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Name 3-1 Date Solve. Write a multiplication equation for each problem. Miguel swam 6 lengths of the pool. Po Lan swam 3 times as far 1 as far as Miguel. as Miguel. Lionel swam __ 3 1. How many lengths did Po Lan swim? 18 3 ⋅ 6 = 18 Write the equation. 2. How many lengths did Lionel swim? 1 __ ⋅6=2 3 Write the equation. 2 Chris cut a length of rope that was 12 feet long. Dayna cut a rope 4 times as long as Chris’s rope. Benita cut a rope 1 __ as long as Chris’s rope. 4 48 ft 3. How long is Dayna’s rope? Write the equation. 4 ⋅ 12 = 48 3 ft 4. How long is Benita’s rope? 1 __ ⋅ 12 = 3 4 Write the equation. Write two statements for each pair of treats. Use the word times. 5. Compare cookies and drinks. There are 3 times as many cookies as drinks. 1 There are __ times as many drinks as cookies. Treat Number © Houghton Mifflin Harcourt Publishing Company 3 24 6. Compare drinks and pizzas. There are 4 times as many drinks as pizzas. 1 times as many pizzas as drinks. There are __ 8 4 7. Compare cookies and pizzas. 2 There are 12 times as many cookies as pizzas. 1 times as many pizzas as cookies. There are ___ 12 Solve. 1 ⋅ 18 = 8. __ 6 1 11. __ of 27 = 9 UNIT 3 LESSON 1 3 1 of 12 = 9. __ 3 3 1 12. __ ⋅ 56 = 8 1 10. __ ⋅ 32 = 4 8 4 7 1 13. __ of 15 = 5 3 Basic Multiplication Concepts 47 Name 3-1 Date Use the number lines to complete Exercises 1–3. Thirds 0 3 1 3 2 3 3 3 Sixths 0 6 1 6 2 6 3 6 4 6 5 6 6 6 Twelfths 0 1 2 3 4 5 6 7 8 9 10 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 2 1. If you run __ mile, how many sixths have you run? 3 4 __ 6 5 2. If you measure __ meter, how many twelfths have you measured? 6 10 ___ 12 8 3. If you have ___ of a pizza, how many thirds do you have? 12 2 __ 3 Write each fraction as a decimal. 76 = 0.076 4. _____ 1,000 7 = 5. ___ 10 0.7 49 = 0.49 6. ____ 100 32 = 0.032 7. _____ 1,000 0.71 8. 0.28 + 0.43 = 0.74 9. 0.7 + 0.04 = 5.85 10. 7.8 - 1.95 = 1 times 30 equals 6. 11. Stretch Your Thinking Draw a diagram that shows __ Possible answer: 48 UNIT 3 LESSON 1 5 Basic Multiplication Concepts © Houghton Mifflin Harcourt Publishing Company Add or subtract. Name 3-2 Date Multiply. 2 ⋅ 15 = 1. __ 10 2 4. __ ⋅ 27 = 6 2 7. __ ⋅ 21 = 14 4 10. __ ⋅ 45 = 20 7 13. __ ⋅ 18 = 14 3 2. __ ⋅8= 6 3 5. __ ⋅ 56 = 21 4 8. __ ⋅ 35 = 28 4 3 9 12 5 9. __ ⋅ 28 = 20 7 5 ⋅ 11. ___ 24 = 10 5 14. __ ⋅ 80 = 50 12 9 3 6. __ ⋅ 16 = 4 5 9 28 8 8 3 7 3. __ ⋅ 32 = 9 ⋅ 12. ___ 70 = 63 4 15. ___ ⋅ 45 = 12 10 15 8 Show your work. Solve. 16. Rebecca has 21 math problems to solve. She has solved 2 __ of them. How many problems has she solved? 7 © Houghton Mifflin Harcourt Publishing Company 6 problems 17. Tessa shot 36 free throws. She made 27 of them. What fraction of her free throws did Tessa make? 3 __ 4 3 18. A carousel has 56 horses. __ of them are white. How 8 many horses are not white? 35 horses 19. Nathan works at a hardware store. Today he sold 5 of the tools he sold were hammers. How 48 tools. __ 6 many hammers did Nathan sell today? 40 hammers UNIT 3 LESSON 2 Multiplication with Non-Unit Fractions 49 Name 3-2 Date Complete each exercise about the pairs of fraction bars. 3 __ __ ,6 1. What equivalent fractions are shown? 4 8 2 2. Identify the multiplier. 12 __ ___ ,4 3. What equivalent fractions are shown? 18 6 3 4. Identify the divisor. Write each amount as a decimal number. 84 5. _____ 0.084 1,000 31564 6. _____ 1,000 31.564 1176 7. ____ 100 11.76 876 8. _____ 1,000 0.876 Solve. Write a multiplication equation for each problem. Jonas has 8 sponsors for the school walk-a-thon. Maura has 3 times as many sponsors as Jonas. 1 as many sponsors as Jonas. Trenton has __ 4 9. How many sponsors does Maura have? Write the equation. 24 8 ⋅ 3 = 24 10. How many sponsors does Trenton have? 1 __ ⋅8=2 4 Write the equation. 2 Jo has driven farther. Jo has 10 miles to go. Hannah as 24 miles to go. 50 UNIT 3 LESSON 2 Multiplication with Non-Unit Fractions © Houghton Mifflin Harcourt Publishing Company 11. Stretch Your Thinking Hannah and Jo are driving separately to a restaurant that is 60 miles away 3 of the distance from their town. Hannah drives __ 5 5 __ and Jo drives of the distance before stopping for 6 gasoline. Who has driven farther? How many more miles does each driver need to drive to reach the restaurant? 5 1 ⋅ 60 = 5 ⋅ (__ of 60) = 5 ⋅ 10 = 50 miles. Jo has driven __ 6 6 3 1 ⋅ 60 = 3 ⋅ (__ ⋅ 60) = 3 ⋅ 12 = 36 miles. Hannah has driven __ 5 5 Name 3-3 Date The campers in each cabin at Bear Claw Camp held a contest to see who could walk the farthest in one day. Use the sign to answer the questions. Write your answers as fractions. 