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1 5th Grade Division 20151125 www.njctl.org 2 Division Unit Topics Click on the topic to go to that section • Divisibility Rules • Division of Whole Numbers • Division of Decimals • Glossary & Standards Teacher Notes • Patterns in Multiplication and Division Vocabu in the p box the linked t of the p word de 3 Divisibility Rules Return to Table of Contents 4 Divisible Divisible is when one number is divided by another, and the result is an exact whole number. five Example: 15 is divisible by 3 three because 15 ÷ 3 = 5 exactly. 5 Divisible two four BUT, 9 is not divisible by 2 because 9 ÷ 2 is 4 with one left over. 6 Divisibility A number is divisible by another number when the remainder is 0. There are rules to tell if a number is divisible by certain other numbers. 7 Divisibility Rules Look at the last digit in the Ones Place! 2 Last digit is even0,2,4,6 or 8 5 Last digit is 5 OR 0 10 Last digit is 0 Check the Sum! 3 Sum of digits is divisible by 3 6 Number is divisible by 3 AND 2 9 Sum of digits is divisible by 9 Look at Last Digits 4 Last 2 digits form a number divisible by 4 8 Divisibility Rules Click for Link Divisibility Rules You Tube song 9 Divisibility Practice Let's Practice! Is 34 divisible by 2? Yes, because the digit in the ones place is an even number. 34 / 2 = 17 Is 1,075 divisible by 5? Yes, because the digit in the ones place is a 5. 1,075 / 5 = 215 Is 740 divisible by 10? Yes, because the digit in the ones place is a 0. 740 / 10 = 74 10 Divisibility Practice Is 258 divisible by 3? Yes, because the sum of its digits is divisible by 3. 2 + 5 + 8 = 15 Look 15 / 3 = 5 258 / 3 = 86 Is 192 divisible by 6? Yes, because the sum of its digits is divisible by 3 AND 2. 1 + 9 + 2 = 12 Look 12 /3 = 4 192 / 6 = 32 11 Divisibility Practice Is 6,237 divisible by 9? Yes, because the sum of its digits is divisible by 9. 6 + 2 + 3 + 7 = 18 Look 18 / 9 = 2 6,237 /9 = 693 Is 520 divisible by 4? Yes, because the number made by the last two digits is divisible by 4. 20 / 4 = 5 520 / 4 = 130 12 Is 198 divisible by 2? Yes No Answer 1 13 Is 315 divisible by 5? Yes No Answer 2 14 Is 483 divisible by 3? Yes No Answer 3 15 294 is divisible by 6. True False Answer 4 16 3,926 is divisible by 9. True False Answer 5 17 Divisibility Some numbers are divisible by more than 1 digit. Let's practice using the divisibility rules. 18 is divisible by how many digits? Let's see if your choices are correct. 9 Click Did you guess 2, 3, 6 and 9? 165 is divisible by how many digits? Let's see if your choices are correct. Click Did you guess 3 and 5? 46 18 Divisibility 28 is divisible by how many digits? Let's see if your choices are correct. Click Did you guess 2 and 4? 530 is divisible by how many digits? Let's see if your choices are correct. Click Did you guess 2, 5, and 10? Now it's your turn...... 19 Divisibility Table Complete the table using the Divisibility Rules. (Click on the cell to reveal the answer) Divisible by2 by 3 by 4 by 5 by 6 by 9 by 10 39 156 429 446 1,218 1,006 28,550 20 What are all the digits 15 is divisible by? Answer 6 21 What are all the digits 36 is divisible by? Answer 7 22 What are all the digits 1,422 is divisible by? Answer 8 23 What are all the digits 240 is divisible by? Answer 9 2 24 What are all the digits 64 is divisible by? Answer 10 25 Patterns in Multiplication and Division Return to Table of Contents 26 Number Systems A number system is a systematic way of counting numbers. For example, the Myan number system used a symbol for zero, a dot for one or twenty, and a bar for five. 27 Number Systems There are many different number systems that have been used throughout history, and are still used in different parts of the world today. Sumerian Roman Numerals wedge = 10, line = 1 28 Our Number System Generally, we have 10 fingers and 10 toes. This makes it very easy to count to ten. Many historians believe that this is where our number system came from. Base ten. 29 Base Ten We have a base ten number system. This means that in a multi digit number, a digit in one place is ten times as much as the place to its right. Also, a digit in one place is 1/10 the value of the place to its left. 30 Base 10 How do you think things would be different if we had six fingers on each hand? 31 Powers of 10 Numbers can be VERY long. $100,000,000,000,000 Wouldn't you love to have one hundred trillion dollars? Fortunately, our base ten number system has a way to make multiples of ten easier to work with. It is called Powers of 10. 