Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Practice Name 9-6 Finding Common Denominators In 1 through 8, find a common denominator for each pair of fractions. 1. 5. Sample answers are given. 3 5 5 2 and __ 4 1 and __ 4 7 __ 2. __ and __ 3. __ 4. ___ and __ 5 7 28 4 20 8 9 72 4 12 9 36 5 7 and __ 1 1 and __ 2 2 and __ 4 7 and __ ___ 6. __ 7. __ 8. __ 5 45 15 3 15 2 3 6 9 8 6 24 In 9 through 16, find a common denominator for each pair of fractions. Then rename each fraction in the pair. Sample answers are given. 3 3 1 2 1 2 ___ __ __ __ __ __ 9. 12 and 8 6 __ 9 24; __ , 24 24 7 and __ 1 13. __ 9 6 10. 8 and 7 9 1 and __ 1 12. __ 5 3 7 and __ 2 15. __ 3 5 16. __ and __ 11. 2 and 9 __ 4 16 7 __ __ 18; , , 56; __ 18 18 56 56 3 1 and __ 14. __ 6 4 8 3 5 __ 3 15; __ , 15 15 8 9 16 14 __ 2 __ 21 __ 3 __ __ , 12; , 24; , 18; __ 18 18 12 12 24 24 6 9 __ 20 24; __ , 24 24 18. Andrew wants to rename _27 and _3 using a common denominator. 4 Which of the following shows these fractions renamed correctly? 17. Train A arrives at Central Station on the hour and every 12 minutes. Train B arrives on the hour and every 15 minutes. When do both trains arrive at the same time? 8 21 and ___ A ___ A On the hour and 30 minutes past the hour B On the hour and 15 minutes to the hour C On the hour and 27 minutes past the hour D On the hour only 28 28 3 2 and ___ B ___ 28 28 6 4 and ___ C ___ 28 28 3 2 and __ D __ 7 7 11 19. Manuel says that you can use one of the denominators of _56 and __ when 30 renaming these fractions using a common denominator. Why is this true? Sample answer: You can use 30 as the common denominator since 30 is a common multiple of 6 and 30. P 9•6 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 Practice Name 9-7 Adding Fractions with Unlike Denominators Find each sum. Simplify if necessary. 2 + __ 1 1. __ 9 3 1 + __ 2 4. __ 4 3 5 1 + ___ 7. __ 6 12 3 1 10. __ + __ 9 4 5 __ 9 11 ___ 12 7 ___ 12 31 ___ 36 3 1 + ___ 2. __ 7 21 4 1 + __ 5. ___ 12 6 1 4 + __ 8. __ 3 6 6 1 11. ___ + __ 12 3 2 __ 7 3 __ 4 2 + __ 1 __ 5 3 3. 1 + __ 2 6. __ 5 2 1 1 + __ 1 9. __ 5 8 5 __ 6 13 ___ 15 9 ___ 10 13 ___ 40 1 4 + __ 1 __ 8 2 12. Jeremy collected nickels for one week. He is making stacks of his nickels to determine how many he has. The thickness of one 1 inch. nickel is __ 16 13. How tall is a stack of 16 nickels? 1 inch 14. What is the combined height of 3 nickels, 2 nickels, and 1 nickel? 3 __ inch 8 5 4? 15. What is the sum of ___ + __ 30 5 A __ 6 6 7 B __ 9 9 D ___ 2 C __ 3 12 11 ? What is the sum? 16. How do you rename _25 so you can add it to __ 25 Use 25 as the common denominator. Multiply the numerator and denominator 10 21 . by 5 to get ___ . The sum is ___ 25 25 P 9•7 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 Practice Name 9-8 Subtracting Fractions with Unlike Denominators Find the difference. Simplify if necessary. 10 1 1. ___ − __ 12 4 7 − __ 1 4. ___ 12 4 4 − __ 1 7. __ 8 4 9 1 10. ___ − __ 15 3 7 ___ 12 1 __ 3 1 __ 4 4 ___ 15 3 ___ 10 7 ___ 15 1 __ 5 1 __ 6 9 3 2. ___ − __ 5 10 4 − __ 1 5. __ 5 3 4 − __ 1 8. ___ 5 10 4 − __ 1 11. ___ 12 6 7 − __ 2 3. __ 8 6 2 − __ 1 6. __ 3 6 9 2 9. __ − __ 9 3 3 14 − __ 12. ___ 5 20 13. The pet shop owner told Jean to fill her new fish tank _34 full 9 full. What fraction of the tank does with water. Jean filled it __ 12 Jean still need to fill? 14. Paul’s dad made a turkey potpie for dinner on Wednesday. The family ate _48 of the pie. On Thursday after school, Paul 2 of the pie for a snack. What fraction of the pie remained? ate __ 16 13 ___ 24 1 __ 2 1 __ 3 1 ___ 10 0 3 __ 8 15. Gracie read 150 pages of a book. The book is 227 pages long. Which equation shows the amount she still needs to read to finish the story? A 150 − n = 227 C n − 150 = 227 B 227 + 150 = n D n + 150 = 227 16. Why do fractions need to have a common denominator before you add or subtract them? The denominator tells you how many equal parts you are adding or subtracting. The parts must be the same when you add or subtract. P 9•8 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 Practice Name 10-1 Improper Fractions and Mixed Numbers 1. Draw a picture to show _86. 