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Summer Math Packet 5Y & 5X Knight Will be 7th graders in Fall Name June 2OI5 Dear Parents and Students, We all know that over the summer, mathematical skills are often weakened which may result in a setback at the beginning of the school year. To avoid the need to play "catch-up" in the fall, an assignment has been prepared to help the students maintain their skills. This assignment is made up of concepts that have been taught in sixth grade and will provide students a thorough review of skills needed for seventh grade. lt is important that this packet be completed to the best of their ability. The objective of this assignment is to help them succeed in the next school year. All questions must have work to support the answers. Work can be done on the question paper, if work space is available. lf not, work should be completed on loose leaf and attached to question paper. Do not squeeze work into a tiny area. Any assignment without work will be considered an incomplete assignment. This packet along with any loose leaf used to show work is to be placed in a folder and submitted on the first day of school. Thank you for your cooperation. Have a great summer! Sincerely, ,l?rs. trorzru Mrs. Kwan ltLL* //rr,$tr Mrs. Knight Reducin Reduce each ratio to its lowest form. An swe rs 2) 42 54 s) 15 24 8) 3s 28 63 11) 27 36 10 60 L4\ 42 30 16) eo 10 L7) e: le) 64 72 20) Ex) 5o :35 1) 3) t2 32 4) 4s 6) t2 7) 2: e) 20 36 10) t4 rz) 70 l0 13) ls) 48 42 18) 5:20 Name: Ratios 4s 21 20 t6 www.CommonCoreSheets.com 42 18 t2 Page 1 of [Jnderstandin Ratios 1 Narne: Answers Solve each problem. 1) A recipe called forthe ratio of sugarto flourto be 5 : l. If you used 35 ounce of sugar, how rnany ounces of flour would you need to use? 2) A teacher had 21 red pens. If the ratio of red pens to blue pens she owned was 3 : l, how many pens did she have total? 3) A chess player played 20 games total. If he won 2 of the garnes, what is the ratio of garnes he lost to games he won? 4) At a pet store the ratio of cats to dogs sold was l0 : l. If there were 60 cats that were sold, how nrany dogs were sold? 5) At a restaurant the ratio of kids meals sold to adult nreals sold was 5:4.1f there were 20 kids meals sold. what is the combined arnount o{'kids and adult meals sold? 6) A student bought 34 pencils fbr school. If he sharpened l6 of the pencils before school, what is his ratio of unsharpened pencils to sharpened pencils? 7) A buffet offers ranch or caesar dressing. The ratio of ranch dressing used is 8 they :3. If the buffet uses T2cases of used to caesar dressing ranch dressing, how many cases of caesardo use'? 8) A student finished 72 of her homework problems in class. If the ratio of problems she flnished to problems she still had left was 8 : l, how many homervork problerns did she have total? 9) At a carnival Cody bought l5 tickets. If he used 6 tickets trying to win the ring toss game, what is the ratio of tickets he has to tickets he's used'/ 10) At a farm l0 Math www.CornmonCoreSheets.com the ratio of cows to horses was many horses were there? about:blank : 3. If there were 20 cows at the fbrm, how 6l17 12014 Usin Ratio Name: uations Answers Solve each problem. l) Every pint is 2 cups. This can be expressed using the equation y x 2: Z, where y is equal to the number of pints and Z is equal to the total number of cups. Using this equation find the total cups in 5 pints. This can be expressed using the equation y x 1.000 : Z, where y is equal to the number of liters and Z is equal to the total number of milliters. Using this equation find the total milliters in l0 liters. 2) Every liter is 1,000 milliters. 3) E,very gallon is 4 quarts. This can be expressed using the equation y x 4: Z,wherey is equal to the number of gallons and Z is equal to the total number of quarts. Using this equation find the total quarts in 5 gallons. 4) For each kilogram there are I,000 grams. This can be expressed using the equation y 1,000 Z, where y is equal to the number of kilogram and Z is equal to the total number of grams. Using this equation find the total grams in 9 kilograms. 5) E,very quarter is 5 nickels. This can be expressed using the equation y x 5 Z, where y is equal to the number of quarters and Z is equal to the total number of nickels. Using : : this equation find the total nickels in 7 quarters. 