32 Powers of 10 Numbers like 10, 100 and 1,000 are called powers of 10. They are numbers that can be written as products of tens. 100 can be written as 10 x 10 or 102. 1,000 can be written as 10 x 10 x 10 or 103. 33 Powers of 10 10 3 The raised digit is called the exponent. The exponent tells how many tens are multiplied. 34 Powers of 10 A number written with an exponent, like 103, is in exponential notation. A number written in a more familiar way, like 1,000 is in standard notation. 35 Powers of 10 Powers of 10 (greater than 1) Standard Notation 10 100 1,000 10,000 100,000 1,000,000 Product of 10s 10 10 x 10 10 x 10 x 10 10 x 10 x 10 x 10 10 x 10 x 10 x 10 x 10 10 x 10 x 10 x 10 x 10 x 10 Exponential Notation 101 102 103 104 105 106 36 Powers of 10 Remember, in powers of ten like 10, 100 and 1,000 the zeros are placeholders. Each place holder represents a value ten times greater than the place to its right. Because of this, it is easy to MULTIPLY a whole number by a power of 10. 37 Multiplying Powers of 10 To multiply by powers of ten, keep the placeholders by adding on as many 0s as appear in the power of 10. Examples: 28 x 10 = 280 Add on one 0 to show 28 tens 28 x 100 = 2,800 Add on two 0s to show 28 hundreds 28 x 1,000 = 28,000 Add on three 0s to show 28 thousands 38 Multiplying Powers of 10 If you have memorized the basic multiplication facts, you can solve problems mentally. Use a pattern when multiplying by powers of 10. Steps 1. Multiply the digits to the left of the 50 x 100 = 5,000 zeros in each factor. 50 x 100 5 x 1 = 5 2. Count the number of zeros in each factor. 50 x 100 3. Write the same number of zeros in the product. 5,000 50 x 100 = 5,000 39 Multiplying Powers of 10 60 x 400 = _______ steps 1. Multiply the digits to the left of the zeros in each factor. 6 x 4 = 24 2. Count the number of zeros in each factor. 3. Write the same number of zeros in the product. 40 Multiplying Powers of 10 60 x 400 = _______ steps 1. Multiply the digits to the left of the zeros in each factor. 6 x 4 = 24 2. Count the number of zeros in each factor. 60 x 400 3. Write the same number of zeros in the product. 41 Multiplying Powers of 10 60 x 400 = _______ steps 1. Multiply the digits to the left of the zeros in each 6 x 4 = 24 2. Count the number of zeros in each factor. 60 x 400 factor. 3. Write the same number of zeros in the product. 60 x 400 = 24,000 42 Multiplying Powers of 10 500 x 70,000 = _______ steps 1. Multiply the digits to the left of the zeros in each 5 x 7 = 35 2. Count the number of zeros in each factor. factor. 3. Write the same number of zeros in the product. 43 Multiplying Powers of 10 500 x 70,000 = _______ steps 1. Multiply the digits to the left of the zeros in each factor. 5 x 7 = 35 2. Count the number of zeros in each factor. 500 x 70,000 3. Write the same number of zeros in the product. 44 Multiplying Powers of 10 500 x 70,000 = _______ steps 1. Multiply the digits to the left of the zeros in each 5 x 7 = 35 2. Count the number of zeros in each factor. 500 x 70,000 factor. 3. Write the same number of zeros in the product. 500 x 70,000 = 35,000,000 45 Practice Finding Rule Your Turn.... Write a rule. Input Output 50 15,000 7 2,100 Rule click 300 90,000 20 6,000 multiply by 300 46 Practice Finding Rule Write a rule. Input 20 7 9,000 80 Output 18,000 Rule 6,300 8,100,000 click multiply by 900 72,000 47 30 x 10 = Answer 11 48 800 x 1,000 = Answer 12 49 900 x 10,000 = Answer 13 50 700 x 5,100 = Answer 14 51 70 x 8,000 = Answer 15 52 40 x 500 = Answer 16 53 1,200 x 3,000 = Answer 17 54 35 x 1,000 = Answer 18 55 Dividing Powers of 10 Remember, a digit in one place is 1/10 the value of the place to its left. Because of this, it is easy to DIVIDE a whole number by a power of 10. Take off as many 0s as appear in the power of 10. Example: 42,000 / 10 = 4,200 Take off one 0 to show that it is 1/10 of the value. 42,000 / 100 = 420 value. 42,000 / 1,000 = 42 value. Take off two 0's to show that it is 1/100 of the Take off three 0's to show that it is 1/1,000 of the 56 Dividing Powers of 10 If you have memorized the basic division facts, you can solve problems mentally. Use a pattern when dividing by powers of 10. 60 / 10 = 60 / 10 = 6 steps 1. Cross out the same number of 0's in the dividend as in the divisor. 