1 of the way to Otter 1. The campers in Cabin A walked __ 4 Ridge. How many miles did they walk? 13 ___ miles 4 2 2. The campers in Cabin B walked __ of the way to Silver 3 Stream. How many miles did they walk? 16 ___ miles 3 3 3. The campers in Cabin C walked __ of the way to Fossil Cave. 5 How many miles did they walk? 27 ___ miles 5 1 4. The campers in Cabin D walked __ of the way to Mammoth 6 Mountain. How many miles did they walk? 25 ___ miles 6 5. Which group of campers walked the farthest that day? Cabin C 2 6. Show __ of 4 on the number line. © Houghton Mifflin Harcourt Publishing Company 3 0 1 2 7. Write __ of 4 as a fraction. 8 __ 2 4 3 3 __ 8. Write 2 of 4 as a mixed number. 3 2 2__ 3 Multiply. Write your answers as fractions. 8 __ 2 2 ⋅ 4= 10. __ ⋅8= 9. __ 7 7 3 40 ___ 2 7 12. __ ⋅ 20 = 13. __ ⋅2= 9 9 9 26 ___ 5 2 15. __ ⋅ 13 = 16. ___ ⋅ 18 = 3 3 12 UNIT 3 LESSON 3 3 16 ___ 3 14 ___ 9 90 ___ 12 5 11. __ ⋅4= 6 3 14. __ ⋅5= 8 5 17. __ ⋅ 12 = 9 20 ___ 6 15 ___ 8 60 ___ 9 Multiplication with Fractional Solutions 51 Name 3-3 Date Compare. 5 > __ 5 1. __ 7 1 < __ 1 2. __ 4 8 > __ 6 3. ___ 6 < __ 7 4. __ 3 2 < __ 5. __ 8 > __ 6 6. __ 8. 0.207 < 0.342 9. 0.5 > 0.47 6 7 5 8 3 10 4 9 8 7 Compare. 7. 0.54 < 0.65 10. 0.76 > 0.67 12. 0.6 > 0.06 11. 0.22 < 0.41 Multiply. 16 2 ⋅ 14. __ 21 = 14 5 ⋅ 15. __ 24 = 15 1 ⋅ 16. __ 36 = 4 3 ⋅ 17. __ 16 = 12 2 ⋅ 18. __ 14 = 4 3 ⋅ 21. __ 45 = 15 5 9 3 ⋅ 19. ___ 24 = 12 6 3 4 8 ⋅ 20. ___ 80 = 10 8 7 64 9 22. Stretch Your Thinking Write a multiplication equation using one whole number and one fraction that have 18 . a product of ___ 8 3 = ___ 18 Possible answer: 6 ⋅ __ 8 8 52 UNIT 3 LESSON 3 Multiplication with Fractional Solutions © Houghton Mifflin Harcourt Publishing Company 4 ⋅ 20 = 13. __ Name 3-4 Date 3 __ Tanith is using a number line to find __ ⋅ 2 . This is her work so far: 4 5 0 1 – 5 2 – 5 3 – 5 4 – 5 1 0 1 – 5 2 – 5 3 – 5 4 – 5 1 0 — 20 1 — 20 2 — 20 3 — 20 4 — 20 5 — 20 6 — 20 7 — 20 8 — 20 9 — 20 10 — 20 11 — 20 12 — 20 13 — 20 14 — 20 15 — 20 16 — 20 17 — 20 18 — 20 19 — 20 20 — 20 1. Explain Tanith’s work so far to someone at home. 3 of each 2. Finish Tanith’s work by circling __ 4 circled fifth. How many 20ths did you circle altogether? 6 3 3 __ 2 ___ or ___ What is __ ⋅ ? 20 10 4 5 2 __ 3. Use the number line to find __ ⋅ 5. 3 6 Label all the parts above and below. 1 – 6 0 0 — 18 1 — 18 2 — 18 3 — 18 2 – 6 4 — 18 5 — 18 6 — 18 10 ___ 18 3 – 6 7 — 18 8 — 18 6 9 — 18 4 – 6 10 — 18 11 — 18 5 – 6 12 — 18 13 — 18 14 — 18 16 — 18 17 — 18 18 — 18 Show your work. Solve. © Houghton Mifflin Harcourt Publishing Company 15 — 18 1 3 of a bag of popcorn. 4. Four friends at a party popped __ 4 They ate half of what was popped. What fraction of the 3 __ popcorn in the bag did they eat? 8 7 5. Ashley brought __ gallon of lemonade to the party. 8 2 of it. How many gallons of Her friends drank __ 3 7 ___ gallon lemonade did they drink? 12 Multiply. You do not need to simplify. 2 ___ 2 __ 1 = 4 __ ⋅ 7. __ ⋅2= 6. __ 21 7 3 9 9 24 ___ 2 4 __ 9. __ ⋅ 12 = 10. __ ⋅2= 7 7 5 3 9 ___ 9 __ 5 1 = 12. ___ ⋅ 13. ___ ⋅3= 20 10 2 12 UNIT 3 LESSON 4 8 ___ 81 8 ___ 15 15 ___ 12 1 __ 8. __ ⋅5= 8 6 1 __ 11. __ ⋅3= 7 5 5 __ 14. __ ⋅1= 6 6 5 ___ 48 3 ___ 35 5 ___ 36 Multiply a Fraction by a Fraction 53 Name 3-4 Date Name the mixed number shown by the shaded parts. 1 5__ 2 1. 5 1__ 7 2. 1 1__ 3 3. Add. 81.46 5. 80.55 + 0.91= 454.65 4. 454 + 0.65 = 37.98 m 6. 31.78 m + 6.2 m = 1 7. Show __ of 7 on the number line. 3 0 1 2 3 4 5 6 7 7 __ 1 of 7 as a fraction. 8. Write __ 3 3 1 2__ 3 3 5 6 10. Stretch Your Thinking Solve for the unknown fraction. Then divide and shade an area model to show the 2 ⋅ = ___ ? 10 . equation. __ 5 2 5 30 5 __ 6 54 UNIT 3 LESSON 4 Multiply a Fraction by a Fraction © Houghton Mifflin Harcourt Publishing Company 1 9. Write __ of 7 as a mixed number. Name 3-5 Date Multiply. Simplify first if you can. 12 ___ 2 __ 1. __ ⋅6= 5 7 5 ___ 3. ___ ⋅ 8 = 3 24 15 3 1 1 5 35 1 12 3 9 6 1 1 7 __ 12. __ ⋅2= 21 49 7 25 5 __ 10. __ ⋅7= 2 ___ 2 1 816 15 7 ___ 11. __ ⋅ 6 = 3 1 1 ___ 1 4 ___ 9. ___ ⋅ 7 = 8 5 ___ 8. ___ ⋅ 2 5= 5 31 1 7 1 __ 1 1 5 __ 6. __ ⋅3= 25 3 ⋅ __ 2 = 7. ___ 5 10 17 9 ___ ⋅ 4 25 12 = ___ 82 2 __ 4. ___ ⋅8= 9 3 3 5. __ 9 1 __ 1 1 1 4 __ 2. __ ⋅1= 35 4 8 3 1 ___ 18 16 ___ 17 15 ___ 56 1 ___ 40 35 ___ 6 7 ___ 12 13. Which fraction is not equivalent to the others? 3 ___ 2 ___ 1 __ 9 ___ 10 ___ 6 ___ 7 ___ 100 ____ 15 10 5 45 50 40 35 500 Solve. Show your work © Houghton Mifflin Harcourt Publishing Company 3 of the animals are birds. Of the 14. In the town zoo, ___ 28 4 ___ are birds of prey. What fraction of the birds, 15 animals at the zoo are birds of prey? 1 ___ 35 5 15. Tuesday at the zoo, ___ of the visitors were adults. Of these 12 3 ___ were men. What fraction of the people who adults, 10 visited the zoo on Tuesday were men? 1 __ 8 14 16. On Tuesday, ___ of the souvenirs purchased at the zoo gift 25 shop were stuffed animals. Of the stuffed animals purchased, 10 ___ were bears. What fraction of the souvenirs purchased at 21 the zoo gift shop on Tuesday were stuffed bears? 