6) 7) 8) 9) Every quarter is 25 pennies. This can be expressed using the equation y x 25 where y is equal to the number of quarters and Z is equal to the total number pennies. Using this equation find the total pennies in 5 quarters. : Z, of Every foot is l2 inches. This can be expressed using the equation y x 12 : Z, wherc y is equal to the number of feet and Z is equal to the total number of inches. Using this equation find the total inches in l0 feet. l0: can be expressed using the equation y x Z, where y is equal to the number of centimeters and Z is equal to the total number millimeters. Using this equation find the total millimeters in l0 centimeters. Every centimeter is l0 rnillirneters. This : Every dollar is l0 dimes. This can be expressed using the equation y x l0 Z, where y is equal to the number of dollars and Z is equal to the total number of dimes. Using this equation find the total dimes in 7 dollars. : 10) Every yard is 3 fbet. This can be expressed using the equation y x 3 Z, where y is equal to the number of yards and Z is equal to the total number of feet. Using this equation find the total feet in 6 yards. 11) Every meter is 100 centimeters. This can be expressed using the equation y x 100 where y is equal to the number of meters and Z is equal to the total number of centimeters. Using this equation find the total centimeters in 4 meters. t2) of : Z, Every cup is 8 ounces. This can be expressed using the equation y x 8 : Z, where y is equal to the number of cups and Z is equal to the total number of ounces. Using this equation find the total ounces in 7 cups. www.CommonCoreSheets.com Name: Dividing Fractions Solve each problem. Write your answer as a mixed number (if possible). 2)4r l)r 4 +J_: 4 4\3 3)t7 +- 23 I + A- s) E __ 53 a J 4 6) I 4-:2 7)z l4 8) 5: 6 e)22 10)35 ..L /t-- 11) t2) 7 2 Math + 62 36 www.Com monCoreSheets.com l3 5- Answers tive Number Location on Numberline Solve each problem. 1) An swe rs Which letter best shows A -ll2? -89 2) Which letter best shows -43? A 3) -95 Which letter best shows -84? A 4) -56 Which letter best shows -105? A 5) -80 Which letter best shows -102? A 6) -76 Which letter best shows -25? A -55 7\ Which letter best shows -10? A 8) -58 Which letter best shows -116? A -96 e) Which letter best shows -52? A -88 10) Which letter best shows -123? A Name: -100 www.CommonCoreSheets.com with Absolute Value Use<rlor-tocompare. 1) l-6ll lsl l. 2) 87 95 2. 3) l40l 144l 4) -33 l-201 s) l2rl l-e0l 6) -28 -42 7) -13 42 8) 64 _-8e e) l-231-l-t7l 10) 27 ls4l 11) l-731 -49 t2) 161l -5 13) ls lsel t4) ls) An swe rs l-e 1 I lsll 22 99 16) 3e -1 t7) 47 l-271 t8) lssl l27l 1e) l-esl l50l 20) -4e lsl www. CommonCoreSheets.com Name: Understandin Absolute Value Use the numberlines to find the ahsolute value. 1) a. What is the value of 'A'? b. How far is'A'from Answers -20 -10 0 l0 20 -20 -r0 0 r0 20 -20 -10 0 l0 -20 -10 0 l0 20 -20 -10 0 l0 20 -20 -10 0 l0 20 -20 -10 0 (absolute value)? 2) a. What is the value of 'A'? b. How far is'A' frotn 0 (absolr"rte value)? 3) a. What is the value of 'A'? b. How far is'A' from 0 <liii lii, litrilai til .iiliritlii 20 il'iirl> (absolute value)? 4) a. What is the value of 'A'? b. How far is'A' fiotn 0 (absolute value)'/ s) a. What is the value of 'A'? b. How far is'A' from 0 (absolute value)? 6) a. What is the value of 'A'? b. How far is'A' from 0 (absolute value)? 7',1 a. What is the value of 'A'? b. How far is'A' fiotn 0 <liir,lar iil irl,riil 0 l0 r lr tilii il't 20 l> A (absolute valr"re)? 8) a. What is the value of 'A'? b. How far is'A' fiom 0 -20 <lrii,li -r0 0 t0 r,liri+l,Or rl ili;+lti iliti 20 l> A (absolute value)? 9) a. What is the value of 'A'? b. How far is'A' fiorn 0 -20 <liir,li -10 i,fiiiilor 0 r0 til ,t li iil t il 20 ,l> (absolute value)? 10) a. What is the value of 'A'? b. How far is'A' from 0 -10 -20 <liitiliitilt+rl (absolute value)? www.CommonCoreSheets.com 0 r0 ii lo i,li,iilrt,iliiiil> 20 Distance on a Grid Find the distance between points. Answers 1* Math www.CommonCoreSheets.com Nome Solving Addition and Subtraction Equations in each equation' Explain how to get the variable alone 1. 