2. Complete the division fact. 57 Practice Dividing More Examples: 700 / 10 700 / 10 = 70 8,000 / 10 8,000 / 10 = 800 9,000 / 100 9,000 / 100 = 90 58 Practice Dividing This pattern can be used in other problems. 120 / 30 120 / 30 = 4 1,400 / 700 1,400 / 700 = 2 44,600 / 200 44,600 / 200 = 223 59 Practice Dividing Rule Your Turn.... Complete. Follow the rule. Rule: Divide by 50 Input 150 250 3,000 Output click click click 3 5 60 60 Practice Dividing Rule Complete. Find the rule. Find the rule. Output Input 40 120 click 240 click 8 2,700 click 90 61 800 / 10 = Answer 19 62 16,000 / 100 = Answer 20 63 1,640 / 10 = Answer 21 64 210 / 30 = Answer 22 65 80 / 40 = Answer 23 66 640 / 80 = Answer 24 67 4,500 / 50 = Answer 25 68 Powers of 10 Remember Powers of 10 (greater than 1) Let's look at Powers of 10 (less than 1) Powers of 10 (less than 1) Standard Notation 0.1 0.01 0.001 0.0001 0.00001 0.000001 Product of 0.1 0.1 0.1 x 0.1 0.1 x 0.1 x 0.1 0.1 x 0.1 x 0.1 x 0.1 0.1 x 0.1 x 0.1 x 0.1 x 0.1 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 Exponential Notation 101 102 103 104 105 106 69 Powers of 10 What if the exponent is zero? (100) The number 1 is also called a Power of 10, because 1 = 100 10,000s 1,000s 100s 10s 1s 0.1s 0.01s 0.001s 0.0001s 104 103 102 101 100 101 102 103 104 . Each exponent is 1 less than the exponent in the place to its left. This is why mathematicians defined 100 to be equal to 1. 70 Multiplying Powers of 10 Let's look at how to multiply a decimal by a Power of 10 (greater than 1) Example: 1,000 x 45.6 = ? Steps 1. Locate the decimal point in the power of 10. 1,000 = 1,000. 2. Move the decimal point LEFT until you get to the number 1. 3. Move the decimal point in the other the same number of places, but to the RIGHT. Insert 0's as needed. That's your answer. 1 0 0 0 . (3 places) factor 4 5 . 6 0 0 So, 1,000 x 45.6 = 45,000 71 Multiplying Powers of 10 Let's look at how to multiply a decimal by a Power of 10 (greater than 1) Example: 1,000 x 45.6 = ? Steps 1. Locate the decimal point in the power of 10. 1,000 = 1,000. 2. Move the decimal point LEFT until you get to the number 1. 3. Move the decimal point in the other the same number of places, but to the RIGHT. Insert 0's as needed. That's your answer. 1 0 0 0 . (3 places) factor 4 5 . 6 0 0 So, 1,000 x 45.6 = 45,000 72 Multiplying Powers of 10 Let's look at how to multiply a decimal by a Power of 10 (greater than 1) Example: 1,000 x 45.6 = ? Steps 1. Locate the decimal point in the power of 10. 1,000 = 1,000. 2. Move the decimal point LEFT until you get to the number 1. 3. Move the decimal point in the other the same number of places, but to the RIGHT. Insert 0's as needed. That's your answer. 1 0 0 0 . (3 places) factor 4 5 . 6 0 0 So, 1,000 x 45.6 = 45,000 73 Practice Multiplying Let's try some together. 10,000 x 0.28 = $4.50 x 1,000 = 1.04 x 10 = 74 100 x 3.67 = Answer 26 75 0.28 x 10,000 = Answer 27 76 1,000 x $8.98 = Answer 28 77 7.08 x 10 = Answer 29 78 Dividing Powers of 10 Let's look at how to divide a decimal by a Power of 10 (less than 1) Example: 45.6 / 1,000 Steps 1. Locate the decimal point in the power of 10. 2. Move the decimal point LEFT until to the number 1. 1,000 = 1,000. you get 1 0 0 0 . (3 places) 3. Move the decimal point in the other number the same number of places to the LEFT. Insert 0 0 4 5 . 6 0's as needed. So, 45.6 / 1,000 = 0.0456 79 Dividing Powers of 10 Let's look at how to divide a decimal by a Power of 10 (less than 1) Example: 45.6 / 1,000 Steps 1. Locate the decimal point in the power of 10. 2. Move the decimal point LEFT until to the number 1. 1,000 = 1,000. you get 1 0 0 0 . (3 places) 3. Move the decimal point in the other number the same number of places to the LEFT. Insert 0 0 4 5 . 6 0's as needed. So, 45.6 / 1,000 = 0.0456 80 Dividing Powers of 10 Let's look at how to divide a decimal by a Power of 10 (less than 1) Example: 45.6 / 1,000 Steps 1. Locate the decimal point in the power of 10. 2. Move the decimal point LEFT until to the number 1. 1,000 = 1,000. you get 1 0 0 0 . (3 places) 3. Move the decimal point in the other number the same number of places to the LEFT. Insert 0 0 4 5 . 6 0's as needed. So, 45.6 / 1,000 = 0.0456 81 Practice Dividing Let's try some together. 