = 180˚( ) ) f f The L.C.M. forfor thethe two numbers 1212 and 30 30 is 60. The L.C.M. two numbers and is 60. ( ( ) ) 2 2 Complete using a suitable sign <, <, >, >, or or = in Complete using a suitable sign = each in each . . aa 4 4 × 16 100 ÷ 2÷ 2 × 16 100 bb 3 3 milliard 965 752 812 milliard 965 752 812 c c Area of of thethe square of of side length 3 dm of the Area square side length 3 dm Area Area of the rectangle whose dimensions areare 9090 cmcm andand 10 10 cm.cm. rectangle whose dimensions d d Perimeter of of a square of of side length 5 cm Perimeter Perimeter a square side length 5 cm Perimeter ofof anan equilateral triangle of of side length 7 cm. equilateral triangle side length 7 cm. e e Measure of of thethe straight angle Sum of the measures Measure straight angle Sum of the measures ofof the angles of of a triangle. the angles a triangle. 3 3 Find: L.C.M. forfor thethe twotwo numbers 6 and 8. 8. Find: a a thethe L.C.M. numbers 6 and b b thethe H.C.F. forfor thethe twotwo numbers 45 45 andand 60.60. H.C.F. numbers 4 4 Draw the triangle ABC, right-angled at at B where BCBC = 8=cm andand Draw the triangle ABC, right-angled B where 8 cm AB == 66 cm. Determine thethe mid-point MM of AC. AB cm. Determine mid-point of AC. 5 5 Join each figure to to thethe suitable name. Join each figure suitable name. Rhombus Rhombus 9090 Mathematics for Primary Stage-Year 4 Parallelogram Parallelogram Trapezium Trapezium Shorouk Press Exercise33 Exercise Complete. 1 1 Complete. 348475 475– –three threehundred hundredthousand thousand= =……… ……… a a 6565348 Thevalue valueofofthe thedigit digit4 4ininthe thenumber number546 546789 789= =……… ……… b b The TheL.C.M. L.C.M.forforthe thenumbers numbers4 4and and8 8isis……… ……… c c The TheH.C.F. H.C.F.forforthe thenumbers numbers6 6and and3030isis……… ……… d d The .......... Theside sidelength lengthofofa asquare squarewhose whoseperimeter perimeterisis3636cm cm= = e e The ……… ……… Completeusing usinga asuitable suitablesign sign<,<,>,>,oror= =inineach each . . 2 2 Complete 407805 805+ +9292716 716 500521 521– –1 1 a a 3 3407 3 3500 256× ×4 4 256× ×5 5 b b 256 256 600÷ ÷5 5 600÷ ÷4 4 c c 9 9600 9 9600 Perimeterofofa asquare squareofofside sidelength length2 2mm Perimeter d d Perimeter Perimeter rectanglewhose whosedimensions dimensionsare are2424dm dmand and1616dm. dm. ofofa arectangle Drawthe therectangle rectangleABCD ABCDininwhich whichBC BC= =4 4cm cmand andAB AB= =3 3cm. cm. 3 3 Draw DrawAC ACand andBD BDwhere whereMMisistheir theirpoint pointofofintersection. intersection. Draw Factorizeeach eachofofthe thetwo twonumbers numbers2424and and3030totoitsitsprime prime 4 4 Factorize factors,then thenfind: find: factors, theL.C.M. L.C.M.forfor2424and and30. 30. a a the theH.C.F. H.C.F.forfor2424and and30. 30. b b the Shorouk Press First Term 91 91 Exercise Exercise4 2 1 1 Complete. Put ( ) for the correct statement and ( ) for the incorrect one a and 3 287 correct 500the + 713 wrong 250statement. – 3 000 750 = ……… b a If 549 13 ×467 45 =+585, one then hundred thousand = 559 467 ( ) b 585 8 256 ÷ 45344 = …… – three and thousand 587 = 45 ×= 8…… 256+044 …… ( ) c c The 906 value ÷ 3 =of302 the digit 3 in the number 3 721 014 is ……( ) d d 4 65 × 765 × 8×=25 800 = …… ( ) e e (25 The × 8) sum – 150 of measures = …… of angles of a triangle = 180˚( ) f The L.C.M. for the two numbers 12 and 30 is 60. ( ) 2 Put (✔) for the correct statement and (✗) for the incorrect one correct the wrong statement. 2 and Complete using a suitable sign <, >, or = in each . a a If 4 ABC × 16 is a triangle 100 ÷in2 which m(∠A) = 70° and b m(∠B) 3 milliard = 20°, then965 it is 752 an acute-angled 812 triangle. ( ) b c The Area square of theis square a quadrilateral of side length in which 3 dm all angles Area are of right the and rectangle all sideswhose are equal dimensions in length.are 90 cm and 10 cm. ( ) c d The Perimeter rectangle ofisa asquare quadrilateral of side in length which5 all cmangles Perimeter are right. of an equilateral triangle of side length 7 cm. ( ) d e InMeasure a parallelogram, of the straight every two angle opposite Sum sidesofare thenot measures parallel. of the angles of a triangle. ( ) 3 3 Complete: Find: a the L.C.M. for the two numbers 6 and 8. a The number b the105 H.C.F. is divisible for the by two...numbers and also45 divisible and 60. by... b The H.C.F. of 16 and 24 = …… 4 c Draw Thethe L.C.M. triangle of 14ABC, and 10 right-angled = …… at B where BC = 8 cm and d ABThe = 6factors cm. Determine of 45 are the ……mid-point M of AC. 1 e 4 a day = …… hours 5 Join each figure to the suitable name. Rhombus 90 Mathematics for Primary Stage-Year 4 92 Parallelogram Trapezium Shorouk Press Exercise35 Exercise Choose the correct answer. 1 1 Complete. 