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Lesson 8.1 Reteach Name Multiples of Unit Fractions A unit fraction is a fraction with a numerator of 1. You can write a fraction as the product of a whole number and a unit fraction. 7 Write __ 10 as the product of a whole number and a unit fraction. 7 Write __ 10 as the sum of unit fractions. 1 7 5 __ __ 10 1 1 __ 1 1 1 1 1 __ __ __ __ __ 10 1 10 1 10 1 10 1 10 1 10 10 Use multiplication to show repeated addition. 7 5 __ 10 1 7 3 __ 10 1 __ 7 5 7 3 So, __ 10 . 10 The product of a number and a counting number is a multiple of the number. You can find multiples of unit fractions. 1. List the next 4 multiples of _ 8 Make a table and use repeated addition. 1 13_ 8 1 23_ 8 _ 331 8 _ 431 8 _ 531 8 1 _ 8 111 _ _ 8 8 2 _ 8 11_ 11_ 1 _ 8 8 8 3 _ 8 11_ 111 _ _11 _ 8 8 8 8 4 _ 8 1 111 111 _1_ _1_ _ 8 8 8 8 8 5 _ 8 1 _ 8 The next 4 multiples of 1_8 are 2 5 _ 3_ 4_ _ and 8 , 8 , 8 , 8 . Write the fraction as the product of a whole number and a unit fraction. 2 1. __ 5 5 2. ___ 5 12 7 3. __ 5 2 5 List the next four multiples of the unit fraction. 1, 4. __ 4 , , 1, 5. __ 6 , Chapter Resources © Houghton Mifflin Harcourt Publishing Company 8-5 , , , Reteach Lesson 8.1 Enrich Name Mixed Numbers and Unit Fractions Write each mixed number as the product of a whole number and a unit fraction. 1. __ 11 3 2. __ 31 2 3. __ 13 5 4. __ 23 8 5. 3 3 __ 4 6. __ 52 3 7. 2 4 __ 5 8. __ 51 5 9. Explain how you found the answer in Exercise 1. Chapter Resources © Houghton Mifflin Harcourt Publishing Company 8-6 Enrich Lesson 8.2 Reteach Name Multiples of Fractions You have learned to write multiples of unit fractions. You can also write multiples of other fractions. 2. Write the next 4 multiples of _ 5 Make a table. 2 13_ 5 2 23_ 5 _ 332 5 _ 432 5 _ 532 5 2 _ 5 212 _ _ 5 5 _4 5 21_ 21_ 2 _ 5 5 5 _6 5 21_ 212 _ _12 _ 5 5 5 5 _8 5 2 212 212 _1_ _1_ _ 5 5 5 5 5 10 __ 5 2 _ 5 4 _ 6 _ 8 _ 10 __ 5 . So, the next 4 multiples of 2_5 are 5 , 5 , 5 , and Write 3 3 2_5 as the product of a whole number and a unit fraction. 2. Use a number line. Make three jumps of _ 5 6 25_ 33_ 5 5 0 1 5 2 5 1 23_ 5 3 5 4 5 5 5 1 43_ 5 6 5 7 5 1 63_ 5 8 5 9 5 1 83_ 5 1 256 _, or 6 3 _ . So, 3 3 _ 5 5 5 List the next four multiples of the fraction. 3, 1. __ , 4 , , 5, 2. __ , 6 , , Write as the product of a whole number and a unit fraction. 3. 4. 0 0 1 2 3 4 5 6 7 8 9 10 8 8 8 8 8 8 8 8 8 8 35 3 3 __ 8 Chapter Resources © Houghton Mifflin Harcourt Publishing Company 8-7 1 3 2 3 3 3 4 3 5 3 6 7 8 9 10 3 3 3 3 3 25 4 3 __ 3 Reteach Lesson 8.2 Enrich Name Multiples of Mixed Numbers List the next three multiples of the mixed number. Write each multiple as a mixed number or as a whole number. 1. __ 11 8 2. __ 21 2 3. __ 12 3 4. __ 21 3 5. 1 3 __ 5 6. 1 1__ 4 7. __ 13 5 8. 3 2 __ 4 9. Describe a method other than multiplication that you can use to find the next three multiples of the mixed number in Exercise 7. Chapter Resources © Houghton Mifflin Harcourt Publishing Company 8-8 Enrich Lesson 8.3 Reteach Name Multiply a Fraction by a Whole Number Using Models You can use a model to multiply a fraction by a whole number. _. Find the product of 4 3 3 5 3 each. Use fraction strips. Show 4 groups of _ 5 1 5 1 5 1 5 1 5 1 5 3 _5_ 1 group of 3 5 5 1 5 1 5 1 5 1 5 1 5 6 _5_ 2 groups of 3 5 5 1 5 1 5 1 5 1 5 1 5 9 _5_ 3 groups of 3 5 5 1 5 1 5 1 5 1 5 1 5 _ 5 12 __ 4 groups of 3 5 5 3 5 12 __. So, 4 3 _ 5 5 Multiply. 1. 2. __ 5 235 6 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 __ 5 337 8 3. 25 6 3 __ 3 4. 9 5 2 3 ___ 10 5. 35 5 3 __ 4 6. 55 4 3 __ 8 7. 25 7 3 __ 5 8. 45 8 3 __ 6 Chapter Resources © Houghton Mifflin Harcourt Publishing Company 8-9 Reteach Lesson 8.3 Enrich Name Fraction of a Whole Number Find the product. Write the product as a whole number. __ 1. 1 3 24 5 __ 2. 2 3 15 5 __ 3. 3 3 10 5 __ 4. 4 3 14 5 __ 5. 5 3 18 5 __ 6. 3 3 16 5 2 7. __ 3 27 5 7 8. __ 3 32 5 8 5 6 9 3 7 4 8 9 9. ___ 3 50 5 4 10. __ 3 45 5 5 11. ___ 3 60 5 __ 12. 