56.7 / 10 = 0.47 / 100 = $290 / 1,000 = 82 73.8 / 10 = Answer 30 83 0.35 / 100 = Answer 31 84 $456 / 1,000 = Answer 32 85 60 / 10,000 = Answer 33 86 $89 / 10 = Answer 34 87 321.9 / 100 = Answer 35 88 Division of Whole Numbers Return to Table of Contents 89 Review from 4th Grade When you divide, you are breaking a number apart into equal groups. The problem 15 ÷ 3 means that you are making 3 equal groups out of 15 total items. Each equal group contains 5 items, so 15 ÷ 3 = 5 90 Review from 4th Grade How will knowing your multiplication facts really well help you to divide numbers? click to reveal Multiplying is the opposite (inverse) of dividing, so you're just multiplying backwards! Find each quotient. (You may want to draw a picture and circle equal groups!) 16 ÷ 4 click 4 24 ÷ 8 click 3 30 ÷ 6 click 5 63 ÷ 9 click 7 91 You will not be able to solve every division problem mentally. A problem like 56 ÷ 4 is more difficult to solve, but knowing your multiplication facts will help you to find this quotient, too! To make this problem easier to solve, we can use the same Area Model that we used for multiplication. Answer Review from 4th Grade How can you divide 56 into two numbers that are each divisible by 4? ( ? + ? = 56) 4 ? ? 56 92 Review from 4th Grade ? ? 40 4 16 Answer You can break 56 into 40 + 16 and then divide each part by 4. 4 56 Ask yourself... What is 40 ÷ 4? (or 4 x n = 40?) What is 16 ÷ 4? (or 4 x n = 16?) The quotient of 56 ÷ 4 is equal to the sum of the two partial quotients. 93 Area Model Division How can you break up 135? Remember... you want the numbers to be divisible by 5. 5 100 Answer Let's try another example. Use the area model to find the quotient of 135 ÷ 5. 5 35 94 Area Model Division Let's try another example. Use the area model to find the quotient of 135 ÷ 15. You can break 135 into 90 + 45 and then divide each part by 15. ? 15 135 Answer ? 15 Ask yourself... What is 90 ÷ 15? What is 45 ÷ 15? (or 15 x n = 90?) (or 15 x n = 45?) The quotient of 135 ÷ 15 is equal to the sum of the two partial quotients. 95 Area Model Division What about remainders? ? ? R. Answer Use the area model to find the quotient. 963 ÷ 20 = 20 20 963 96 Answer 36 Use the area model to find the quotient. 645 ÷ 15 = 15 40 + 3 = 97 Answer 37 Use the area model to find the quotient. Write any reminder as a fraction. 695 ÷ 30= 10 + 3 = 98 Answer 38 Use the area model to find the quotient. Write any reminder as a fraction. 385 ÷ 75 = 99 • Determine the number that each letter in the model represents and explain each of your answers. • Write the quotient and remainder for • Explain how to use multiplication to check that the quotient is correct. You may show your work in your explanation. Answer 39 A teacher drew an area model to find the value of 6,986 ÷ 8. From PARCC PBA sample test #15 100 Division Key Terms Some division terms to remember.... • The number to be divided into is known as the dividend. • The number which divides the dividend is known as the divisor. • The answer to a division problem is called the quotient. 4 quotient divisor 5 20 dividend 20 ÷ 5 = 4 __ 20 5 = 4 101 Estimating Estimating the quotient helps to break whole numbers into groups. 102 Estimating: OneDigit Divisor 8) 689 Divide 8) 68 8 8)689 80 8)689 Write 0 in remaining place. 80 is the estimate. 103 OneDigit Estimation Practice Estimate: 9)507 Remember to divide 50 by 9 Then write 0 in remaining place in quotient. Is your estimate 50 or 40? Click Yes, it is 40. 104 OneDigit Estimation Practice Estimate : 5)451 Remember to divide 45 by 5 Then write 0 in remaining place in quotient. Is your estimate 90 or 80? Click Yes, it is 90 105 40 The estimation for 8)241 is 40? Answer True False 106 ÷ 7. Answer 41 Estimate 663 107 Answer 42 Estimate 4)345 . 108 Answer 43 Solve using Estimation. Marta babysat fo r four hours and earned $19. ABOUT how much money did Marta earn each hour that she babysat? 109 Estimating: TwoDigit Divisor 26)6,498 Round 26 to its greatest place. 30)6,498 2 30) 6,498 200 30)6,498 Divide 30)64 . Write 0 in remaining places. 200 is the estimate. 110 TwoDigit Estimation Practice Estimate: 31)637 Remember to round 31 to its greatest place 30, then divided 63 by 30. Finally, write 0's in remaining places in quotient. Is your estimate 20 or 30? click to reveal Yes, it is 20. 111 TwoDigit Estimation Practice Estimate: 87)9,321 Remember to round 87 to its greatest place 90, then divide 93 by 90 Finally, write 0's in remaining places in quotient. Is your estimate 100 or 1,000? click to reveal Yes, it is 100. 