10: 100 n * 10 - 10: 100 - 2, n+ 10 x-75:49 x-75+_-:49+-_ answer' Solve each equation and check your 3, g - B:25 4.25+Y:42 6.30: m-18 7' 5, r + 82:97 8, a-51:12 150: e + 42 15 - s Al $t S. She had $t S left' Solve the equation she made the loan' to find how much money Jo had before 9. Jo loaned - 15 A$o B $ts , c $so D $60 : what isthe varue of the 10. criticar Thinking rf n + 10 40, then exPression n - 25? A5 825 c30 D50 the equation 11. writing to Explain Explain how to solve 35 + P - 92. Then solve' ,: Copyright @ Rights Reserved' 6 Pearson Education, lnc', or its affiliates' All Nome Solving Addition and SubtraLtion Equations alone in each equation' Explain how to get the variable -2, n + 1.1 :22'3 1, n + 1.1 - 1.1 :22'3 - 1'1 x-6.7 :28.8 :28.8 + x-6.7+ .7 + Y - 54'4 3. g - 3-2:20 4. 6. 3.9: m-22'1 7. 100: e + 91 '8 g. 31 5. r+16.9:88'2 8. a-31 :12'6 He drove more in the afternoon' Tom drove 11.g miles in the morning. how far equation courd you use to find He drov e 32.4 mires in all" which Tom drove in the afternoon? A 11.8 + 32.4 - m B 11.8 +m:32'4 G 11.8 -m:32'4 D m - 32.4: 11'8 : 45'5,then what is the value of the 10. critical Thinking lf n + 10 * expression n 25? A 10.5 825 c 25-5 D 45.5 ll.WritingtoExplainExplainhowtosolvetheequation 4.8 + P - 12-2'Then solve' Copyright @ 6 affiliates' All Rights Reserved' Pearson Education' lnc'' or its Nome solving Multiplication and Division Equations get the variable alone in each equation' For 1 through 3, explain how to 2, 1" rx7 - 42 rx7 +7 - 42+7 m+6:12 m+6x.-:12x- Check your answer' For 4 through 9, solve the equation. 4.9n -72 7. w + 7 :15 3. 44:2k 5. yx5:60 6. v + 13:2 8. 216 - 9. 17:t+3 36P get the variable m alone on )/Youtd 10. writing to Explain Tell how you : one side of the equation 15m 45' problem that can be solved with the 11, Write a Problem Write a equationr+6- 14. can you use to 12. Number sense which equation solve this Problem? will bought 84 muffins' There are 12 muffins in a package. How many Packages did he buY? A 12xP:84 B 84x12:P G 12+p--84 D 84:12+P Copyright @ All Rights Reserved' 6 Pearson Education, lnc" or its affiliates' Nome Solving Equations with Decimals in each equation' Explain how to get the variable alone 1. 7n - 2. 6.3 3. 67.3 - x+5.2:8 3.2Q Check your answers' For 4through 9, solve each equation' 7, 56: 4. x + 8:5.6 8. n.2.1 :12 5. pX3.4:7'48 6. 4z - 1.4t 9.5_s+3.7 50.8 a pens that cost 65 cents each. she spent 10. sonja purchased some totalof$9.10'Howmanypensdidshepurchase?Writeanequation to describe the situation and solve' 11. Griticar Thinking n A 3.1 32n : B 12.4 gg.2,then what is the value of the expression 8n? solution as m 12" which equation has the same + 2'6 : 3'5? C 2.6m: 3.5 D 3.5m :2-6 A,m+3.5:2,6 B yn + 9,1 :2,6 ig. D32 G 24,8 get the variable p alone on one side writing to Explain Tell how you would of the equationS2'4 - 4P' 6 its affiliates' All Rights Reserved' Copyright o Pearson Education, lnc'' or Name #omrnon Core Standards Pnactice O.ruS.C.S Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world explaining the meaning of O in each creditydebits, context", situation. 2. 1. Which of the following represents a negative number? Circle all that apply. A B C D li,, l' rri Temperature can be measured in these temperatures is the coldest? A 1O.F deposit of $75 an increase of 2 inches in height a debt of $2 a loss of 5 pounds in weight B O"F c 5"F D 10"F 3. Write an integer to represent 25 feet underground. Explain your answer. 4. Write an integer to represent a rise of 150 feet. Explain your answer. 5. During a football game, Howard's team gained 14 yards in one play and lost 12 yards in the next play. Write integers to represent the two plays. copyright @ @ Pearson Education, tnc., or its affiliates. All Rights Reserved. 6 : i Wf ich of the following can be represented with -B? Circle all that apply. A A loss of $B B A rise of 8 feet uP to sea level C A temperature 8 degrees below zero D An oil drill digging 8 miles below the surface E F A deposit of $g in a bank account A change in temperature from 56"F to 64"F T. net income Last week, Cy earned slightly more money than he spent. ls his represented Oy , positive number or a negative number? Explain' g. be A submarine travels 875 feet below sea level. Should the depth represented by a positive number or a negative number? Explain. 9. During the day, the temperature changes from -5"F to *5'F' a, Does the temperature become Warmer or cooler? b. was the temperature that day ever 0'F? Explain how you know. 6 Copyright o Pearson Education, lnc., or its affiliates' All Rights Reserved'