4 ___ 15 UNIT 3 LESSON 5 Multiplication Strategies 55 Name 3-5 Date Add or subtract. 1 + __ 2. 5__ 35 4 + __ 1. 1__ 52 5 5 6 1 7__ 3 3 + __ 5 4. __ 4 2 3 1 1__ 9 5 4 2 - __ 1 3. 1__ 6 3 8 - __ 35 5. 7__ 9 9 3 1 __ 4 or 4__ 9 3 1 6. 6 - 4__ 8. 132.76 - 87.24 = 9. 968.29 - 217.5 = 2 1 1__ 2 Subtract. 7. 31,763 - 6.51 = 45.52 31,756.49 750.79 3 __ 10. Use the number line to find __ ⋅ 2 . Label all the parts 4 5 above and below. ⋅ __2 = 4 5 3 __ 6 ___ 20 1 5 0 1 20 2 20 3 20 4 20 5 20 6 20 7 20 8 20 1 9 20 10 20 11 20 12 20 13 20 14 20 15 20 16 20 17 20 18 20 19 20 20 20 11. Stretch Your Thinking Write a word problem that will 2 ___ ⋅ 8 = x in order to solve. Then use the equation __ 6 10 simplify and multiply to solve. 8 of the basketball team’s points in Possible answer: Jacob scored ___ 10 Saturday’s basketball game. Two sixths of the points Jacob scored were from free throws. What fraction of the team’s points did Jacob score 2 ___ 1 __ 4 from free throws? __ ⋅ 8 = __ ⋅ 4 = ___ 6 56 UNIT 3 LESSON 5 10 3 5 15 Multiplication Strategies © Houghton Mifflin Harcourt Publishing Company 0 20 2 5 Name 3-6 Date Find each product by first rewriting each mixed number as a fraction. 3 ⋅ 2__1 = 1. __ 7 2 2 3. 2__ ⋅ 4__1 = 5 3 3 __ 15 = ___ __ ⋅ 5 = ___ 11 7 2 2 5 3 7 2. 1___ ⋅5= 14 10 5 5 5 __ 7 __ ⋅ 7 = __ 9 5 1 7. 3__ ⋅ 3__1 = 14 8 ___ 56 = 1 __ ⋅ 21 = ___ 11__ 5 5. __ ⋅ 1__2 = 9 2 5 2 4 3 8 3 = 6. 12 ⋅ 2__ 9 4 49 = 7 __ 1 __ ⋅ 7 = ___ 12__ 2 1 __ 4. 5__ ⋅3= 4 9 = 1 8. __ ⋅ 3___ 9 10 Solve. 17 __ 17 = __ ___ ⋅ 5 = ___ 81 1 10 2 2 16 __ ___ ⋅3=2 3 8 12 ___ ___ ⋅ 11 = 33 1 4 13 1 ___ __ ⋅ 39 = ___ 9 10 30 Show your work. © Houghton Mifflin Harcourt Publishing Company 9. The bottom of Zeyda’s jewelry box is a rectangle with 3 1 inches and width 3__ inches. What is the area length 5__ 4 8 of the bottom of the jewelry box? 15 17___ square inches 32 10. The Patel family went apple picking. The number of 2 times the number of red apples they picked was 2__ 9 green apples they picked. If they picked 45 green apples, how many red apples did they pick? 100 red apples 1 11. The art museum is 8__ miles from Alison’s house. 2 2 of the way there so far. Alison has ridden her bike __ 3 How far has she gone? 2 miles 5__ 3 UNIT 3 LESSON 6 Multiply Mixed Numbers 57 Name 3-6 Date Add. 3 + __ 1 1. __ 8 3 1 + __ 2. __ 5 6 5 + __ 1 3. __ 4 6 8 13 ___ 19 ___ 23 ___ 24 20 24 1 + __ 2 4. __ 2 + __ 1 5. __ 7 3 3 4 + ___ 1 6. __ 5 9 10 13 ___ 7 __ 9 ___ 21 9 10 Use the Commutative Property to solve for n. 7. 55,207 + 87,331 = 87,331 + n n = 55,207 8. 48.76 + 20.08 = 20.08 + n n = 48.76 Multiply. Simplify first if you can. 1 __ 3 = 2 __ 7 __ ⋅ 10. ___ ⋅6= 9. __ 2 3 4 10 7 6 25 2 __ 1 __ ⋅4= 13. __ 5 2 7 5 2 __ 7 3 __ 11. __ ⋅5= 5 6 2 __ 14. __ ⋅3= 9 8 1 __ 2 1 ___ 12 15. Stretch Your Thinking Complete the mixed number equation that is represented by the area model. ⋅ 2 1 __ 58 2 1__ 3 = UNIT 3 LESSON 6 5 __ 6 Multiply Mixed Numbers © Houghton Mifflin Harcourt Publishing Company 5 ___ ⋅ 12 = 12. __ 3 __ 3-7 Name Date Solve. 3 __ ⋅1 1. __ 4 8 3 ___ 32 2 - __ 1 2. __ 2 4. __ ⋅ 12 7 24 = __ ___ 33 7 7 1 + __ 2 5. __ 5 __ 7. __ ⋅5 7 6 25 ___ 42 11 + 8. ___ 3 1 __ 10. __ ⋅1 3 8 1 ___ 24 3 1 + __ 1 3. ___ 9 10 5 __ 3 ___ 9 10 5 5 3 1 + __ 6. __ 4 3 8 5 __ 8 13 ___ 15 4 - __ 2 9. __ 12 9 11 3___ 9 2 __ 12 9 1 12. 10 - __ 9 89 = __ ___ 98 9 9 7 __ 11. __ ⋅3 8 4 21 ___ 32 Show your work. Solve. 7 gallon of water. It is 13. Rodrigo’s fish bowl holds __ 8 1 now __ full. How much water is in it? 2 7 ___ gallon 16 © Houghton Mifflin Harcourt Publishing Company 1 14. Kenya jumped 7__ feet. Janet jumped 6 How much farther did Kenya jump? 5 __ foot 6 1 6__ feet. 3 7 15. A group of hikers walked 8___ miles to Caribou Cave 10 1 __ and then 5 miles to Silver Stream. How far did they 5 walk altogether? 9 13___ miles 10 3 16. A recipe calls for __ cup of flour. Estevan wants to make 4 1 __ of the recipe. How much flour will he need? 3 1 __ cup 4 1 17. A truck was carrying 2__ tons of sand. When it arrived, 8 1 only 1__ tons of sand were left. How much sand was 2 lost along the way? 5 __ ton 8 UNIT 3 LESSON 7 Relate Fraction Operations 59 Name 3-7 Date Subtract. 3 - __ 1 1. __ 4 2 - ___ 1 2. __ 6 9 10 7 - __ 1 3. __ 4 8 7 ___ 11 ___ 5 __ 12 90 8 6 - __ 1 4. __ 7 4 - __ 2 5. __ 5 3 3 1 - __ 1 6. __ 2 8 11 ___ 2 ___ 3 __ 21 15 8 Sample estimates shown; accept reasonable estimates. 8. $44.25 - $21.76 $22 9. 14.6 + 2.4 17 Estimate each sum or difference. 7. 