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Chapt Name: Date: er Fractions and Mixed Numbers Practice 1 Adding Unlike Fractions Find two equivalent fractions for each fraction. Example © 2009 Marshall Cavendish International (Singapore) Private Limited 2 3 4 6 6 9 1. 3 4 2. 2 5 3. 5 6 4. 1 7 Express each fraction in simplest form. 5. 6 8 6. 8 20 7. 10 15 8. 9 21 Lesson 3.1 Adding Unlike Fractions G5_WB_Ch03.indd 93 93 1/12/09 6:24:24 PM Rewrite each pair of unlike fractions as like fractions. Example 1 4 1 4 9. 1 4 5 12 10. 1 10 2 5 11. 5 9 2 3 12. 3 8 9 16 Write equivalent fractions for each fraction. Then find the least common denominator of the fractions. Example 2 1 2 4 G5_WB_Ch03.indd 94 2 3 3 4 The least common denominator The least common denominator 6 . 1 4 is 15. . 5 6 5 6 3 8 The least common denominator The least common denominator is 94 13. 4 2 3 6 is 14. 3 = 6 . © 2009 Marshall Cavendish International (Singapore) Private Limited 2 4 1 2 is . Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:24 PM Name: Date: Shade and label each model to show the fractions. Then complete the addition sentence. Example 1, 1 2 3 © 2009 Marshall Cavendish International (Singapore) Private Limited 1 2 16. Find the multiples of 2 and 3. Choose the least common multiple. Use it to rewrite 12 and 13 as like fractions. 1 3 1 1 2 3 3 6 5 6 2 6 1, 1 5 2 1 1 5 2 Lesson 3.1 Adding Unlike Fractions G5_WB_Ch03.indd 95 95 1/12/09 6:24:24 PM Shade and label each model to show the fractions. Then complete the addition sentence. 1, 1 6 4 1 1 6 4 © 2009 Marshall Cavendish International (Singapore) Private Limited 17. 18. 1 2 5, 3 1 2 5 3 96 G5_WB_Ch03.indd 96 Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:24 PM Name: Date: Look at the model. Write two addition sentences. 11 12 19. Addition sentence 1: © 2009 Marshall Cavendish International (Singapore) Private Limited 12 20. 12 12 Addition sentence 2 (fractions in simplest form): Add. Express each sum in simplest form. 21. 1 1 3 9 22. 5 2 8 4 23. 1 6 2 7 24. 4 1 8 5 Lesson 3.1 Adding Unlike Fractions G5_WB_Ch03.indd 97 97 1/12/09 6:24:24 PM Use benchmarks to estimate each sum. Example 1 4 3 7 0 2 2 3 9 26. 7 1 3 9 7 5 98 G5_WB_Ch03.indd 98 1 4 7 0 1 + 4 is about 1. 3 7 25. 1 2 1 2 1 © 2009 Marshall Cavendish International (Singapore) Private Limited 1 is about 1 . 3 2 4 is about 1 . 2 7 1 +4 3 7 1 + 1 =1 2 2 1 3 Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:24 PM Name: Date: Practice 2 Subtracting Unlike Fractions Rewrite the fractions as like fractions and complete the subtraction sentence. Example 3 1 2 2 3 1 3 6 © 2009 Marshall Cavendish International (Singapore) Private Limited 3 1 2 1 3 2 6 What is the least common multiple of 2 and 3? 2 3 6 2 6 1 1 2 3 3 6 1 6 2 6 Lesson 3.2 G5_WB_Ch03.indd 99 Subtracting Unlike Fractions 99 1/12/09 6:24:24 PM Rewrite the fractions as like fractions and complete the subtraction sentence. 1. 1 3 1 4 1 4 © 2009 Marshall Cavendish International (Singapore) Private Limited 1 3 1 1 3 4 Subtract. Express each difference in simplest form. 2. 7 2 12 4 3. 4 1 5 3 4. 1 1 56 12 5. 7 1 9 6 100 G5_WB_Ch03.indd 100 Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:25 PM Name: Date: Use benchmarks to estimate each difference. Example 4 5 © 2009 Marshall Cavendish International (Singapore) Private Limited 4 3 5 8 4 is about 1. 5 3 is about 1 . 8 2 4– 3 5 8 1– 1 = 1 2 2 4 – 3 is about 1 . 2 5 8 6. 9 1 10 6 7. 5 1 12 9 0 1 2 1 1 2 1 3 8 0 Lesson 3.2 G5_WB_Ch03.indd 101 Subtracting Unlike Fractions 101 1/12/09 6:24:25 PM Darren drew a model to find 45 21 . His model is drawn incorrectly. Explain his mistakes. Then draw the correct model and find the difference. 