112 44 The estimation for 17)489 is 2? Answer True False 113 ÷ 25. Answer 45 Estimate 5,145 114 Answer 46 Estimate 41) 2,130 . 115 Answer 47 Estimate 31)7,264 . 116 Answer 48 Solve using Estimation. Brandon bought cookies to pack in his lunch. He bought a box with 28 cookies. If he packs five cookies in his lunch each day , ABOUT how many days will the days will the cookies last? 117 Division When we are dividing, we are breaking apart into equal groups. Find 132 3 44 Step 1: Can 3 go 3 132 into 1, no so can 12 Click for step 1 3 go into 13, yes 1 2 12 0 Step 2: Bring down the 2. Can 3 Click for step 2 go into 12, yes 3 x 4 = 12 13 12 = 1 Compare 1 < 3 3 x 4 = 12 12 12 = 0 Compare 0 < 3 118 Division Step 3: Check your answer. 44 x 3 132 119 Answer 49 Divide and Check 8)296 . 120 Answer 50 Divide and Check 9)315 121 ÷ 6. Answer 51 Divide and Check 252 122 ÷ 2. Answer 52 Divide and Check 9470 123 Answer 53 Adam has a wire that is 434 inches long. He cuts the wire into 7inch lengths. How many pieces of wire will he have? 124 Answer 54 Bill and 8 friends each sold the same number of tickets. They sold 117 tickets in all. How many tickets were sold by each person? 125 Answer 55 There are 6 outs in an inning. How many innings would have to be played to get 348 outs? 126 56 How many numbers between 23 and 41 have NO remainder when divided by 3? A 4 C 6 D 11 Answer B 5 127 Division Problem John and Lad are splitting the $9 that John has in his wallet. Move the money to give John half and Lad half. Sometimes, when we split a whole number into equal groups, there will be an amount left over. Click when finished. The left over number is called the remainder. 128 Long Division Lets look at remainders with long division. For example: 4 7)30 28 2 We say there are 2 left over, because you can not make a group of 7 out of 2. 129 Long Division For example: 4 7)30 30÷7 = 4 R 2 28 2 This is the way you may have seen it. The R stands for remainder. 130 Long Division Another example: 23 15)358 30 58 45 13 We say there are 13 left over (R) because you can not make a group of 15 out of 13. 358 ÷ 15 = 23 R 13 131 Answer 57 A group of six friends have 83 pretzels. If they want to share them evenly, how many will be left over? 132 Answer 58 Four teachers want to evenly share 245 pencils. How many will be left over? 133 Answer 59 Twenty students want to share 48 slices of pizza. How many slices will be left over, if each person gets the same number of slices? 134 A 149 packages, 2 left over B 148 packages, 2 left over Answer 60 Suppose there are 890 packages being delivered by 6 planes. Each plane is to take the same number of packages and as many as possible. How many packages will each plane take? How many will be left over? Fill in the blanks. Each plane will take _______ packages. There will be _______ packages left over. 135 Long Division Instead of writing an R for remainder, we will write it as a fraction of the 30 that will not fit into a group of 7. So 2/7 is the remainder. 4 2 7 7)30 28 2 136 Long Division Examples More examples of the remainder written as a fraction: 7 5 6 6)47 42 5 The Remainder means that there is 5 left over that can't be put in a group containing 6 To Check the answer, use multiplication and addition. 7 x 6 + 5 = 42 + 5 = 47 Multiply the quotient and the divisor. Then, add the remainder. The result should be the dividend. 137 Long Division Example Example: 37 7)264 21 54 49 5 5 7 Check the answer using multiplication and addition.Way 1: 37 x 7 + 5 = 259 + 5 = 264 Way 2: 37 quotient x divisor x 7 259 + 5 + remainder 264 dividend 138 Answer 61 Divide and Check 4)43 (Put answer in as a mixed number.) 139 Answer 62 Divide and Check 61 ÷ 3 = (Put answer in as a mixed number.) 140 63 Divide and Check 145 ÷ 7 Answer (Put answer in as a mixed number.) 141 64 Divide and Check 2)811 Answer (Put answer in as a mixed number.) 142 65 Divide and Check 309 ÷ 2 = Answer (Put answer in as a mixed number.) 