6.759 + 2.099 9 Find each product by first rewriting each mixed number as a fraction. 5 ___ 25 = ___ __ ⋅ 10 = ___ 21 5 1 = ⋅ 3__ 10. __ 8 3 12 12 8 3 3 11. 4__ ⋅5= 5 2 12. 1__ ⋅ 3__4 = 5 9 5 8 5 1 1 7 ___ 217 = ___ __ ⋅ 31 = ___ 4 37 5 9 45 45 © Houghton Mifflin Harcourt Publishing Company 1 __ 13. 6__ ⋅5= 23 __ 23 = ___ ⋅ 5 = ___ 23 31 __ 31 = __ ___ ⋅ 5 = ___ 37 5 8 8 8 14. Stretch Your Thinking Give an example that shows how to use the Distributive Property to multiply a number by a sum. All of the numbers you use should be mixed numbers or fractions. 5 = __ 2 1 + __ 1 + __ 2 __ Possible answer: __ ⋅ (2__ ) 2 ⋅ 2__ ⋅5= 4 4 3 6 3 3 6 3 + __ 5 = ___ 37 = ___ 2 __ 2 __ __ ⋅ 9 + __ ⋅ 5 = __ 21 3 4 3 6 2 9 18 18 60 UNIT 3 LESSON 7 Relate Fraction Operations Name 3-8 Date Complete each fraction box. 1. 3 7 __ and __ > + - ⋅ 8 3 6 7 > __ 7 > __ __ or __ 4 8 8 8 7 __ 8 7 __ 8 7 __ 8 2. 3 1 __ and __ 3 = __ 6 = ___ 13 = __ 7 + __ + __ 15 4 8 8 8 8 3 = __ 6 = __ 7 - __ 1 - __ 4 8 8 8 3 = ___ 21 ⋅ __ 4 32 5 2 4 > + - ⋅ 3 > __ 6 > ___ 5 1 __ or ___ 5 2 10 3 = ___ 5 + 1 + __ __ 5 2 10 3 - __ 6 1 = ___ __ 5 2 10 3 1 __ __ ⋅ 3 = ___ 2 5 10 10 6 = ___ 10 5 = ___ 10 11 = ___ ___ 11 10 1 ___ 10 10 Show your work. Solve. 7 ton of 3. The Eagle Trucking Company must deliver __ 8 5 __ cement blocks and ton of bricks to one place. 8 How much will this load weigh? 1 1__ tons 2 © Houghton Mifflin Harcourt Publishing Company 1 1 4. A truck carried 3__ tons of sand, but lost __ ton along 4 3 the way. How many tons of sand were delivered? 1 3___ tons 12 2 5. The trucking company also needs to deliver 1__ tons of 3 7 ___ oak logs and 1 tons of maple logs. Which load 12 weighs more? oak logs 3 1 6. In a load of __ ton of steel rods, __ of them are bent. 4 8 How many tons of steel rods are bent? 3 ___ ton 32 3 7. The company delivered 1__ tons of bricks to one building site. 5 1 __ They delivered 2 times this much to a second site. What was 2 the weight of the load the company delivered to the second site? 4 tons UNIT 3 LESSON 8 Solve Real World Problems 61 Name 3-8 Date Multiply. 1. 2. 2,548 × __5 3. 945 12,740 4. 21 × 45 _ 5. 33 × _4 132 3,015 × __6 18,090 65 × 87 _ 6. 215 × __9 1,935 5,655 Find each product by first rewriting each mixed number as a fraction. 40 __ 320 = 23 ___ ⋅ 8 = ___ 11___ 4 2 = 7. 4__ ⋅ 2__ 9 3 27 27 9 3 5 9. 3__ 6 23 ___ 12 = ___ 6 ⋅ 13 1 8. 6__ ⋅ 10 = 13 5 5 46 = ___ 12 = ___ ⋅ ___ 37 13 31 ___ 62 = ___ ⋅ 10 = ___ 62 1 10. 5__ 13 3 16 ___ 3 = __ 3 ⋅5 1 1 3 = ___ 16 = __ ⋅ __ 31 5 5 5 Solve. 6 - __ 2 11. __ 7 7 4 __ 7 4 + __ 2 12. __ 9 3 1 1__ 9 2 ___ 13. __ ⋅ 9 3 10 3 __ 5 3 __ ⋅5 14. __ 1 15. 8 - __ 3 1 + __ 16. __ 5 7 8 6 55 = __ ___ 76 7 7 8 13 ___ 24 © Houghton Mifflin Harcourt Publishing Company 3 __ 8 17. Stretch Your Thinking Write and solve a word problem that requires multiplying two mixed numbers. 5 Possible answer: Taylor worked 6__ hours doing yard 6 work one weekend. The next weekend, he worked 1 1__ times as long as he did the previous weekend. 2 How many hours did Taylor work on the second 1 weekend? 10__ hours 4 62 UNIT 3 LESSON 8 Solve Real World Problems Name 3-9 Date Predict whether the product will be greater than, less than, or equal to the second factor. Then compute the product. Predictions may vary. 4 1. __ ⋅6=x 1 2. 1__ ⋅6=x 5 Predict: x < 6 4 4__ 5 Compute: x = 2 __ 4. __ ⋅5=x 2 10 3. ___ ⋅6=x 9 10 Predict: x > 6 2 6__ 3 Compute: x = 5 __ 5. __ ⋅5=x 6 6 5 Predict: x = __ 6 __ 5 Compute: x = 6 Compute: x = 6 Compute: x = 1 __ 6. 1__ ⋅5=x 6 Predict: x < Predict: x = 6 3 5 __ 6 ___ 25 36 6 5 Predict: x > __ 6 Compute: x = 1 1__ 9 Show your work. Solve. 3 times as tall as his brother. His brother 7. James is 1__ 7 1 __ is 3 feet tall. 2 1 feet? Is James’s height more or less than 3__ 2 © Houghton Mifflin Harcourt Publishing Company more How tall is James? 5 feet 8. South Middle School has 750 students. North Middle 13 times as many students as South. School has ___ 15 Does North Middle School have more or fewer than 750 students? fewer How many students attend North Middle School? 650 students UNIT 3 LESSON 9 Make Generalizations 63 Name Date Perry measured the foot length of four friends for a science fair experiment. Then, he made a bar graph to display his results. Foot length (in.) Foot Length 1. How much longer is Brennen’s foot than Clara’s foot? 0.7 inch 2. What is the difference between the longest foot and the shortest foot? 9 8.8 8.6 8.4 8.2 8 7.8 7.6 7.4 n a Ch Br en ne ar Cl ey 0.9 inch ne Ty e 0 en 3-9 Student Name Solve. 7 7 __ 3. __ ⋅ 4 ___ 8 9 18 1 3 4. 