251 475 309 –+ three 748 691 = ……thousand = ……… a a 657 348 hundred milliard , 8546 million thousand) b The value of the digit 4 in(8the number 789 ,= 8……… 5 000 000 for – 324 = …… c b The L.C.M. the 067 numbers 4 and 8 is ……… (95 3246076 91is675 933 , 4 675 933) d The H.C.F. for the numbers and, 30 ……… 8 ×side 641 length × 125 of = ... e c The a square whose perimeter is 36 cm = ..... (641 thousand , 641 hundred , 641 million) ……… d The number 2 100 is divisible by …… (35 , 11 , 13 , 17) e XYZ using is a triangle in which m(∠X) and m (∠Y) = 30°, 2 Complete a suitable sign <, >, or == 40° in each . ∆XYZ is …… a 3 then 407 805 + 92 716 triangle.3 500 521 – 1 (a right-angled , an obtuse-angled , an acute-angled) b 256 × 4 256 × 5 f The L.C.M. of 15 and 35 is …… (15 , 105 , 35 , 5) c 9 600 ÷ 5 9 600 ÷ 4 Perimeter of a square of sideside length 2 m3 cm. Join Perimeter 2 d Draw the square XYZL whose length its of a rectangle whose dimensions are 24 dm and 16 dm. diagonals XZ and YL. 3 3 Draw the rectangle in which BC …… = 4 cm and AB = 3 cm. a Multiples of 6 ABCD are ……, …… and Draw AC and BD where Mare is their intersection. b Prime factors of 350 ……,point ……ofand …… c The perimeter of a rectangle whose dimensions are 7 cm 4 Factorize two numbers 24 and=30 to its and each 11 cmof=the ………………………… …… cmprime factors, then find:of 18 and 30 is …… d The H.C.F. a e the14 L.C.M. for=24 andhours 30. = …… minutes. of a day …… b the H.C.F. for 24 and 30. 4 a Calculate 2 106 425 + 894 075 – 3 000 500. b Find the number that if subtracted from 256 412 307, then the remainder will be 255 million. Shorouk Press First Term 93 91 General revision on the Mathematics syllabus for Fourth form Primary - for the first term 1 Complete each of the following : 1. The Smallest 7-digit number is ............ 2. The Smallest different 6-digit number is ............ 3. The greatest 7-digit number is ............ 4. The greatest 5-digit number is ............ 5. The million is the smallest number formed from ............ digits. 6. Without repeating digits , the greatest number formed from the digits : 0 , 3 , 2 , 5 , 1 , 6 is ............ 7. Ten million is the smallest number formed from ............ digits. 8. 49 × 830 = ............ In the Exercises (9 → 15) , the place value of the digit 9. 6 in the number 2641 ............ 10. 4 in the number 54678 ............ 11. 2 in the number 762618 ............ 12. 8 in the number 73985241 ............ 13. 7 in the number 54365724 ............ 14. 5 in the number 135649728 ............ 15. 3 in the number 2834571 ............ 16. Rewrite the following numbers using the digits : (a) 2 million , 37 thousand , 9 (b) 24 million , 35 thousand , 47 (c) 4 million , 7 thousand , 706 (d) 5 million , one thousand (e) 4 million , five hundred and thirty eight. (f) 45 million , 30 thousand , 99 (g) 32 million , 8 thousand , 15 (h) 6 million , 727 thousand , 704 (j) 71 million , 354 thousand , 12 17. 350 tens = ............ hundreds. 18. 15 0000 = ............ hundreds. 19. 3092000 = ............ million , ............ thousand. 20. 342 million = ............ thousand. 21. 240 thousand = ............ hundreds = ............ 22. L.C.M of the numbers 36 , 24 and 12 is ............ 94 Mathematics for Primary Stage-Year 4 Shorouk Press 23. H.C.F of the numbers 35 , 42 and 28 is ............ Exercise 5 1 2 3 4 24. The greatest number formed from the digits 5 , 8 , 4 , and 9 is ............ 25. The place of the answer. digit 3 in the number 8 376 542 is ............ Choose thevalue correct prime numbers that are included between 2 , 30 is ............ a 26.7The 251 309 + 748 691 = …… 27. The prime numbers that lie between and 10 is ............ (86 milliard , 8 million , 8 thousand) number prime067 factors 2 , 3 and 5 is ............ b 28.5The 000 000whose – 324 = are …… , 552324 , 175076 , 577 ,, 546 29. From the numbers 865 , 570(95 91 675 933 , 4 675 933) Complete the following : c 8 × 641 × 125 = ... (a) Numbers that are divisible by 2 are ............ (641 thousand , 641 hundred , 641 million) (b) Numbers that are divisible 5 are ............ d The number 2 100 is by divisible by …… (35 , 11 , 13 , 17) (c) Numbers that are divisible 10 are ............ e2 XYZ is a triangle in which m(∠X) = 40° and m (∠Y) = 30°, Choose the correct answer : ∆XYZ issmallest …… number triangle. 1.then The million is the formed from ............ digits. a. 3 (a right-angled , an b. 7 obtuse-angled , anc.acute-angled) 4 f 2.The L.C.M. of 15 and 35inisthe…… (15is ............ , 105 , 35 , 5) The digit which represents million number 46835714 a. 6 b. 8 c. 3 Draw XYZL whose side length 3 cm. Join its 3. 50the × 40 square = ............ hundreds. a. 2 b. 200 c. 2000 diagonals XZ and YL. 4. 805 × 100 = ............ × 10 a. 85 8050 Multiples of 6 are ……,b.…… c. 250 and …… ............ 28 hundreds. 5.Prime 280 tens factors of 350 are ……, …… and …… a. > b. < c. = The perimeter of a rectangle whose dimensions are 7 cm 6. The value of the digit 8 in the number 587627 is ............ and 11 cm = ………………………… = …… cm a. 80 000 b. 800 000 c. 8000 d 7.The H.C.F.= of 18 and 30 is …… ............ 