143 Long Division with 2digit Divisor You can divide by twodigit divisors to find out how many groups there are or how many are in each group. When dividing by a twodigit divisor, follow the steps you used to divide by a onedigit divisor. Repeat until you have divided all the digits of the dividend by the divisor. STEPS Divide Multiply Subtract Compare Bring down next number 144 Long Division Practice Find 4575 25 183 Step 1: Can 25 25 4575 go into 4, no so 25 can 25 go into 45, 20 7 yes 200 Step 2: Bring down the 7. Can Click for step 2 25 go into 207, yes Step 3: Bring down the 5. Can 25 go into 75, yes Click for step 3 25 x 1 = 25 45 25 = 20 Compare 20 < 25 75 75 0 25 x 8 = 200 207 200 = 7 Compare 7 < 25 25 x 3 = 75 Click for step 1 75 75 = 0 Compare 0 < 25 145 Long Division Practice Step 3: Check your answer. 183 x 25 146 Long Division Example Mr. Taylor's students take turns working shifts at the school store. If there are 23 students in his class and they work 253 shifts during the year, how many shifts will each student in the class work? 147 Long Division Example 23)253 Step 1 Compare the divisor to the dividend to decide where to place the first digit in the quotient. Divide the tens. Think: What number multiplies by 23 is less than or equal to 25. Step 2 Multiply the number of tens in the quotient times the divisor. Subtract the product from the dividend. Bring down the next number in the dividend. Step 3 Divide the result by 23. Write the number in the ones place of the quotient. Think: What number multiplied by 23 is less than or equal to 23? 11 23) 253 23 23 23 Step 4 Multiply the number in the ones place of the quotient by the divisor. Subtract the product from 23. If the difference is zero, there is no remainder. 0 Each student will work 11 shifts at the school store. 148 Long Division Division Steps can be remembered using a "Silly" Sentence. David Makes Snake Cookies By Dinner. Divide Multiply Subtract Compare Bring Down What is your "Silly" Sentence to remember the Division Steps? 149 Silly Steps Example Click boxes to show work Find 374 ÷ 22 Step 1 1 22) 374 divide Think 20) 374 Step 4 1 bring 22) 374 22 down 154 bring down Step 5 17 repeat Step 2 1 22) 374 multiply 22 1 x 22 Step 3 1 subtract 22) 374 22 15 15 less than 22 compare 22) 374 22 repeat 154 154 0 Final Step 17 x 22 34 Check +340 374 150 A 38 B 40 C 41 D 45 Answer 66 A candy factory produces 984 pounds of chocolate in 24 hours. How many pounds of chocolate does the factory produce in 1 hour? 151 A $230 B $320 C $325 Answer 67 Teresa got a loan of $7,680 for a used car. She has to make 24 equal payments. How much will each payment be? 152 Answer 68 Solve 16)176 153 ÷ 47 Answer 69 Solve 329 154 Answer 70 If 280 chairs are arranged into 35 rows, how many chairs are in each row? 155 Answer 71 There are 52 snakes. There are 13 cages. If each cage contains the same number of snakes, how many snakes are in each cage? 156 Answer 72 Solve 46)3,588 157 ÷ 72 Answer 73 Solve 3,672 158 74 Enter your answer. Answer 1,534 ÷ 26 = From PARCC EOY sample test #27 159 Division Steps Divide Multiply . Subtract Compare Bring Down Repeat When dividing by a TwoDigit Divisor, there may be a Remainder. Follow the Division Steps. If the Difference in the Last Step of Division is not a Zero, and there are no other numbers to Bring Down, this is the Remainder. The definition of a Remainder is an amount "left over" that does not make a full group (Divisor). Write the Remainder as a Fraction. top number Difference 62 bottom number Divisor 77 This means there are 62 "left over" that do not make a full group of 77. Use Multiplication and Addition to check you Answer. Problem: 5 62 77 5 x 77 + 62 = 447 77) 447 385 62 OR 77 x 5 375 + 62 447 160 Let's Practice Remember your Steps: Divide, Multiply, Subtract, Compare, Bring Down, Write the Remainder as a Fraction, Check your work 21 36 17 36) 633 36 Solve 633 36 273 252 21 17 CHECK 36 x Divisor 102 x Quotient + 510 + Remainder = Dividend 612 + 21 633 161 A 8 B 7 C 19 D 10 Answer 75 What is the remainder when 402 is divided by 56? 162 A 5 B 8 C 13 D 26 Answer 76 What is the remainder when 993 is divided by 38? 163 77 Divide 80) 104 Answer (Put answer in as a mixed number.) 164 78 Divide 556 ÷ 35 Answer (Put answer in as a mixed number.) 165 Answer 79 Divide 45) 1442 (Put answer in as a mixed number.) 166 80 Divide 4453 ÷ 55 Answer (Put answer in as a mixed number.) 167 81 Divide 83) 8537 Answer (Put answer in as a mixed number.) 168 Interpreting the Remainder In word problems, we need to interpret the what the remainder means. For example: Celina has 58 pencils and wants to share them with 5 people. 