11 - __ 10__ 4 4 1 9 - ___ 5 __ 6. ___ 12 12 3 7 + __ 2 7. ___ 15 3 15 = __ 4 + ___ 7 ___ 5. __ 11 5 10 10 2 17 = ___ ___ 12 15 15 15 5 ___ ⋅ 9 ___ 8. __ 6 11 22 Complete each fraction box. 5 7 ___ and __ 12 4 2 __ and __ 6 5 + − ⋅ 6 12 12 5 10 7 __ + ___ = ___ + 6 12 12 5 - ___ 10 − 7 = ___ __ 6 12 12 5 35 7 __ ⋅ ___ = ___ 6 12 72 12 7 ___ = 12 7 = ___ 12 > 17 = ___ ___ 15 12 12 3 = __ 1 ___ 4 12 + − ⋅ 3 10 4 > __ 2 12 > ___ __ or ___ 5 15 3 4 + __ 2 = ___ 12 + __ 5 15 3 4 − __ 2 = ___ 12 − __ 5 15 3 8 4 __ __ ⋅ 2 = ___ 5 3 15 15 10 ___ = 15 10 = ___ 15 22 = ___ ___ 17 15 15 2 ___ 15 9. Stretch Your Thinking Write two multiplication equations using fractions and mixed numbers. Write one equation that will have a product greater than the first factor. Then write another equation that will have a product less than the first factor. 3 = ___ 25 = ___ 4 1 __ ⋅ 2__ 3 31 ; 3__ ⋅ 2 = ___ 21 Possible answer: 1__ 9 8 72 8 3 12 12 64 UNIT 3 LESSON 9 Making Generalizations © Houghton Mifflin Harcourt Publishing Company 5 > ___ 10 > ___ 7 7 > __ or ___ Name 3-10 Date Divide 5 __ 1. 5 ÷ 6 = 3. 33 ÷ 30 = 5. 3 ÷ 10 = 1 = 7. 100 ÷ __ 6 1 ÷ = 9. __ 8 5 1 ÷ = 11. __ 9 2 6 10 3 ___ 10 600 1 ___ 40 1 ___ 18 45 1 = 4. 8 ÷ __ 48 1 = 6. 4 ÷ __ 36 5 11 = ___ ___ 11 10 1 = 2. 9 ÷ __ 6 9 1 ___ 8. 1 ÷ 100 = 100 1 ___ 1 ÷ = 10. __ 7 56 8 1 ___ 1 ÷ = 12. __ 5 15 3 Show your work. Solve. 13. Alexander is dividing oranges into eighths. He has 5 oranges. How many eighths will he have? 40 eighths © Houghton Mifflin Harcourt Publishing Company 14. Carrie has 32 ounces of ice cream to divide equally among 10 people. How much ice cream will each person get? 1 3__ ounces 5 15. Nayati wants to swim 50 miles this school year. She plans to swim _1_ mile each day. How many days will it take her to 4 swim 50 miles? 200 days 1 16. Eric has __ of a watermelon to share equally with 3 friends. 3 How much will each person get? 1 ___ watermelon 12 17. A gardener needs to pack 16 pounds of beans into 20 bags. He wants all the bags to weigh about the same. About how much will each bag weigh? _4_ pound 5 UNIT 3 LESSON 10 When Dividing Is Also Multiplying 65 Name 3-10 Add or subtract. 3 1. 2__ Date 2. 4 5 - 1__ _8 1 1__ 5. 1 - 2__ _6 5 4__ 12 8. 5 6 __ and __ 7 6 7 10 2 14 > ___ > __ or ___ 7 35 35 10 2 14 __ ___ ___ + = + = 7 35 35 10 = 2 = ___ 14 − ___ − __ 7 35 35 2 = ___ 4 __ ⋅ 7 35 3 3 + 1__ _4 1 10___ 30 2 __ 5 2 __ 5 2 __ 5 2 __ 5 1 8__ 6. 7 8___ 5 ⋅ 10 5 5 + 4__ _6 Complete each fraction box. 7. 2 2 __ and __ − 7 6___ 2 3__ 6 + 2 6__ 2 4 - 3__ _5 9 7 > 1 3. 10__ 3 5 + 1__ _9 8 4. 2 4__ 6 > __ 5 36 > ___ 35 __ or ___ > 24 ___ 35 4 ___ 35 7 6 42 42 6 5 36 35 __ + __ = ___ + ___ = 7 6 42 42 6 − __ 5 = ___ 36 − ___ 35 = __ 7 6 42 42 6 5 30 5 __ ⋅ __ = ___ = __ 7 6 7 42 + − ⋅ 71 = ___ ___ 1 29 42 42 1 ___ 42 Predict whether the product will be greater than, less than, or equal to the second factor. Then compute the product. Predictions may vary. 3 2 1 ⋅5=x 10. __ ⋅5=x 11. 1__ ⋅5=x 9. __ 3 Compute: x = 1 3__ 3 6 Predict: x > 5 Predict: x = 5 Compute: x = 5 Compute: x = 5 5__ 6 12. Stretch Your Thinking Draw a diagram to show how many twelfths there are in 3. Describe a situation in which you would need to know how many twelfths there are in 3. 1 of a foot, so the Possible answer: An inch is ___ 12 number of inches in 3 feet is the number of twelfths in 3. 66 UNIT 3 LESSON 10 When Dividing Is Also Multiplying © Houghton Mifflin Harcourt Publishing Company Predict: x < 5 3 3-11 Name Date 1 ÷ 1. Consider the division problem __ 3. 2 Describe a situation this division could represent. Situations will vary. Draw a diagram to represent the division. Then find the solution. 1 __ ; Diagrams will vary. Check students’ work. 6 Write an equation. Then solve. Equations may vary. Show your work. 2. A rectangle has an area of 12 square feet and a length of 5 feet. What is its width? 2 5 ⋅ w = 12; 2__ feet 5 © Houghton Mifflin Harcourt Publishing Company 1 3. A tortoise must walk ___ mile to visit a friend. He plans to 12 break the journey into four equal parts with breaks in between. How long will each part of his journey be? 1 ÷ 1 4; ___ mile x = ___ 12 48 1 4. Harry worked 7 hours last week. This is __ as many hours as 3 Aidan worked. How many hours did Aidan work? 1 __ ⋅ a = 7; 21 hours 3 5. Lin is a camp counselor. She is making small bags of trail mix for campers to take on a hike. She has 2 pounds of raisins and 1 pound in each bag. How many bags can she fill is putting __ 8 before she runs out of raisins? 1 ; 16 bags x = 2 ÷ __ 8 1 6. Mr. Ramirez bought __ pounds of cashews. He divided the 4 cashews equally among his three children. How much did each child get? 1 ÷ 1 3; ___ pound x = __ 4 12 UNIT 3 LESSON 11 Solve Division Problems 67 Name 3-11 Date Add or subtract. 1. 1 1__ 2. 8 2 + 4__ _3 19 5___ 4. 1 6__ 3. 4 5 – 4__ _6 12 4 5. 7 11 + 5___ 14 __ 6. 