150 thousands 1 e 4a. 150 of a day = …… hours =thousands …… minutes. c. 1500 hundreds tens b. 15 a b c a b 8. Three millions , three thousands and three is ............ Calculate 2 106 425 b.+ 30 894 a. 300 3003 300 075 – 3 000 500. c. 3030 ............256 412 307, then 9.Find The value the digit 7 in the number 40735126 isfrom theofnumber that if subtracted a. 7 million b. 70 million. thousand c. 700 thousand the remainder will be 255 10. 71 million , 354 thousand and 12 a. 71354120 b. 7135412 11. 365274 ............ 359876 a. > 12. 30 × 40 ............ 20 × 60 a. < 13. 6934 + 3359 = ............ Shorouk Press c. 71354012 b. < c. = b. > c. = First Term 95 93 a. 12093 14. 5 million ............ 500 000 a. < b. 10293 c. 20193 b. > c. = 15. The value of the digit 8 in the number 1096835 is ............ a. 8 b. 800 16. ............ is one of the factors of the number 8 a. 16 b. 4 17. 70 × 20 = 14 × ............ a. 10 18. 40 × 500 ............ 20 × 10 a. > c. 8000 c. 20 b. 100 c. 1000 b. = c. < 19. The numbers 1 , 5 , 7 are ............ a. even b. odd 20. 54 is a number that is divisible by ............ a. 4 b. 6 21. The number ............ is divisible by 5 a. 495 b. 594 c. prime c. 7 c. 54 3 Find the result of each of the following : a. 879156 + 498068 = ............ b. 608467 - 129585 = ............ c. 2525 ÷ 25 = ............ d. 4803 × 67 = ............ e. 471564 + 126469 = ............ f. 738594 – 153037 = ............ 4 Solve the following problems : 1. Factorize the number 120 to its prime factors. 2. Underline the numbers that are divisible by 2 and 3 , 1926 – 3431 – 3330 – 2112 – 1064 3. In a certain year the profit of one factory was L.E. 7316 , if the profit is distributed equally among 31 workers , find the share of each worker 4. Find the result of 502 × 6 , 502 × 90 , then deduce the product of 502 × 96 5. Find a prime number lies between 11 and 37 6. Find L.C.M , H.C.F for the numbers 12 and 15 7. A hotel contains 204 rooms divided equally by a number of floors , each floor contains 17 rooms. How many floors are there in this hotel ? 8. Draw D ABC right at B , where BC = 4 cm. , AB = 3 cm. , Write the type of this triangle according to its side lengths. 9. Using the geometric instruments - Draw D XYZ in which XY = 7 cm. , YZ = 5 cm. 96 Mathematics for Primary Stage-Year 4 (2015 - 2016) Shorouk Press ,m( 2 3 5 Put the suitable relation (< , > or =) : ............ 652 × 5 1. 652 × 4 square Draw the XYZL whose side length 3 cm. Join its 2. The area of a square of side length 6 ............ the area of rectangle whose dimensions diagonals XZ , and YL. a b c d e 4 4 cm 5 cm 1 Exercise 5 XYZ) = 40° 10. If the sum of two perimeters of two squares is 88 cm. and if the side length of one of , then find : the two squares is 12 cm. Choose the correct answer. (a) The side length of the other square. a 7(b)251 309 + 748 691 = …… The difference between the areas of the two squares. , 8 thousand) , ( milliard 11. Draw D ABC in which AB = 5 cm.(8 B) = 90° ,,BC8=million 5 cm. , then complete : ............ b 5(a)000 000 – 324 067 = …… AC = cm. (b) The perimeter of D ABC(95 = ............ 324cm. 076 , 91 675 933 , 4 675 933) (c) The type of the D ABC according to its side lengths is ............ c 8 × 641 × 125 = ... (d) The type of the D ABC according to the measures of its angles is ............ (641 thousand , 641 hundred , 641 million) 12. Draw the square ABCD of side length 4 cm. , Join its diagonals AC , BD to intersect d The 2 of 100 is divisible , 17) at M ,number Find the area the square ABCD by …… (35 , 11 , 613 cm e 13.XYZ is a triangle in which m(∠X) = 40° and m (∠Y) = 30°, The opposite figure : Shows∆XYZ a rectangle another one. then is drawn ……inside triangle. (a) Find area of the shaded (atheright-angled , part. an obtuse-angled , an acute-angled) (b) Find the difference between the perimeters of the two rectangles f The L.C.M. of 15 and 35 is …… (15 , 105 ,5 cm 35 , 5) are 4 cm. 6 cm. 3. 12 500 ÷ 5 ............ 10 × 25 Multiples of 6 are ……, …… and …… 4. 678345 ............ 578344 + 100 000 factors of 350angle are............ ……, ……of the angle of a 5.Prime The measure of the straight the…… sum ofand the measure triangle. The perimeter of a rectangle whose dimensions are 7 cm 6.and The measure the………………………… right angle ............ the measure of=the obtusecm angle. 11 cmof = …… 7. 2 0000 ÷ 4 ............ 2 000 ÷ 4 Theperimeter H.C.F.ofof 18 and 30 is …… 8. The a square of side length 6 cm. ............ The perimeter of an 1 of a day = …… = …… minutes. triangle of side hours length 7 cm. 4equilateral ............ 9. 4 milliard 40 × 1000 000 a 10.Calculate 425 + 894 075 – 3 000 500. 6 × 15 ............ 902÷ 106 2 ............ 40 that 6 × 4 milliard × 1000if000 b 11. Find the number subtracted from 256 412 307, then 12. 6 × 70 × 10 ............ 5 tens × 100 the remainder will be 255 million. ............ 13. 200 – 120 160 ÷ 2 2 ............ 14. 800 dm . 8 m2. 15. 3 meters , 5 centimeters ............ 350 cm. 16. The value of the digit 4 in the number 94876 ............ the value of the digit 8 in the number 94876. 6 Choose the correct answer : 1. The numbers 2 Shorouk Press , 3 , 5 , 7 are called ............ numbers. ( prime – odd – even ) First Term 97 93 ( 45 – 90 – 150 ) 2. The measure of any angle of a square equals ............ 3. The two perpendicular straight lines form 4 ............ angles. 4. The number of the factors of the prime number is 5. The number ............ is a prime number. ( a cute – right – obtuse ) ............ ( one – two – three ) ( 15 – 17 – 21 ) 6. Number of sides of any polygon does not equal number of its ............ ( diagonals – angles – vertices ) 7. If the perimeter of an equilateral triangle is 12 cm. , then its side length is ............ cm. ( 3 – 36 – 4 ) 8. 3 1 km. = ............ m. 2 ( 35 – 3500 – 350 ) 9. L.C.M for the numbers 8 , 12 is ............ ( 24 – 48 – 4 ) 10. The value of the digit 3 in the number 736542 is ............ ( thousands – ten thousands – hundred thousands – millions ) 11. The number ............ is divisible by each of 2 and 5. 12. The prime number after the number 399 is ............ ( 72 – 25 – 100 ) ( 400 – 401 – 403 ) 13. The diagonals of the square are ............ ( equal in length and not perpendicular – perpendicular but not equal in length – equal in length and perpendicular) 98 Mathematics for Primary Stage-Year 4 Shorouk Press Exercise Model (1) 5 1 Complete each of the following : 1 , 45 million , 473 thousand is written in digits as ............ 1. The number 3 milliardanswer. Choose the correct prime number whose sum = of its factors 6 is ............ a 2.7The 251 309 + 748 691 …… 3. The prime number has only ............ (8factors. milliard , 8 million , 8 thousand) 1 . 5. of a day = ............ hour. m2. ............ b 4.53 000 000 dm – 2324 067 = …… 3 (95 324 076 , 91 675 933 , 4 675 933) dimension of a=door c 6.8If×the641 × 125 ... in the form of a rectangle are 180 cm. , 10 dm. , then its perimeter = ............ cm. (641 thousand , 641 hundred , 641 million) d2 Choose The the number 2 100: is divisible by …… (35 , 11 , 13 , 17) correct answer ............ The number is a common multiple m(∠X) for the two=numbers e 1.XYZ is a 15 triangle in which 40° and m (∠Y) = 30°, a. 2,5 b. 3,4 c. 5,3 then ∆XYZ is …… triangle. 2. The diagonals are equal in length in ............ (a right-angled , an obtuse-angled , an acute-angled) a. square and rectangle b. parallelogram and rectangle f The L.C.M. 15 and 35 is (15 , 105 , 35 , 5) c. rectangle and of rhombus d. square and…… rhombus 2 Drawa.the square XYZLb.whose thousand million side length c. tens 3 cm. Join its diagonals XZthousands and YL. d. hundred 3 3. The value of the digit 5 in the number 5612816 is ............ a b c 4. ............ is a common multiple for all numbers Multiples of 6 are ……, a. zero b. 1 …… and c.…… 10 d. 100 ............ 5.Prime The milliard is the smallest formed from factors of 350number are ……, …… anddigits. …… a. 7 perimeter of a b. 8 c. 9 dimensions d. 10 The rectangle whose 6. The perimeter of a square whose area 36 cm2. is ............ are 7 cm and 11 cm = ………………………… = …… cm a. 24 cm. b. 144 cm. c. 1296 cm. d. 72 cm. d The H.C.F. of 18 and 30 is …… 1 the result of each of the following : 3 e Find hours = …… minutes. 4 of a day = …… ............ ............ 4 a 4 b (a) 8752013 + 439815 = (c) 436 × 59 = ............ Calculate (b) 7256312 – 7056300 = (d) 15408 ÷ 36 = ............ 2 106 425 + 894 075 – 3 000 500. (a) Factorize the two numbers 24 , 30 to their prime factors , then find Find the number that if subtracted from 256 412 307, 1. H.C.F 2. L.C.M the remainder willABbe= 6255 (b) Draw D ABC in which cm. ,million. m ( B) = 60° , BC = 4 cm. , then 1. By using the ruler find the length of AC 2. State the type of D ABC according to its side lengths. then 5 (a) Find the greatest and the smallest number formed from 6 digits using the following using the following digits : 7 , 0 , 2 , 5 , 9 , 4 then Calculate the difference between them. (b) Eman bought 24 meters of cloth for L.E. 648 find the price of one metere. Shorouk Press First Term 99 93 1 Complete each of the following : Model (2) 1. The smallest number formed from 7 digits from the digits 5 , 8 , 4 , 7 , 0 , 2 , 3 is ............ 2. The area of the square whose side length 5 cm. is ............ 3. The value of the digit 3 in the number 3721014 is ............ 4. The value of the digit 3 in the number 3721014 is ............ 5. The two diagonals are equal in length in ............ , ............ 6. If the dimension of a door in the form of a rectangle are 180 cm. , 10 dm. , then its perimeter = ............ cm. 2 Choose the correct answer : 1. L.C.M for the numbers 20 and 12 is ............ ( 2 or 4 or 30 or 60 ) ............ 2. The smallest prime number is ( 1 or 2 or 3 or 5 ) 510309 + 7489691 = ............ ( 8 milliards or 8 millions or 8 thousands or 8 hundreds ) 3. 7251309 4. If 45 × 13 = 585 , then 589 = 45 × 13 + ............ ( 2 or 4 or 30 or 60 ) 5. If the perimeter of a square is 28 cm. , then its side length is ............ ( 7 or 14 or 4 or 12 ) 6. A rectangle , its dimensions are 3 cm. , 7 cm. then its perimeter = ............ ( 7 or 17 or 20 or 40 ) 3 Complete using (< , > or =) : 1. 4 cm2. ............ 400 cm2. 3. 5 km. ............ 500 m. 5. 3 × 14 ............ 90 ÷ 2 2. 8 dm. ............ 80 cm. 4. 300 ............ 3 milliard 6. 1 of a day ............ 12 hours. 6 4 (a) Draw D ABC in which AB = 7 cm. , m ( A) = 45° , m ( C) = 75° , Find the area of the shaded part (b) In a school if 756 pupils are distributed equally on 18 classes. Find number of pupils in each class 8 cm 5 (a) In the opposite figure : 6 cm Find m ( B). Write the type of the triangle according to the measure of its angles. (b) Find H.C.F , L.C.M for 24 and 30 6 cm 9 cm 100 Mathematics for Primary Stage-Year 4 Shorouk Press Exercise Exercise Model (3) (3)5 5 Model 1 Choose the correct answer : : 1 Choose the correct answer , five , five Ten million hundred seventy two two thousand = ............ 1. Ten million hundred seventy thousand = ............ 1 11. Choose the correct answer. Choose the correct answer. ( 10507200 or 10510072 or 105721 or 10572000 ) ) 10507200 or 10510072 or 105721 or 10572000 a a7 251 309 + 748 691 = (…… 7 251 309 + 748 691 = …… , , ............ , , ............ 2. The triangle whose length of itsofsides 3 cm. 7 cm. and and 5 cm. is is 2. The triangle whose length its sides 3 cm. 7 cm. 5 cm. (8 milliard , 8 million ,or 8isosceles (8 milliard , 8 million , thousand) 8 triangle thousand) ( scalene triangle or equilateral triangle or isosceles ) ) ( scalene triangle or equilateral triangle triangle b The 000 000 –is324 =multiples …… ............ b5The 5number 000 000 –is324 067 =multiples …… ............ 3. number the common of all ( 0 (or0 2oror2 3oror3 1or) 1 ) 3. the067 common ofnumbers. all numbers. ............ ............ (95 324 076 ,in 91 675 933 , 4, 675 933) 4. The geometric figure which its four sides equal in length called (95 324 076 , is91 933 4 675 933) 4. The geometric figure which its four sides equal length is675 called ( trapezium or parallelogram or rhombus ) ( trapezium or parallelogram or rhombus ) c c8 ×8641 × 125 = ... × 641 × 125 = ... ............ 5. The number is divisible by 3by 3 (hundred 28( or 24 5. The number ............ is(641 divisible 28 13 or or 13 or 17 or )million) 24 ) thousand , 641 , 17 641 million) (641 thousand , 641 hundred , or 641 ............ 6. L.C.M of 16 20 is20 is ............ ( 80( or 6. L.C.M ofand 16 and 80 40 or or 40 20 or or 20 10 or )10 ) d dThe number 2 100 is divisible by by …… (35(35 , 11 , 13 , 17) The number 2 100 is divisible …… , 11 , 13 , 17) 2 Complete the following : : 2 Complete the following e XYZ isis ais triangle in which m(∠X) = 40° and m (∠Y) = 30°, e XYZ athetriangle informed which m(∠X) = 40° and m (∠Y) = 30°, ............ ............ 1. The million the number fromfrom digits. 1. The million is smallest smallest number formed digits. then is …… triangle. ∆XYZ is............, …… triangle. ,1621∆XYZ ............, ,,2126 ,............, ............, ............, 16,then complete in same pattern. 2. 112.,11 26 ............, complete in same pattern. (a right-angled , an obtuse-angled , an acute-angled) (a right-angled , an obtuse-angled , an acute-angled) ............ ............ 3. The value of the 4 in4the 5467813 is is 3. The value of digit the digit in number the number 5467813 f f4.The L.C.M. ofeach 15 and 35 is …… (15(15 , 105 , 35 , 5) L.C.M. of two 15 and 35 is............ …… , 105 , 35 , 5) ............ in length. In4.aThe rectangle each two opposite sides are in length. In a rectangle opposite sides are , 6 ,cmits,perimeter 6 cm = ............ 5. The rectangle whose dimensions are 8are cm8 ,cm its perimeter = ............ 5. The rectangle whose dimensions 2 2Draw thethe square XYZL whose side length 3 cm. Join its its Draw square XYZL side length 3 cm. Join ............ ............ 6. H.C.F of two numbers 12 and 16whose equals 6. H.C.F of two numbers 12 and 16 equals diagonals XZXZ and YL.YL. diagonals and , , <=)or: =) : 3 (a) the suitable signsign (> (> < or 3 Put (a) Put the suitable 1. 3 1. milliard 475956432 3 milliard 475956432 3 3a aMultiples of 6 are ……, …… and …… Multiples of 6 are ……, …… and …… ............ ............ 2. 7423856 – 5018738 2415117 2. 7423856 – 5018738 2415117 b bPrime factors of 350 areare ……, …… and …… factors of m. 350 ……, …… and …… ............ ............ 3. 3Prime km. 3000 m. 3. 3 km. 3000 c cThe perimeter of a whose dimensions areare 7 cm The perimeter ofrectangle a rectangle whose dimensions 7 cm (b) Put (✓) (✓) in front of the statement or (✗) of the one one : : (b) Put in front of correct the correct statement or in (✗)front in front of incorrect the incorrect and 11 11 cm = ………………………… = …… cmcm cm ==………………………… = …… 1. and 345962 + 154048 50000 ( () ) 1. 