11 5) 58 5 08 5 3 5 people will each get 11 pencils, and there will be 3 left over. 169 Interpreting the Remainder What does the remainder below mean? Violet is packing books. She has 246 books and, 24 fit in a box. How many boxes does she need? 10 24) 246 24 06 The remainder means she would have 6 books that would not fit in the 10 boxes. She would need 11 boxes to fit all the books. 170 A 47 B 48 C 49 D 50 Answer 82 If you have 341 oranges to transport from Florida to New Jersey, and 7 oranges are in each bag, how many bags will you need to ship all of the oranges? 171 A 6 B 7 C 8 D 9 Answer 83 At the bakery, donuts are only sold in boxes of 12. If 80 donuts are needed for the teacher's meeting, how many boxes should be bought? 172 84 Apples cost $4 for a 5 pound bag. If you have $19, how many bags can you buy? B 3 19 4 = 4 R 3 Answer A 2 C 4 D 5 173 85 The school is ordering carry cases for the calculators. If there are 203 calculators and 16 fit in a case, how many cases need to be ordered? A 10 B 11 C 12 D 13 174 A 5 B 6 C 7 D 8 Answer 86 For the class trip, 51 people fit on a bus and 267 people are going. How many buses will be needed? 175 Answer 87 Greg is volunteering at a track meet. He is in charge of providing the bottled water. Greg knows these facts. • The track meet will last 3 days. • There will be 117 athletes, 7 coaches, and 4 judges attending the track meet. • Once case of bottled water contains 24 bottles. The table shows the number of bottles of water each athlete coach, and judge will get for each day of the track meet. What is the fewest number of cases of bottled water Greg will need to provide for all the athletes, coaches, and judges at the track meet. Show your work or explain how you found your answer using From PARCC PBA sample test #16 equations. 176 Division of Decimals Return to Table of Contents 177 Dividing Decimals To divide a decimal by a whole number: Use long division. Bring the decimal point up in the answer. 21 31 3 63.93 178 Decimal Division Examples Match the quotient to the correct problem. 4 8.12 4 81.2 4 0.812 4 0.0812 0.0203 0.203 2.03 20.3 179 A 1285 B 1.285 C 12.85 D 128.5 5 64.25 Answer 88 Which answer has the decimal point in the correct location? 180 89 Which answer has the decimal point in the correct location? 561 B 56.1 C 5.61 D 0.561 4 224.4 Answer A 181 90 Which answer has the decimal point in the correct location? 51 B 5.1 C 0.51 D 0.051 9 0.459 Answer A 182 91 Select the answer with the decimal point in the correct location. 0.1234 B 1.234 C 12.34 D 123.4 E 1234 3 37.02 Answer A 183 92 Select the answer with the decimal point in the correct location. 501 B 50.1 C 5.01 D 0.501 E 0.0501 5 .2505 Answer A 184 20.52 Answer 93 6 185 321.6 Answer 94 4 186 2.198 Answer 95 7 187 70.62 Answer 96 11 188 251.2 Answer 97 4 189 Zero Place Holder Be careful, sometimes a zero needs to be used as a place holder. 5.08 7 35.56 35 0 56 56 0 7 can not go into 5. So, put a 0 in the quotient, and bring the 6 down. 190 98 What is the next step in this division problem? 3 27.21 27 0 2 A Put a 2 in the quotient. B Put a 0 in the quotient. C Put a 1 in the quotient. Answer 9. 191 99 What is the next step in this division problem? 5 3.205 30 2 A Put a 0 in the quotient. B Put a 2 in the quotient. C Bring down the 0. Answer 0.6 192 100 What is the next step in this division problem? 8 64.48 64 0 4 A Put a 0 in the quotient. B Put a 4 in the quotient. C Put a 2 in the quotient. Answer 8. 193 0.636 Answer 101 6 194 2.406 Answer 102 3 195 Zero Place Holder Be careful! Sometimes there is not enough to make a group, so put a zero in the quotient. .076 8 0.608 56 48 48 0 196 first step in this division 6 .468 A Put a 0 in the ones place of the quotient. B Put a 0 in the tenths place of the quotient. C Put a 7 in the quotient. Answer 103 What is the problem? 197 first step in this division 24 .1104 A Put a 0 in the quotient in the tenths and hundredths place. B Put a 0 in the quotient in the ones place. C Put a 4 in the quotient. Answer 104 What is the problem? 198 .435 Answer 105 5 199 Another Way to Handle Remainders Instead of writing a remainder, continue to divide the remainder by the divisor (by adding zeros) to get additional decimal points. 9.4 8 75.6 72 3 6 32 4 Instead of leaving the 4 as a remainder, add a zero to the dividend. 