2. Draw a picture to show 3_56. Check students’ drawings. Write each improper fraction as a whole number or mixed number in simplest form. 5 30 3. __ 6 5_29 47 4. __ 9 52 5. __ 7 Write each mixed number as an improper fraction. __ 24 5 6. 4_45 __ 55 4 7. 13_34 8. 9_58 7_37 __ 77 8 __ 32 9. Write 8 as an improper fraction with a denominator of 4. 4 Which letter on the number line corresponds to each number? F 4 27 10. __ 5 A C D B 5 7 11. 4__ 10 D E C 6 12. 4_35 A 13. Which number does the model represent? 12 A __ 8 B 2_38 C 2_47 20 D __ 8 14. Can you express _99 as a mixed number? Why or why not? No, _99 can be expressed only as a fraction or as a whole number (1). P 10•1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 Practice Name 10-4 Adding Mixed Numbers In 1 through 6, find each sum. Simplify, if possible. Estimate for reasonableness. 5 2 + 8__ 1. 7__ 3 6 9 1 3. 11___ + 3___ 10 20 8 1 5. 5__ + 3__ 9 2 16_12 19 14__ 20 7 9__ 18 3 2 2. 4__ + 2__ 5 4 6 2 4. 7__ + 5__ 7 7 11 + 17__ 2 6. 21___ 12 3 3 7__ 20 13_17 7 39__ 12 7. Write two mixed numbers that have a sum of 3. Sample answer: 1_14 + 1_34 = 3 8. What is the total measure of an average man’s brain and heart in kilograms (kg)? 7 1__ kg 10 Vital Organ Measures Average woman’s brain 3 1___ kg 4 lb 2__ 5 Average man’s brain 2 kg 1__ 5 3 lb Average human heart 3 ___ kg 10 7 lb ___ 10 9. What is the total weight of an average woman’s brain and heart in pounds (lb)? 10. What is the sum of the measures of an average man’s brain and an average woman’s brain in kilograms? 10 3_12 lb 7 2__ kg 10 11. Which is a good comparison of the estimated 11 ? sum and the actual sum of 7_78 + 2__ 12 A Estimated < actual C Actual > estimated B Actual = estimated D Estimated > actual 12. Can the sum of two mixed numbers be equal to 2? Explain why or why not. No; Sample answer: It is impossible for two mixed numbers to equal 2 because every mixed number is greater than 1. P 10•4 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 Practice Name 10-5 Subtracting Mixed Numbers For 1 through 10, find each difference. Simplify, if possible. 3 10__ 1. 3 7__ 1 7 2. 4 1 − 7__ 8 − 2___ 1 3__ 1 5___ 4 1 − 3__ 1 7. 6__ 4 3 2 − 7__ 1 9. 8__ 7 3 13 2___ 1 __ 3 5 5__ 12 8 1 − 3__ 7 8. 5__ 5 8 9 1 10. 2___ − 2__ 10 The table shows the length and width of several kinds of bird eggs. 1_12 in. longer 12. How much wider is the turtledove egg than the robin egg? 3 1 2___ 12 13 1___ 40 17 ___ 30 Egg Sizes in Inches (in.) 11. How much longer is the Canada goose egg than the raven egg? 3 __ 10 3 − 12___ 3 2 6. 4__ − 2__ 4 3 18 11 2___ 12 20 ___ 21 8 2 − 2__ 21 5 5 − 6__ 5. 9__ 9 6 71 17__ 4. 3 21 2 31 3. Bird Length Width Canada goose 2 3__ 3 2___ Robin 3 __ 3 __ 4 5 Turtledove 1 1__ 9 ___ Raven 9 1___ 3 1___ in. wider 5 10 5 10 10 10 15 13. Which is the difference of 21__ − 18_34 ? 16 7 A 2___ 16 9 B 2___ 16 3 C 3___ 16 9 D 3___ 16 14. Explain why it is necessary to rename 4_14 if you subtract _34 from it. Sample answer: You cannot subtract _34 from _14 , so you must borrow 1 whole from the 4 and rename 4_14 as 3_54 . P 10•5 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5