4 5 ? Darren’s model is wrong because: © 2009 Marshall Cavendish International (Singapore) Private Limited 1 2 The correct model is: 102 G5_WB_Ch03.indd 102 Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:25 PM Name: Date: Practice 3 Fractions, Mixed Numbers, and Division Expressions Look at the diagram. Complete. © 2009 Marshall Cavendish International (Singapore) Private Limited Example 3 4 3 4 1. Lesson 3.3 Fractions, Mixed Nu mbers, and Division Expressions G5_WB_Ch03.indd 103 103 1/12/09 6:24:25 PM Write each division expression as a fraction. 2. 3. 3 10 5 7 4. 5. 2 11 4 9 Write each fraction as a division expression. 7 7 8 7. 8 1 10 6. 5 12 8. 6 7 Look at the diagram. Complete. Example 4 3 4 3 104 G5_WB_Ch03.indd 104 © 2009 Marshall Cavendish International (Singapore) Private Limited Example 1 1 3 Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:25 PM Name: Date: Look at the diagram. Complete. © 2009 Marshall Cavendish International (Singapore) Private Limited 9. Complete. 10. 11. 35 11 7 4 1 3 Lesson 3.3 Fractions, Mixed Nu mbers, and Division Expressions G5_WB_Ch03.indd 105 105 1/12/09 6:24:26 PM Divide. Express each quotient as a mixed number. Example 12. 5 3 1 2 3 1 3 5 3 2 14. 9 4 2 18 5 3 Write each fraction in simplest form. Then divide to express each quotient as a mixed number. 15. 106 G5_WB_Ch03.indd 106 16. 18 4 22 6 © 2009 Marshall Cavendish International (Singapore) Private Limited 13. 7 2 3 Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:26 PM Name: Date: Practice 4 Expressing Fractions, Division Expressions and Mixed Numbers as Decimals Write each fraction as a decimal. Example 3 5 © 2009 Marshall Cavendish International (Singapore) Private Limited 2. 6 10 1. 13 20 0.6 19 25 3. 47 50 Express each division expression as a mixed number in simplest form and as a decimal. Division expression 4. 72 5. 94 6. 21 5 7. 101 25 Express division expression as a mixed number a decimal Lesson 3.4 Expressing Fractions, D ivision Expressions and Mixed Numbers as Decimals G5_WB_Ch03.indd 107 107 1/12/09 6:24:26 PM Express each improper fraction as a decimal. Example 3 2 =2+ 1 8. 22 5 10. 32 25 2 2 =1+ 1 2 = 1 + 0.5 9. 47 20 Solve. Show your work. 11. 108 G5_WB_Ch03.indd 108 A coil of rope 603 feet long is cut into 25 equal pieces. What is the length of each piece? Express your answer as a mixed number and as a decimal. © 2009 Marshall Cavendish International (Singapore) Private Limited = 1.5 Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:26 PM Name: Date: Practice 5 Adding Mixed Numbers Add. Express each sum in simplest form. Example 3 5 1 2 8 4 3 5 2 8 © 2009 Marshall Cavendish International (Singapore) Private Limited 5 2 8 7 5 8 8 1. 1 1 4 2 1 2 3 4 1 2 3 1 4 2 3 2. 2 1 1 3 5 2 2 5 3 1 5 1 2 Lesson 3.5 G5_WB_Ch03.indd 109 Adding Mixed Numbers 109 1/12/09 6:24:26 PM Add. Express each sum in simplest form. 5 3 27 2 14 4. 7 5 12 3 14 5. 1 3 4 15 110 6. 12 19 9 56 © 2009 Marshall Cavendish International (Singapore) Private Limited 3. Add. Express each sum in simplest form. 7. 145 2 13 1 2 3 4 110 G5_WB_Ch03.indd 110 4 5 1 3 Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:26 PM Name: Date: Add. Express each sum in simplest form. 8. 5 1 23 3 12 3 1 © 2009 Marshall Cavendish International (Singapore) Private Limited 4 5 5 12 2 3 9. 2 34 3 25 10. 2 59 156 11. 5 7 89 9 12 12. 7 5 12 134 Lesson 3.5 G5_WB_Ch03.indd 111 Adding Mixed Numbers 111 1/12/09 6:24:26 PM Use benchmarks to estimate each sum. Example 3 5 5 3 is about 1 . 5 2 So, 6 3 is about 6 1 . 5 2 0 5 6 5 is about 1. 6 So, 4 5 is about 5. 6 0 63 + 4 5 5 6 6 1 + 5 = 11 1 2 2 6 3 + 4 5 is about 11 1 . 5 6 6 2 5 13. 9 7 7 12 14. 4 12 10 9 112 G5_WB_Ch03.indd 112 7 1 1 2 1 2 1 © 2009 Marshall Cavendish International (Singapore) Private Limited 3 65 46 1 Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:26 PM Name: Date: Practice 6 Subtracting Mixed Numbers Subtract. Express each difference in simplest form. Example 2 5 3 3 12 3 8 12 © 2009 Marshall Cavendish International (Singapore) Private Limited 3 5 12 3 12 1 3 2 3 4 1. 