200 Another Way to Handle Remainders 9.45 8 75.60 72 3 6 3 2 40 40 0 Add a zero to the dividend. No remainder now. 201 3.26 Answer 106 5 202 87.3 Answer 107 2 203 Answer 108 6 0.795 204 0.843 Answer 109 30 205 0.363 Answer 110 15 206 Decimal Division Example When you have a remainder, you can add a decimal point and zeros to the end of a whole number dividend. Example: You want to save $284 over the next 5 months. How much money do you need to save each month? $284 ÷ 5 = _____ 207 Decimal Division Example 56 5 $284 25 34 30 4 Don't leave the remainder 4, or write it as a fraction, add a decimal point and zeros to get the cents. 208 Decimal Division Example 56.8 5 $284.0 25 34 30 4 0 4 0 0 Since the answer is in money, write the answer as $56.80. 209 Decimal Division Example 11.714 7 $82.000 7 12 7 50 49 10 7 30 28 2 Since the answer is in money, add a decimal point and 3 zeros. Round the answer to the nearest cent (hundredths place). $82 ÷ 7 = $11.71 210 Answer 111 5 $63 211 Answer 112 $782 ÷ 9 = 212 Answer 113 7 $593 213 Answer 114 4 $352 214 Answer 115 $48 ÷ 22 = 215 Divisor as a Decimal To divide a number by a decimal: • Change the divisor to a whole number by multiplying by a power of 10 • Multiply the dividend by the same power of 10 • Divide • Bring the decimal point up in the answer Divisor Dividend 216 Divisor as Decimal Examples: 2.4 15.696 24 156.96 Multiply by 10, so that 2.4 becomes 24. 15.696 must also be multiplied by 10. .64 6.4 64 640 Multiply by 100, so that .64 becomes 64. 6.4 must also be multiplied by 100. 217 Divisor as Decimal Practice By what power of 10 should the divisor and dividend be multiplied? .007 4.9 0.3 42.69 218 Divisor as Decimal Examples By what power of 10 should the divisor and dividend be multiplied? 7.59 ÷ 2.2 2.0826 ÷ 0.06 means means 219 116 Answer 0.3 42.48 220 117 Divide Answer 2.592 ÷ 0.08 = 221 118 Enter your answer. Answer 6.3 ÷ 0.1 = From PARCC EOY sample test #19 222 119 Enter your answer Answer 6.3 x 0.1 = From PARCC EOY sample test #19 223 120 Answer 0.3 0.6876 224 121 Answer 20 divided by 0.25 225 Answer 122 Yogurt costs $.50 each, and you have $7.25. How many can you buy? 226 Teacher Notes Glossary & Standards Vocabu in the p box the linked of the p word d Return to Table of Contents 227 Standards for Mathematical Practices MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP6 Attend to precision. MP7 Look for and make use of structure. MP8 Look for and express regularity in repeated reasoning. Click on each standard to bring you to an example of how to meet this standard within the unit. 228 Base Ten In a multi digit number, a digit in one place is ten times as much as the place to its right and 1/10 the value of the place to its left. Back to Instruction 229 Dividend The number being divided in a division equation. 3 8 24 Dividend Dividend 24 ÷ 8 = 3 Dividend 24 = 3 8 Back to Instruction 230 Divisible When one number is divided by another, and the result is an exact whole number. 5 5 15 is divisible by 3 because 3 15 ÷ 3 = 5 exactly. 2 11 ÷ 2 = 5 R.1 Back to Instruction 231 Divisor The number the dividend is divided by. A number that divides another number without a remainder. 3 8 24 Divisor 24 ÷ 8 = 3 Divisor 25 = 3 R1 8 Must divide evenly. Back to Instruction 232 Exponent A small, raised number that shows how many times the base is used as a factor. Exponent 3 2 = x 2 3 = x x 3 3 3 3 3 x 32 2 Base "3 to the second power" 3 3 3 3 3 x 33 Back to Instruction 233 Exponential Notation A number written using a base and an exponent. Standard 1,000 Word One Thousand Exponential 103 Back to Instruction 234 Number System A systematic way of counting numbers, where symbols/digits and their order represent amounts. Base Ten Roman Numerals Others Back to Instruction 235 Power of 10 Any integer powers of the number ten. (Ten is the base, the exponent is the power). 10 = 1= 10x10 = 2 10x10x10 = 3 = 1,000 10 10 10 10 100 = Back to Instruction 236 Quotient The number that is the result of dividing one number by another. Quotient 12 ÷ 3 = 4 Quotient 4 3 12 12 = 4 3 Quotient Back to Instruction 237 Remainder When a number is divided, the remainder is anything that is left over. (Anything in addition to the whole number.) 5 5 Remainder 2 11 ÷ 2 = 5 R.1 5 R.1 2 11 3 No remainder Back to Instruction 238 Standard Notation A general term meaning "the way most commonly written". A number written using only digits, commas and a decimal point. Standard 3.5 Word Three and five tenths Expanded 3 + 0.5 Back to Instruction 239