2 – 2__ _5 3 1__ 5 1 11___ 14 3 8 + 7__ _9 2 17__ 5 1___ 24 2 5__ 1 9__ 9 5 6__ 8 1 + 3__ _2 1 10__ 8 Predict whether the product will be greater than, less than, or equal to the second factor. Then compute the product. Predictions may vary. 5 ⋅9=x 7. __ 7 8. __ ⋅9=x 5 Predict: x = 9 5 Predict: x < 9 9 Compute: x = 1 __ 10. 1__ ⋅4=x 2 3 9. 1__ ⋅9=x 8 7 7__ 8 Compute: x = 6 __ 11. __ ⋅4=x 5 6 4 Predict: x > __ 5 Compute: x = 1 1__ 5 Predict: x > 9 2 14__ 5 Compute: x = 2 __ 12. __ ⋅4=x 5 5 4 Predict: x = __ 5 Compute: x = 4 __ 5 5 4 Predict: x < __ 5 8 ___ 25 Compute: x = Divide. 4 1 = 16. 200 ÷ __ 4 24 800 14. 2 ÷ 3 = 1 ÷ = 17. __ 8 4 2 __ 3 1 ___ 32 15. 10 ÷ 3 = 1 ÷ = 18. __ 6 7 1 3__ 3 1 ___ 42 19. Stretch Your Thinking Harrison is playing a board game that 1 of the has a path of 100 spaces. After his first turn, he is __ 5 1 fewer way along the spaces. On his second turn, he moves __ 4 spaces than he moved on his first turn. On his third turn, he 1 times as many spaces than he moved on his first moves 1__ 4 turn. What space is he on after three turns? 60 68 UNIT 3 LESSON 11 Solve Division Problems © Houghton Mifflin Harcourt Publishing Company 1 = 13. 6 ÷ __ Name 3-12 Date Solve. 1 = 1. 5 ⋅ __ 3 1 ÷ = 3. __ 2 8 1 = 5. 5 ÷ ____ 100 3 ___ 7. __ ⋅ 10 = 5 27 1 ÷ 9. __ 10 = 5 1 11. __ ⋅ 14 = 8 5 __ 3 1 = 2. 5 ÷ __ 3 1 ___ 16 4. 27 ÷ 10 = 500 1 = 6. 12 ⋅ __ 2 __ 9 1 ___ 50 3 1__ 4 15 7 2___ 10 1 1__ 9 3 1 = 8. 16 ÷ __ 64 1 = 10. 10 ÷ __ 50 4 5 12. 18 ÷ 20 = Tell whether you need to multiply or divide. Then solve. Equations will vary. Possible equations are given. 9 ___ 10 Show your work. 1 ounce. Jody has 1 pound 13. A dime weighs about ___ 12 (16 ounces) of dimes. About many dimes does she have? Divide; 192 dimes 1 14. Maddie has 180 coins. Of these coins, ___ are dimes. 12 About how many dimes does she have? © Houghton Mifflin Harcourt Publishing Company Multiply; 15 dimes 1 15. A rectangle has length 3 feet and width __ foot. What is the 4 area of the rectangle? 3 square foot Multiply; __ 4 1 16. A rectangle has area 3 square feet and width __ foot. 2 What is the length of the rectangle? Divide; 6 feet 17. Nisha wants to study 5 hours for the spelling bee. If she 1 hour per night, how many nights will she studies __ 3 have to study? Divide; 15 nights UNIT 3 LESSON 12 Distinguishing Multiplication from Division 69 Name 3-12 Date Multiply. 1. 134 ⋅ 5 = 670 4. 4,507 ⋅ 3 = 13,521 2. 44 ⋅ 21 = 924 3. 7 ⋅ 57 = 399 5. 36 ⋅ 76 = 2,736 6. 1,928 ⋅ 6 = 11,568 1 = 8. 100 ÷ __ 1 ÷ = 9. __ 4 Divide. 1 ÷ = 7. __ 2 9 10. 4 ÷ 5 = 1 ___ 18 4 __ 5 3 11. 12 ÷ 5 = 300 2 2__ 5 5 1 = 12. 8 ÷ __ 7 1 ___ 20 56 Show your work. Write an equation. Then solve. Equations may vary. 14. Stretch Your Thinking Using a whole number and a fraction as factors, write a multiplication equation with a product less than the whole number factor. Draw a picture to show how the product is less than the whole number factor. 9 7 Possible answer: ___ ⋅ 3 = 2___ 10 10 70 UNIT 3 LESSON 12 Distinguishing Multiplication from Division © Houghton Mifflin Harcourt Publishing Company 13. Marc is running 5 kilometers at track practice. He decides to break the run into 3 equal lengths. How long will each length be? 2 x = 5 ÷ 3; 1__ km 3 Name 3-13 Date Show your work. Solve. 1. Dan’s Ice Cream comes in cartons of two sizes. The large 3 1 pounds. The small carton holds 1__ pounds carton holds 4__ 4 2 less. How much ice cream does the small carton hold? 3 2__ pounds 4 2. Mac picked four baskets of blueberries. The weights of the berries in pounds are given below. Order the weights from lightest to heaviest. 5 __ 9 ___ 4 __ 13 ___ 4 10 5 20 13 __ 9 __ ___ , 4 , ___ ,5 20 5 10 4 1 3. Four cones of Dan’s Ice Cream hold __ pound. How much 2 ice cream does each cone hold? 1 __ pound 8 1 4. If a dish of ice cream holds __ pound, how many dishes can 4 1 __ you get from a 4 -pound carton of Dan’s Ice Cream? 18 dishes 2 © Houghton Mifflin Harcourt Publishing Company Solve. Give your answer in simplest form. 1 = 5. 3 ÷ __ 5 9 7. ___ ⋅ 2__1 = 14 3 = 1 + __ 9. __ 5 3 1 ÷ = 11. __ 4 8 5 - __ 13. 3__ 11 = 7 2 UNIT 3 LESSON 13 4 1 1__ 2 3 7 2___ 3 + ___ 11 = 6. 1__ 15 14 ___ 3 8. 2__ ⋅6= 6 1 ___ 9 2 - ___ 1 = 12. __ 32 5 3 2___ 14 3 15__ 5 5 5 + __ 8 = 10. __ 15 16 16 10 7 __ 14. __ ⋅2= 8 7 13 1___ 18 3 ___ 10 1 __ 4 Review Operations with Fractions 71 Name 3-13 Date 1 Use benchmarks of 0, __ , and 1 to estimate the sum or 2 difference. Then find the actual sum or difference. 5 + __ 4 1. ___ 10 13 – __ 3 2. ___ 14 9 1 Estimate: 85 17 ___ or ___ Sum: 90 18 1 __ Estimate: 2 1 __ 2 Difference: 8 – __ 7 3. __ 9 7 13 + __ 3 4. ___ 8 14 0 1 ___ Estimate: 2 Estimate: 72 Difference: 4 Sum: 19 1___ 28 Show your work. Write an equation. Then solve. Equations may vary. 5. A rectangle has an area of 20 square feet and a length of 6 feet. What is its width? 