8 1 49 33 8 4 9 3 1 8 9 Lesson 3.6 G5_WB_Ch03.indd 113 Subtracting Mixed Numbers 113 1/12/09 6:24:26 PM Subtract. Express each difference in simplest form. 2. 3 7 3 2 12 8 3 2 1 3 5 1 1 9 2 4. 7 5 1 2 6 4 © 2009 Marshall Cavendish International (Singapore) Private Limited 3. 7 12 Subtract. Express each difference as a mixed number. 5. 3 7 1 18 4 3 1 7 8 1 4 114 G5_WB_Ch03.indd 114 Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:26 PM Name: Date: Subtract. Express each difference as a mixed number. 6. 5 1 3 5 3 12 5 3 5 12 © 2009 Marshall Cavendish International (Singapore) Private Limited 1 3 1 1 1 5 3 7. 4 9. 7 4 5 12 G5_WB_Ch03.indd 115 1 11 3 5 3 8 6 8. 6 10. 83 44 1 3 Lesson 3.6 Subtracting Mixed Numbers 115 1/12/09 6:24:27 PM Use benchmarks to estimate each difference. Example 2 9 5 2 is about 0. 9 So, 7 2 is about 7. 9 0 72 6 5 12 1 1 762 2 7 2 6 5 is about 1 . 9 12 2 11. 12 2 8 7 12. 20 8 5 9 116 G5_WB_Ch03.indd 116 5 12 1 3 1 1 2 1 5 12 5 is about 1 . 12 2 5 so, 6 is about 6 1 . 12 2 9 1 2 0 © 2009 Marshall Cavendish International (Singapore) Private Limited 2 7 9 6 12 Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:27 PM Name: Date: Practice 7 Real-World Problems: Fractions and Mixed Numbers © 2009 Marshall Cavendish International (Singapore) Private Limited Solve. Show your work. 1. Elena has 12 pieces of banana bread. She gives an equal amount of banana bread to 5 friends. How many pieces of banana bread does she give each friend? 2. A utility bill shows that a household used 2,001 gallons of water in a 5-day period. What was the average amount of water used by the household each day? 3. A ball of string is 50 yards long. A shipper uses 5 yards of string to tie packages. The remaining string is then cut into 7 equal pieces. What is the length of each of the 7 pieces of string? Lesson 3.7 Real-World Problems: Fractions and Mixed Numbers G5_WB_Ch03.indd 117 117 1/12/09 6:24:27 PM 4. Steve picks 55 pounds of pears. He packs an equal amount of pears into 6 bags. He then has 4 pounds of pears left. What is the weight of pears in each bag? 5. Jeremy puts an empty container under a leaking faucet. In the 3 first hour, quart of water collects. In the second hour, 8 1 quart of water collects. How much water collects in the 6 container in the two hours? 118 G5_WB_Ch03.indd 118 © 2009 Marshall Cavendish International (Singapore) Private Limited Solve. Show your work. Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:27 PM Name: Date: Solve. Show your work. © 2009 Marshall Cavendish International (Singapore) Private Limited 6. 7. 8 3 Arnold buys pound of ground turkey. He uses pound of the 9 4 ground turkey to make meatballs. How many pounds of ground turkey are left? A snail is at the bottom of a well. In the first 10 minutes, the snail climbs 7 5 23 inches. In the next 10 minutes, it climbs 19 inches. How far is 12 6 the snail from the bottom of the well after 20 minutes? Lesson 3.7 Real-World Problems: Fractions and Mixed Numbers G5_WB_Ch03.indd 119 119 1/12/09 6:24:27 PM Solve. Show your work. 8. Johnny is jogging along a track. He has already jogged 1 1 2 miles. 3 © 2009 Marshall Cavendish International (Singapore) Private Limited He plans to jog a total of 3 miles. How many miles does 4 he have left to jog? 120 G5_WB_Ch03.indd 120 Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:27 PM Name: Date: Practice 8 Real-World Problems: Fractions and Mixed Numbers © 2009 Marshall Cavendish International (Singapore) Private Limited Solve. Show your work. 1. Susanne and Barry each buy 4 equal-sized bagels. They divide the bagels equally among themselves and 3 other friends. How many bagels does each person get? 2. Maya has 5 sheets of paper. She cuts each sheet into 3 equal-sized rectangles. The rectangles are shared equally among 6 students. How many rectangles does each student get? Lesson 3.7 Real-World Problems: Fractions and Mixed Numbers G5_WB_Ch03.indd 121 121 1/12/09 6:24:27 PM Solve. Show your work. Mrs. Quirk buys 1 quart of milk. Michael drinks 2 quart of it. 7 1 Joel drinks quart of it. How many quarts of milk are left? 3 © 2009 Marshall Cavendish International (Singapore) Private Limited 3. 