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Multiples of Unit Fractions Lesson 8.1 Name Reteach 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 __1 __1 __1 __1 __1 __1 __7 5 1 1 1 1 1 1 10 10 10 10 10 10 10 10 Use multiplication to show repeated addition. __7 5 7 3 __1 10 10 __1 So, __7 5 7 3 10 10 . The product of a number and a counting number is a multiple of the number. You can find multiples of unit fractions. List the next 4 multiples of _1 . 8 Make a table and use repeated addition. 1 3 _1 2 3 _ 1 3 3 _1 4 3 _1 5 3 _1 8 8 8 8 8 1 _ _1 1 _1 _1 1 _1 1 _1 _1 1 _1 1 _1 1 _1 _1 1 _1 1 _1 1 _1 1 _1 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 _2 _3 _4 _5 _1 8 8 8 8 8 2 3 4 5 _ _ _ _ _1 The next 4 multiples of 8 are 8 , 8 , 8 , and 8 . Write the fraction as the product of a whole number and a unit fraction. 1. __2 5 2. ___5 5 3. __7 5 5 12 2 List the next four multiples of the unit fraction. 4. __1 , 5. __1 , 4 , , , 6 , , , Chapter Resources 8-5 Reteach © Houghton Mifflin Harcourt Publishing Company Lesson 8.1 Name Enrich Mixed Numbers and Unit Fractions Write each mixed number as the product of a whole number and a unit fraction. 1 1 1. 1 __ 2. 3 __ 3 2 3 3 3. 1 __ 4. 2 __ 5 8 3 2 5. 3 __ 6. 5 __ 4 3 2 1 7. 4 __ 8. 5 __ 5 5 9. Explain how you found the answer in Exercise 1. Chapter Resources 8-6 Enrich © Houghton Mifflin Harcourt Publishing Company Lesson 8.2 Name Reteach Multiples of Fractions You have learned to write multiples of unit fractions. You can also write multiples of other fractions. Write the next 4 multiples of _2 . 5 Make a table. 1 3 _2 2 3 _ 2 3 3 _2 4 3 _2 5 3 _2 5 5 5 5 5 2 _ _2 1 _2 _2 1 _2 1 _2 _2 1 _2 1 _2 1 _2 _2 1 _2 1 _2 1 _2 1 _2 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 2 _4 _6 _8 __10 _ 5 5 5 5 5 _4 _6 _8 __10 _2 So, the next 4 multiples of 5 are 5 , 5 , 5 , and 5 . 3 _2 Write 3 5 as the product of a whole number and a unit fraction. Use a number line. Make three jumps of _2 . 5 3 3 _2 5 _6 5 5 0 1 2 3 4 5 6 7 8 9 5 5 5 5 5 5 5 5 5 2 3 _1 4 3 _1 6 3 _1 8 3 _1 5 5 5 5 2 6 _1 So, 3 3 _ 5 _ , or 6 3 . 5 5 5 List the next four multiples of the fraction. 1. __3 , 2. __5 , 4 , , , 6 , , , Write as the product of a whole number and a unit fraction. 3. 4. 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 8 8 8 8 8 8 8 8 8 8 3 3 3 3 3 3 3 3 3 3 3 2 3 3 __ 5 4 3 __ 5 8 3 Chapter Resources 8-7 Reteach © Houghton Mifflin Harcourt Publishing Company Lesson 8.2 Name Enrich 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 1 1. 1 __ 2. 2 __ 8 2 2 1 3. 1 __ 4. 2 __ 3 3 1 1 5. 3 __ 6. 1 __ 5 4 3 3 7. 1 __ 8. 2 __ 5 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 8-8 Enrich © Houghton Mifflin Harcourt Publishing Company Lesson 8.3 Name Reteach 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 Use fraction strips. Show 4 groups of _3 each. 5 1 1 1 1 1 1 group of _3 5 _3 5 5 5 5 5 5 5 1 1 1 1 1 2 groups of _3 5 _6 5 5 5 5 5 5 5 1 1 1 1 1 3 groups of _3 5 _9 5 5 5 5 5 5 5 1 1 1 1 1 4 groups of _3 5 12__ 5 5 5 5 5 5 5 So, 4 3 _3 5 __12 . 5 5 Multiply. 1. 2. 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 5 7 2 3 __ 5 3 3 __ 5 6 8 2 9 3 3. 6 3 __ 5 4. 2 3 ___ 5 5. 5 3 __ 5 3 10 4 5 2 4 6. 4 3 __ 5 7. 7 3 __ 5 8. 8 3 __ 5 8 5 6 Chapter Resources 8-9 Reteach © Houghton Mifflin Harcourt Publishing Company Lesson 8.3 Name Enrich 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 8 3 3. __3 3 10 5 4. __4 3 14 5 5 7 5. __5 3 18 5 6. __3 3 16 5 6 4 7. __2 3 27 5 8. __7 3 32 5 9 8 9. ___9 3 50 5 10. __4 3 45 5 10 5 11. ___5 3 60 5 12. __8 3 54 5 12 9 13. Explain how you can tell if the product of a fraction and a whole number will be a whole number. Chapter Resources 8-10 Enrich © Houghton Mifflin Harcourt Publishing Company Lesson 8.4 Name Reteach 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. _1 A recipe for one loaf of bread calls for 2 4 cups of flour. How many cups of flour will you need for 2 loaves of bread? Step 1 Write and solve an equation. 2 3 2 _1 5 _2 3 _9 Write 2 as _2 . Write 2 _1 as a fraction. 4 1 4 1 4 3 5 _____2 9 Multiply the numerators. 1 3 4 Then multiply the denominators. 5 __18 Simplify. 4 Step 2 Write the product as a mixed number. __ 18 5 _1 1 _1 1 _1 1 _1 1 _1 1 _1 1 _1 1 _1 1 _1 1 _1 1 _1 1 _1 1 _1 1 _1 1 _1 1 _1 1 _1 1 _1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 _1 1 1 1 1 1 1 1 1 1 _1 4 4 _1 1 _ 5 4 + 4 + 4 Combine the wholes. Then combine the remaining parts. _2 _1 4 4 5 4 , or 2 Add. Write the sum as a mixed number. 1 4 _ So, you will need 2 cups of flour. Multiply. Write the product as a mixed number. 2 3 1 1. 3 3 __ 5 2. 4 3 __ 5 3. 5 3 __ 5 5 8 3 3 2 1 4. 2 3 1 ___ 5 5. 4 3 1 __ 5 6. 7 3 1 __ 5 10 3 6 Chapter Resources 8-11 Reteach © Houghton Mifflin Harcourt Publishing Company Lesson 8.4 Name Enrich Unknown Numbers Find the unknown number that makes each equation true. 3 1 3 1. 3 __ 5 2 __ 2. 4 3 __ 5 1 __ 4 4 5 5 5 1 2 3. 7 3 5 1 __ 4. 2 3 __ 5 6 __ 9 3 3 5 1 2 5 5. 3 1 __ 5 9 __ 6. 3 2 __ 5 13 __ 6 6 7 7 7. Explain how you found the unknown number in Exercise 3. Chapter Resources 8-12 Enrich © Houghton Mifflin Harcourt Publishing Company Lesson 8.5 Name Reteach Problem Solving • Comparison Problems with Fractions _4 The Great Salt Lake in Utah is about 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? Draw a comparison model. Compare the heights above sea level of the Great Salt Lake I need to find about how high above and Lake Titicaca, in miles.
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