1 6 ⋅ w = 20; 3 __ feet 3 6. Bailey attends gymnastics practice for 8 hours each week. 1 the number of hours that the gym is open for This is __ 4 practice. How many hours is the gym open for practice? 1 __ ⋅ a = 8; 32 hours 4 Solve. 1 ÷ = 7. __ 3 4 1 ___ 12 1 8. __ ⋅3= 4 3 __ 4 1 = 9. 14 ⋅ __ 6 1 2 __ 3 © Houghton Mifflin Harcourt Publishing Company 1 ÷ 5 different 10. Stretch Your Thinking How is solving __ 8 1 from solving __ ⋅ 5? 8 1 ÷ 1 5, multiply __ by Possible answer: To solve __ 8 8 1 __ 1. 1 the reciprocal of 5: __ ⋅ 1 = ___ To solve __ ⋅ 5, first 8 5 40 8 5. rewrite 5 as __ Then, multiply the two fractions: 1 5. 1 __ __ ⋅ 5 = __ 8 1 8 72 UNIT 3 LESSON 13 Review Operations with Fractions Name 3-14 Date These graphs show the instruments in two different high school marching bands. Carter School Marching Band Reagan School Marching Band 1 – 3 1 – 3 percussion 2 – 5 brass 1 – 6 percussion woodwind 1 – 2 brass 4 — 15 woodwind Show your work. Solve. Use the circle graphs. 1. The Reagan School Marching Band has three percussion musicians. How many musicians altogether are in the band? 18 musicians 2. There are 30 musicians in the Carter School Marching Band. How many of them play brass instruments? © Houghton Mifflin Harcourt Publishing Company 12 musicians Suppose both bands decide to combine and perform as one band. 3. What fraction of the band members will play a brass instrument? 7 ___ 16 4. What fraction of the band members will play a percussion instrument? 13 ___ 48 5. What fraction of the band members will play a woodwind instrument? 7 ___ 24 UNIT 3 LESSON 14 Focus on Mathematical Practices 73 Name 3-14 Date Show your work. Solve. Explain how you know your answer is reasonable. Explanations may vary. 1 feet and a width 1. James’s garden has a length of 12__ 4 2 of 9__ feet. What length of fencing will he need to 3 surround his garden? 5 feet 43__ 6 Answer: Why is the answer reasonable? 1 2 12__ rounds to 12. 9__ rounds to 10. The answer 4 3 should be about 12 + 12 + 10 + 10, or 44 Solve. 1 ÷ = 2. ___ 3 11 1 ÷ = 5. ___ 5 12 1 ___ 33 1 ___ 60 1 = 3. 6 ÷ __ 3 1 = 6. 7 ⋅ __ 8 18 7 __ 8 2 __ 4. __ ⋅5= 3 7 1 7. __ ⋅ 12 = 5 10 ___ 21 2 2__ 5 Show your work. Solve. 1 pound altogether. What 8. Kayla packs 4 boxes that weigh __ 6 does each box weigh? 1 ___ pound 24 © Houghton Mifflin Harcourt Publishing Company 2 9. Mrs. Blackwell put 4__ grams on the scale during a lab in 3 5 grams to the scale. How science class. Then, she added 2__ 6 many grams are on the scale in all? 1 7__ grams 2 10. Stretch Your Thinking If you start with 1 and repeatedly 1 , will you reach 0? Explain why or why not. multiply by __ 2 No. Possible explanation: Each fraction has twice the denominator as the fraction preceding 1 __ 1 ___ , 1 , __ , 1 , . . . The fraction will get closer it: 1, __ 2 4 8 16 and closer to zero without ever reaching zero. 74 UNIT 3 LESSON 14 Focus on Mathematical Practices Name 3-1 Date Solve. Write a multiplication equation for each problem. Miguel swam 6 lengths of the pool. Po Lan swam 3 times as far 1 as far as Miguel. as Miguel. Lionel swam __ 3 1. How many lengths did Po Lan swim? 18 3 ⋅ 6 = 18 Write the equation. 2. How many lengths did Lionel swim? 1 __ ⋅6=2 3 Write the equation. 2 Chris cut a length of rope that was 12 feet long. Dayna cut a rope 4 times as long as Chris’s rope. Benita cut a rope 1 __ as long as Chris’s rope. 4 48 ft 3. How long is Dayna’s rope? Write the equation. 4 ⋅ 12 = 48 3 ft 4. How long is Benita’s rope? 1 __ ⋅ 12 = 3 4 Write the equation. Write two statements for each pair of treats. Use the word times. 5. Compare cookies and drinks. There are 3 times as many cookies as drinks. 1 There are __ times as many drinks as cookies. Treat Number © Houghton Mifflin Harcourt Publishing Company 3 24 6. Compare drinks and pizzas. There are 4 times as many drinks as pizzas. 1 times as many pizzas as drinks. There are __ 8 4 7. Compare cookies and pizzas. 2 There are 12 times as many cookies as pizzas. 1 times as many pizzas as cookies. There are ___ 12 Solve. 1 ⋅ 18 = 8. __ 6 1 11. __ of 27 = 9 UNIT 3 LESSON 1 3 1 of 12 = 9. __ 3 3 1 12. __ ⋅ 56 = 8 1 10. __ ⋅ 32 = 4 8 4 7 1 13. __ of 15 = 5 3 Basic Multiplication Concepts 47 Name 3-1 Date Use the number lines to complete Exercises 1–3. Thirds 0 3 1 3 2 3 3 3 Sixths 0 6 1 6 2 6 3 6 4 6 5 6 6 6 Twelfths 0 1 2 3 4 5 6 7 8 9 10 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 2 1. If you run __ mile, how many sixths have you run? 3 4 __ 6 5 2. If you measure __ meter, how many twelfths have you measured? 6 10 ___ 12 8 3. If you have ___ of a pizza, how many thirds do you have? 12 2 __ 3 Write each fraction as a decimal. 