8 3 54 5 10 12 13. 5 9 Explain how you can tell if the product of a fraction and a whole number will be a whole number. Chapter Resources © Houghton Mifflin Harcourt Publishing Company 8-10 Enrich Lesson 8.4 Reteach Name Multiply a Fraction or Mixed Number by a Whole Number To multiply a fraction by a whole number, multiply the numerators. Then multiply the denominators. A recipe for one loaf of bread calls for 2 1_4 cups of flour. How many cups of flour will you need for 2 loaves of bread? Step 1 Write and solve an equation. 9 _52 _3_ 2 3 21 4 1 4 39 _____ 52 134 2. Write 21 _ as a fraction. Write 2 as _ 1 4 Multiply the numerators. Then multiply the denominators. __ Simplify. 5 18 4 Step 2 Write the product as a mixed number. 18 5 _ 11_ 11_ 111 11_ 11_ 11_ 11_ 11_ 11_ 11_ 11_ 11_ 11_ 11_ 11_ 111 _ __ _1_ 4 4 4 4 4 4 4 1 1 1 _1 _ 4 4 5 + + 4 1 _ 42 4_ 4 2 5 , or 1 4_ 2 So, you will need 4 4 1 1 4 4 4 4 4 4 5 5 4 5 5 4 1 1 1 4 4 1 _ 1_11 4 4 Combine the wholes. Then combine the remaining parts. Add. Write the sum as a mixed number. cups of flour. Multiply. Write the product as a mixed number. 1. 25 3 3 __ 5 2. __ 5 433 8 3. __ 5 531 3 4. 3 5 2 3 1___ 10 5. 25 4 3 1__ 3 6. __ 5 7 3 11 6 Chapter Resources © Houghton Mifflin Harcourt Publishing Company 8-11 Reteach Lesson 8.4 Enrich Name Unknown Numbers Find the unknown number that makes each equation true. 1. 3. 5. 1 3 5 2__ 3 __ 4 4 2. 3 4 3 __ 5 1__ 5 5 5 5 1__ 9 4. 23 73 1 55 9 __ 3 1__ 6 6 6. 2 1 __ 5 6 __ 3 3 5 2 5 13 __ 3 2__ 7 7 Explain how you found the unknown number in 7. Exercise 3. Chapter Resources © Houghton Mifflin Harcourt Publishing Company 8-12 Enrich Lesson 8.5 Reteach Name Problem Solving • Comparison Problems with Fractions The Great Salt Lake in Utah is about 4_5 mile above sea level. Lake Titicaca in South America is about 3 times as high above sea level as the Great Salt Lake. About how high above sea level is Lake Titicaca? Read the Problem Solve the Problem What do I need to find? I need to find about how high above sea level Lake Titicaca is. Draw a comparison model. Compare the heights above sea level of the Great Salt Lake and Lake Titicaca, in miles. Great Salt Lake 4 _ 5 Lake Titicaca _4 5 What information do I need to use? _4 5 _4 5 _4 5 5 mile The Great Salt Lake is about above sea level. Lake Titicaca is about 3 times as high above sea level. t Write an equation and solve. How will I use the information? I can draw a diagram to compare the heights. t is the height above sea level of Lake Titicaca, in miles. t5 3 t5 t5 _4 3 5 12 __ 5 _ 22 5 Write an equation. Multiply. Write the fraction as a mixed number. _ 22 So, Lake Titicaca is about 5 miles above sea level. 1. 2. Amelia is training for a triathlon. She swims 3_5 mile. Then she runs about 6 times farther than she swims. About how far does Amelia run? Chapter Resources © Houghton Mifflin Harcourt Publishing Company 8-13 Last week, Meg bought 1 3_4 pounds of fruit at the market. This week, she buys 4 times as many pounds of fruit as last week. In pounds, how much fruit does Meg buy this week? Reteach Lesson 8.5 Enrich Name Heights and Depths Solve each problem. You may find it helpful to draw a diagram. 1. The depth of Lake Carl is about 1 1_8 miles. Lake Susan is 3 times as deep as Lake Carl. Lake Wayne is 2 times as deep as Lake Susan. How much deeper is Lake Wayne than Lake Susan? 2. Mount Rogers rises 1_4 mile above sea level. Mount Taylor rises 6 times as high as Mount Rogers. Mount Sullivan rises 2 times as high as Mount Rogers. What is the difference in the elevation of Mount Taylor and the elevation of Mount Sullivan? 3. A certain tree was 5 1_3 feet tall when it was first planted. A few years later, the tree is 4 times as tall as it was when it was first planted. How much has the tree grown since it was first planted? 4. Explain how you solved Problem 3. Chapter Resources © Houghton Mifflin Harcourt Publishing Company 8-14 Enrich