122 G5_WB_Ch03.indd 122 Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:27 PM Name: Date: Solve. Show your work. 4. An organic farmer buys a piece of land. She plants tomatoes on 5 of the land and green beans on 1 of the land. 9 12 © 2009 Marshall Cavendish International (Singapore) Private Limited She plants potatoes on the remaining piece of land. What fraction of the land does she plant with potatoes? Lesson 3.7 Real-World Problems: Fractions and Mixed Numbers G5_WB_Ch03.indd 123 123 1/12/09 6:24:27 PM Solve. Show your work. 5. A package contains three types of bagels, plain, wheat and sesame. 2 3 The weight of the plain bagels is 1 pounds. The weight of the wheat 5 6 bagels is 2 pounds. The total weight of the three types of bagels is © 2009 Marshall Cavendish International (Singapore) Private Limited 5 pounds. What is the weight of the sesame bagels? 124 G5_WB_Ch03.indd 124 Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:27 PM Name: Date: Solve. Show your work. 6. 1 4 Reggie and Jay go for a walk every morning. Reggie walks 2 miles. 3 8 Jay walks 1 miles less than Reggie. What is the total distance © 2009 Marshall Cavendish International (Singapore) Private Limited they walk every morning? Lesson 3.7 Real-World Problems: Fractions and Mixed Numbers G5_WB_Ch03.indd 125 125 1/12/09 6:24:27 PM Solve. Show your work. 7. Alicia uses 3 gallon of paint to paint her room. Becca uses 4 gallon 4 5 © 2009 Marshall Cavendish International (Singapore) Private Limited more than Alicia to paint her room. How many gallons of paint do they use altogether? 126 G5_WB_Ch03.indd 126 Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:27 PM Name: Date: Solve. Show your work. 3 A monkey climbs 3 feet up a coconut tree that has a height 5 of 10 feet. It rests for a while and continues to climb another 2 4 feet up the tree. How many more feet must the monkey climb to 3 reach the top of the tree? © 2009 Marshall Cavendish International (Singapore) Private Limited 8. Lesson 3.7 Real-World Problems: Fractions and Mixed Numbers G5_WB_Ch03.indd 127 127 1/12/09 6:24:27 PM 1 2 8 3 ? 2 1 to . 3 8 © 2009 Marshall Cavendish International (Singapore) Private Limited Draw a model, and explain the steps you can use to add 128 G5_WB_Ch03.indd 128 Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:27 PM Name: Date: Put On Your Thinking Cap! Challenging Practice Solve. Show your work. Tina, Troy and Nate had a total of 25 equal-sized square tiles to place over a square grid. Tina used 8 of the square tiles. Troy used 1 of the square tiles. Shade the 25 5 square grid below to show how Tina and Troy could have placed the square tiles. What fraction of the square grid must Nate place the tiles on so that 1 of the 5 © 2009 Marshall Cavendish International (Singapore) Private Limited square grid is not covered? Chapter 3 Fractions an d Mixed Numbers G5_WB_Ch03.indd 129 129 1/12/09 6:24:27 PM Put On Your Thinking Cap! Problem Solving Solve. Use a model to help you. © 2009 Marshall Cavendish International (Singapore) Private Limited Paul mixes cement with sand. He uses 3 3 kilograms of cement and 1 kilogram 4 2 more sand than cement. He needs 10 kilograms of the mixture. Does he have enough mixture? If yes, how much more does he have and if no, how much more does he need? 130 G5_WB_Ch03.indd 130 Chapter 3 Fractions and Mixed Numbers 1/12/09 6:24:28 PM