345962 + 154048 = 50000 d dThe H.C.F. of 18 and 30 is …… 2. The The two parallel lines never intersect each other. ( () ) H.C.F. of lines 18 and 30 is …… 2. The two parallel never intersect each other. 13. L.C.M 13. L.C.M , , of 12 30 is 60 ( () ) 30 is hours 60 e e 4 of a dayof=12…… = …… minutes. 4 of a day = …… hours = …… minutes. ............ ............ , find, find 4 1.4 The perimeter of aof square is 32iscm. its area. 1. The perimeter a square 32 cm. its area. Calculate 487 487 × 25 4 4a a2.Calculate 2×106 425 + 894 075 – 3–000 500. 2.Calculate Calculate 25 2 106 425 + 894 075 3 000 500. , subtracted , mfrom , determine b5 b the that subtracted 412 307, then ,( m256 , determine (a) Draw D ABC innumber which AC =that 6if= cm. m ,( mA) C) =C) 65° the the 307, then 5Find (a)Find Draw Dnumber ABC in which AC 6ifcm. ( =A)40° =from 40° ( 256 = 412 65° the type of this triangle according to the of itsofangles. type of this triangle according to measures the measures its angles. the remainder will be be 255 million. the remainder will 255 million. , if the , if price (b) Hazem bought 26 books fromfrom the book fair fair of series animal world of of (b) Hazem bought 26 books the book of series animal world the price one one bookbook is P.T FindFind out the that that Hazem Paid.Paid. is 725. P.T 725. out money the money Hazem Shorouk Press 101 93 101 93 First Term Model (4) 1 Complete the following : 1. The smallest number formed from 8 digits is ............ 2. The value of the digit 8 in the number 147385 is ............ 3. 59 million , 42 thousand , 63 = ............ 4. The H.C.F for 12 , 30 is ............ 5. The sum of the measures of the interior angles of a triangle is ............ 6. The multiples of the number 6 that included between 30 , 45 is ............ 2 Put the suitable relation (< , > or =) : 1. 360 cm. ............ 6 m 3. 7200 ÷ 3 ............ 60 × 40 5. 3 milliard ............ 965752812 2. 356705 + 3622195 ............ 8 million. 4. 75 thousand ............ 750 hundred 6. 83 dm2. ............ 840 cm2. 3 Complete the following : 1. 50 × 600 = ............ tens. 2. The factors of the number 8 is ............ 3. The triangle whose side lengths are different is called ............ 4. L.C.M of the two numbers 24 and 18 is ............ 5. The diagonals of the rectangle are ............ , ............ 6. Number of vertices in the hexagon is ............ 4 (a) Draw D ABC , where AB = AC , m ( B) = 60° , then find : 1. Length of AC 2. Perimeter of D ABC 3. Type of this triangle according to the lengths of its sides. (b) In a school if 798 pupils are distributed equally among 19 classes. Find the number of pupils in each class 5 (a) Find the result of : 1. 17620 + 5356 = ............ 2. 267 × 18 = ............ (b) Reda bought a T.V. set by L.E 4420 , he paid L.E 500 in cash , then he paid the rest in 28 equal installments. Find the value of each installment. 102 Mathematics for Primary Stage-Year 4 Shorouk Press Model (5) 5 Exercise 1 2 3 4 1 Complete the following : 1. The rectangle is a parallelogram Choose the correct answer.in which its angles ............ 2 ............ 2 2 dm309 == ............. m .m .691 = …… a 2.75600 251 + 748 numbers. , 8 million , 8 thousand) 3. ............ is the common multiple for(8allmilliard × ............ perimeter square = ............ b 4.5The 000 000 of – the 324 067 = …… 5. The number 3 million , 132(95 thousand in digits is ............ 324, 81 076 , 91 675 933 , 4 675 933) ............ digit=3 ... in the number 21538006 is c 6.8The × value 641 of× the 125 2 Choose the correct answer (641 : thousand , 641 hundred , 641 million) ............ , is divisible2by100 2 3 is divisible by …… (35 , ( 11 10 or ) d 1.The number , 18 13or, 21 17) ............ 32605108 23511998 > or < or = ) e 2.XYZ is a triangle in which m(∠X) = 40° and m( (∠Y) = 30°, ............ are divisible by 2 ( odd or even or prime ) 3. All the then ∆XYZnumbers is …… triangle. , ............ 4. The H.C.F of 8 12 is ( 2 or 4 or 8 ) (a right-angled , an obtuse-angled , an acute-angled) 5. 25 × 7 × 4 = ............ is divisible by 3 ( 36 or 700 or 179 ) f 6.The L.C.M. of side 15lengths and 35 (15 , 105 , 35 , 5) ............ The triangle whose 6 cm.isis…… ( scalene triangle or equilateral triangle or isoscles triangle ) Draw the square XYZL whose side length 3 cm. Join its 3 Complete the following : diagonals XZofand YL. of the prime number is ............ 1. The number the factors a b c 2. The diagonals of the parallelogram ............ each other. …… and …… factors of angles 350 of are ……,are…… and …… , then 64 this triangle is ............ 4.Prime If the measures of two a triangle 62° , 81° angledperimeter triangle. The of a rectangle whose dimensions are 7 cm 5.and 2418011 ÷ 60cm = ............ = ………………………… = …… cm d4 (1)The FindH.C.F. the result of of :18 and 30 is …… 1 ............ = …… minutes. e 4(a)of5034567 a day+ 3203456 = ……= hours a b ofmillion 6 are= ............ ……, 3.Multiples 2565178 – one (b) 893756 – 431877 = ............ (c) 235 × 85 = ............ Calculate 2 106 425 + 894 075 – 3 000 500. (2) A hotel contains 192 rooms divided equally by a number of floors , each floor Find the number that if subtracted from 256 412 307, then contains 16 room How many floors are there in this hotel ? the remainder will be 255 million. 5 1. Find H.C.F , L.C.M of the numbers 28 and 42 2. Rectangle its dimensions are 9 cm. , 12 cm. Find : (a) Its area (b) Its perimerter. Shorouk Press First Term 103 93 Model (6) 1 Find the result of each of the following : (a) 70070 ÷ 35 = ............ (c) 123 × 15 = ............ 2 Choose the correct answer : (b) 35859 + 7936 = ............ (d) 90000 – 78456 = ............ 1. Hundred thousand and three hundred seventy five is ............ ( 10315 or 100375 or 1375 ) 2. The greatest number formed from the digits 4 , 1 , 5 , 3 , 2 and 9 is ............ ( 45321 or 123459 or 954321 ) ............ 3. The smallest prime number is ( 1 or 0 or 2 ) ............ 4. The value of the digit 4 in the number 546789 is ( 40000 or 4000 or 400000 ) 5. The perimeter of square whose side length 3 cm. = ............ ( 9 cm. or 6 cm. or 12 cm. ) 6. 105 is divisible by ............ 3 (a) Complete the following : , 3oror{55, 2} , 2 oror{55,,3}3 ) ( {2( 2, 3} 1. The number which has only two factors is called ............ 2. The diagonals of the rectangle ............ in length. 3. 5 dm. = ............ cm. (b) A number if it is divided by 11 the quotient is 488 and remainder 4 , what is this number ? 4 Complete the following : 1. H.C.F for the two numbers 18 , 30 is ............ 2. L.C.M. for the two numbers 7 , 3 is ............ 3. The polygon of 5 sides is called ............ 4. The measure of the right angle = ............ ° 5. 4 × 25 ............ 100 ÷ 2 (by using > , < or =) 6. 5348475 – 3 hundred thousand 5 (a) Draw D XYZ in which XY = 5 cm. , m ( X) = m ( Y) = 45° , find 1. Measure Z 2. What is the type of D XYZ according to the measures of its angles. (b) In the opposite figure : the outer shape is a square of side length 4 cm and the inner shape is a rectangle of dimensions 3 cm. , 2 cm. 2 cm Find the area of the shaded part , 3 cm 5 cm 104 Mathematics for Primary Stage-Year 4 Shorouk Press Model (7)5 Exercise 1 2 3 1 Complete the following : , 35 thousand , 15 = ............ 1. 94 million Choose the correct answer. The value of the digit 3 in the number 3721014 = ............ a 72. 251 309 + 748 691 = …… 3. The H.C.F of the two numbers 16 and 24 = ............ (8 milliard , 8 million , 8 thousand) 4. The L.C.M of t he two numbers 14 , 10 = ............ b 55. 000 – hundred 324 067 = …… 465276000 + three thousand = ............ (95square 324whose 076perimeter , 91 675 , 4 675 933) 6. The length of the side of the 36 cm933 =............ c 2 8Choose × 641 125answer = ... : the × correct , 641ormillion) ............thousand , 641( hundred 1. 950000 – 324067 =(641 324076 or 625933 675933 ) ............ 2. The number 2100 is divisible by ( 7 or 11 13 ) d The number 2 100 is divisible by …… (35 , 11 , 13 ,or17) 3. D XYZ in which m ( in X) =which 40° , m m(∠X) ( Y) = 30° then Dand XYZ is e XYZ is a triangle =, 40° m............ (∠Y) = 30°, ( acute angled triangle or right angled triangle or obtuse angled triangle ) then ∆XYZ is …… triangle. 4. The number 108 is divisible by the two prime numbers 3 , ............ ( 5 or 7 or 2 ) right-angled , number an obtuse-angled , an acute-angled) ............ is prime 5. The (a number . ( 6 or 8 or 2 ) ............ f The …… (15hundred , 105or, 641 35million , 5) ) 6. 8 × L.C.M. 641 × 125 of = 15 and 35 is ( 641 thousand or 641 3 Put (✓) in front of the correct statement or (✗) in front of the incorrect one : Draw1. the 4816 square ÷ 4 = 124 XYZL whose side length 3 cm. Join its , if mYL. 2. In the XZ D ABC ( B) = 105° , then it is possible to be an obtuse angled diagonals and a b c d e 4 a b triangle. 3. The squareof metre (m2.) is……, used for measuring perimeters of the shapes. Multiples 6 are …… andthe …… 4. The two parallel straight lines never intersect each other Prime factors of 350 are ……, …… and …… 5. The area of the square = side × side The of sides a rectangle whose dimensions are 6. In aperimeter rhombus , all the are equal in length 11 cm = ………………………… 4 and 1. Find the quotient of 19836 ÷ 6 5 7 ( ) ( ( ( ( cm ( ) ) ) ) ) = …… cm (without using the calculator) The 30(5is× 4…… 2. FindH.C.F. L.C.M ofof the18 two and numbers × 11) , (5 × 6 × 11) 1 of atheday = …… hours = BC …… minutes. , AB = 3 cm. 1. rectangle ABCD in which = 4 cm. 4 Draw draw AC intersects BD at M , its+width , Calculate its perimeter Calculate 2 106 425 894equals 075half – 3its000 2. A rectangular piece of land length500. if itsthe width = 24 metre. Find number that if subtracted from 256 412 307, then the remainder will be 255 million. Shorouk Press First Term 105 93 1 Complete the following : Model (8) 1. 7288316 – 6 million = ............ 2. The value of the digit 4 in the number 354267198 = ............ 3. The L.C.M for two numbers 12 , 16 is ............ 4. 4 × 765 × 25 = ............ 5. In D ABC , m ( A) = 60° , m ( B) = 70° , m ( C) = ............ ° 2 Put the suitable relation (> , < or =) : 1. 3407805 + 3592195 = ............ 7 hundred thousand. 2. 3 m2. ............ 30000 cm2. 3. 9200 ÷ 4 ............ 60 × 40 4. The perimeter of a square whose side length 4 cm. ............ the perimeter of a rectangle whose dimensions 35 dm. , 45 dm. 3 1. Find the H.C.F for the two numbers 54,72 2. Arrange the following numbers in an ascending order : 41328 , 43182 , 42138 , 42138 , 42183 4 1. Find the smallest number divisible by 2 , 3 , and 5 2. Which is greater ? The area of the square of side length 6 cm. or the area of the rectangle whose dimensions are 5 cm. , 7 cm. 5 1. Draw D ABC in which AB = BC = 4 cm. , m ( B) = 60° , then find : (a) The length of AC (b) The type of the triangle according to the measures of its angles. 2. Sally bought 26 metres of cloth for L.E 286 , find the price of 8 metres of the same kind. 106 Mathematics for Primary Stage-Year 4 Shorouk Press Model (9)5 Exercise 1 2 3 1 Choose the correct answer : 1. Thethe smallest prime number is ............ ( 0 or 1 or 2 ) Choose correct answer. 45 tens = ............ ( 45 or 450 or 4500 ) a 72. 251 309 + 748 691 = …… 3. ............ is the smallest number divisible by each of 2 and 5 ( 5 or 10 or 20 ) (8 milliard , 8 million , 8 thousand) ............ 4. All the sides are equal in length in the b 5 000 000 – 324 067 = …… ( square or rectangle or parallelogram ) (95 324 076 are , 91 675 4 675 933) 5. The area of the rectangle whose dimensions 3 cm. and 5933 cm. is, ............ ( 16 cm. or 15 cm. or 8 cm. ) c 8 × 641 × 125 = ... ............ ( 800 or 80 or 800000 ) 6. The value of the digit 8 in the number 437839562 (641 thousand , 641 hundred , 641 million) , < divisible Put thenumber suitable relation or =) : d 2 The 2 100(> is by …… (35 , 11 , 13 , 17) ............ 50 thousand 1. 44302 + 5698 e XYZ is a triangle in which m(∠X) = 40° and m (∠Y) = 30°, 2. 4 metre ............ 40000 cm. then ∆XYZ is …… triangle. 3. 999 ............ 50 × 20 right-angled , an............ obtuse-angled , right an angle. acute-angled) 4. The (a measure of the acute angle the measure of the f The of 15100 and is …… (15 , 105 , 35 , 5) 5. 100L.C.M. thousand ............ ten 35 thousand. 6. 580 600 718 ............ 580 600 708. Draw the square XYZL whose side length 3 cm. Join its 3 Complete the following : diagonals and 1. H.C.F XZ for the two YL. numbers 20 and 30 is ............ a b c 2. The prime even numbers is ............ 3. 300 × 500 = ............ , 250 = ............ 4. 5 million , of 75 thousand Multiples 6 are ……, …… and …… 5. The factors of theof number are ............ Prime factors 35015are ……, …… and …… 6. In the rectangle all angles are ............ The perimeter of a rectangle whose dimensions are 7 cm and 11 cm = ………………………… = …… cm 1. 62491 + 251542 = ............ The H.C.F. of 18 and 30 is …… 2. 93642 – 32161 = ............ 3. 9180 ÷ 45 = ............ 1 of abought day = hours (b) 25 …… metres of cloth , = the…… price ofminutes. one mere P.T. 475 , How much 4 Nada 4 (a) Find the result of each of the following : d e 4 a b money did Nada pay ? 5 Calculate 2 106 425 + 894 075 – 3 000 500. (1) Which is greater : the area of the square whose side length 6 cm. or the area of the Find the number that if7 cm. subtracted rectangle whose dimensions and 6 cm. ? from 256 412 307, then the remainder will AB be =255 , BC = 4 cm. , m ( B) = 90° , then find the (2) Draw D ABC in which 3 cm.million. length of AC Shorouk Press First Term 107 93 ‫‪116‬‬ ‫‪116‬‬ ‫‪116‬‬ ‫‪116‬‬ ‫‪116‬‬ ‫‪116‬‬ ‫‪611‬‬ ‫‪611‬‬ ‫مق‬ ‫اليا‬ ‫عاي‬ ‫‪9099‬د‬ ‫‪99099‬ع‪/‬ا‬ ‫االيداع‪0/9‬‬ ‫‪02‬‬ ‫‪2012‬‬ ‫مرقر‬ ‫‪2012‬الا‬ ‫‪/‬د‬ ‫‪9909‬‬ ‫االيداع‪9‬‬ ‫رقم‪2/10221‬‬ ‫رقم‬ ‫‪2012‬‬ ‫‪/ 9099‬‬ ‫االيداع‬ ‫رقم‬ ‫‪2012‬‬ ‫‪/ 9099‬‬ ‫االيداع‬ ‫رقم‬ ‫‪2012‬‬ ‫‪/‬‬ ‫‪9099‬‬ ‫االيداع‬ ‫رقم‬ ‫االيداع ‪2012 / 9099‬‬ ‫رقم‬ ‫‪�116‬صفحة‬ ‫‪116‬‬ ‫‪116‬‬ ‫‪116‬‬ ‫‪611‬‬ ‫‪661111‬‬ ‫‪116‬‬ ‫الاممقرقر‬ ‫ععاادديي‬ ‫‪999900//999099‬‬ ‫‪// 2‬‬ ‫االيداع‪1002‬‬ ‫رقمااليداع‪2‬‬ ‫‪2012‬‬ ‫‪9099‬‬ ‫‪116‬رقم‬ ‫‪116‬‬ ‫ا‬ ‫ال‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2012‬‬ ‫الا‬ ‫عداديدي‬ ‫‪//9/99‬ععاا‬ ‫‪99099‬‬ ‫‪2‬‬ ‫رقم ‪1000222‬‬ ‫‪9099‬‬ ‫رقم‬ ‫مرققرر‬ ‫‪2012‬الي‬ ‫االيداع‪000999///‬‬ ‫االيداع‪2‬‬ ‫‪11‬‬ ‫رقم‬ ‫‪116‬‬ ‫الاممق‬ ‫‪2012‬ا‬ ‫‪9‬‬ ‫‪9‬‬ ‫االيداع‪2‬‬ ‫‪2012‬‬ ‫‪9099‬‬ ‫‪116‬‬ ‫‪116‬‬ ‫‪2012‬‬ ‫االيداع ‪9099‬‬ ‫رقمااليداع‬ ‫رقم‬ ‫‪2012‬‬ ‫‪//9099‬‬ ‫‪9099‬‬ ‫‪2012‬‬ ‫‪9099‬‬ ‫االيداع‬ ‫رقم‬ ‫‪2012‬‬ ‫رقمااليداع‬ ‫رقم‬ ‫‪2012‬‬ ‫‪///2012‬‬ ‫‪9099‬‬ ‫االيداع‬ ‫االيداع ‪9099‬‬ ‫رقمااليداع‬ ‫رقم‬ ‫‪2012‬‬ ‫‪//9099‬‬ ‫‪9099‬‬ ‫‪2012‬‬ ‫‪/‬‬ ‫‪9099‬‬ ‫االيداع‬ ‫رقم‬ ‫‪2012‬‬ ‫‪/‬‬ ‫االيداع‬ ‫رقم‬ ‫رقم االيداع ‪2012 / 9099‬‬ ‫الحديثة للطباعة والتغليف‬ ‫القاهرة ‪ 8 :‬شارع سيبويه املرصى ـ ت ‪ 24023399 :‬ـ فاكس ‪)02( 24037567 :‬‬ ‫مدينة العبور ـ املنطقة الصناعية‬

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