76 = 0.076 4. _____ 1,000 7 = 5. ___ 10 0.7 49 = 0.49 6. ____ 100 32 = 0.032 7. _____ 1,000 0.71 8. 0.28 + 0.43 = 0.74 9. 0.7 + 0.04 = 5.85 10. 7.8 - 1.95 = 1 times 30 equals 6. 11. Stretch Your Thinking Draw a diagram that shows __ Possible answer: 48 UNIT 3 LESSON 1 5 Basic Multiplication Concepts © Houghton Mifflin Harcourt Publishing Company Add or subtract. Name 3-2 Date Multiply. 2 ⋅ 15 = 1. __ 10 2 4. __ ⋅ 27 = 6 2 7. __ ⋅ 21 = 14 4 10. __ ⋅ 45 = 20 7 13. __ ⋅ 18 = 14 3 2. __ ⋅8= 6 3 5. __ ⋅ 56 = 21 4 8. __ ⋅ 35 = 28 4 3 9 12 5 9. __ ⋅ 28 = 20 7 5 ⋅ 11. ___ 24 = 10 5 14. __ ⋅ 80 = 50 12 9 3 6. __ ⋅ 16 = 4 5 9 28 8 8 3 7 3. __ ⋅ 32 = 9 ⋅ 12. ___ 70 = 63 4 15. ___ ⋅ 45 = 12 10 15 8 Show your work. Solve. 16. Rebecca has 21 math problems to solve. She has solved 2 __ of them. How many problems has she solved? 7 © Houghton Mifflin Harcourt Publishing Company 6 problems 17. Tessa shot 36 free throws. She made 27 of them. What fraction of her free throws did Tessa make? 3 __ 4 3 18. A carousel has 56 horses. __ of them are white. How 8 many horses are not white? 35 horses 19. Nathan works at a hardware store. Today he sold 5 of the tools he sold were hammers. How 48 tools. __ 6 many hammers did Nathan sell today? 40 hammers UNIT 3 LESSON 2 Multiplication with Non-Unit Fractions 49 Name 3-2 Date Complete each exercise about the pairs of fraction bars. 3 __ __ ,6 1. What equivalent fractions are shown? 4 8 2 2. Identify the multiplier. 12 __ ___ ,4 3. What equivalent fractions are shown? 18 6 3 4. Identify the divisor. Write each amount as a decimal number. 84 5. _____ 0.084 1,000 31564 6. _____ 1,000 31.564 1176 7. ____ 100 11.76 876 8. _____ 1,000 0.876 Solve. Write a multiplication equation for each problem. Jonas has 8 sponsors for the school walk-a-thon. Maura has 3 times as many sponsors as Jonas. 1 as many sponsors as Jonas. Trenton has __ 4 9. How many sponsors does Maura have? Write the equation. 24 8 ⋅ 3 = 24 10. How many sponsors does Trenton have? 1 __ ⋅8=2 4 Write the equation. 2 Jo has driven farther. Jo has 10 miles to go. Hannah as 24 miles to go. 50 UNIT 3 LESSON 2 Multiplication with Non-Unit Fractions © Houghton Mifflin Harcourt Publishing Company 11. Stretch Your Thinking Hannah and Jo are driving separately to a restaurant that is 60 miles away 3 of the distance from their town. Hannah drives __ 5 5 __ and Jo drives of the distance before stopping for 6 gasoline. Who has driven farther? How many more miles does each driver need to drive to reach the restaurant? 5 1 ⋅ 60 = 5 ⋅ (__ of 60) = 5 ⋅ 10 = 50 miles. Jo has driven __ 6 6 3 1 ⋅ 60 = 3 ⋅ (__ ⋅ 60) = 3 ⋅ 12 = 36 miles. Hannah has driven __ 5 5 Name 3-3 Date The campers in each cabin at Bear Claw Camp held a contest to see who could walk the farthest in one day. Use the sign to answer the questions. Write your answers as fractions. 1 of the way to Otter 1. The campers in Cabin A walked __ 4 Ridge. How many miles did they walk? 13 ___ miles 4 2 2. The campers in Cabin B walked __ of the way to Silver 3 Stream. How many miles did they walk? 16 ___ miles 3 3 3. The campers in Cabin C walked __ of the way to Fossil Cave. 5 How many miles did they walk? 27 ___ miles 5 1 4. The campers in Cabin D walked __ of the way to Mammoth 6 Mountain. How many miles did they walk? 25 ___ miles 6 5. Which group of campers walked the farthest that day? Cabin C 2 6. Show __ of 4 on the number line. © Houghton Mifflin Harcourt Publishing Company 3 0 1 2 7. Write __ of 4 as a fraction. 8 __ 2 4 3 3 __ 8. Write 2 of 4 as a mixed number. 3 2 2__ 3 Multiply. Write your answers as fractions. 8 __ 2 2 ⋅ 4= 10. __ ⋅8= 9. __ 7 7 3 40 ___ 2 7 12. __ ⋅ 20 = 13. __ ⋅2= 9 9 9 26 ___ 5 2 15. __ ⋅ 13 = 16. ___ ⋅ 18 = 3 3 12 UNIT 3 LESSON 3 3 16 ___ 3 14 ___ 9 90 ___ 12 5 11. __ ⋅4= 6 3 14. __ ⋅5= 8 5 17. __ ⋅ 12 = 9 20 ___ 6 15 ___ 8 60 ___ 9 Multiplication with Fractional Solutions 51 Name 3-3 Date Compare. 5 > __ 5 1. __ 7 1 < __ 1 2. __ 4 8 > __ 6 3. ___ 6 < __ 7 4. __ 3 2 < __ 5. __ 8 > __ 6 6. __ 8. 0.207 < 0.342 9. 0.5 > 0.47 6 7 5 8 3 10 4 9 8 7 Compare. 7. 0.54 < 0.65 10. 0.76 > 0.67 12. 0.6 > 0.06 11. 0.22 < 0.41 Multiply. 16 2 ⋅ 14. __ 21 = 14 5 ⋅ 15. __ 24 = 15 1 ⋅ 16. __ 36 = 4 3 ⋅ 17. __ 16 = 12 2 ⋅ 18. __ 14 = 4 3 ⋅ 21. __ 45 = 15 5 9 3 ⋅ 19. ___ 24 = 12 6 3 4 8 ⋅ 20. ___ 80 = 10 8 7 64 9 22. Stretch Your Thinking Write a multiplication equation using one whole number and one fraction that have 18 . a product of ___ 8 3 = ___ 18 Possible answer: 6 ⋅ __ 8 8 52 UNIT 3 LESSON 3 Multiplication with Fractional Solutions © Houghton Mifflin Harcourt Publishing Company 4 ⋅ 20 = 13. __ Name 3-4 Date 3 __ Tanith is using a number line to find __ ⋅ 2 . This is her work so far: 4 5 0 1 – 5 2 – 5 3 – 5 4 – 5 1 0 1 – 5 2 – 5 3 – 5 4 – 5 1 0 — 20 1 — 20 2 — 20 3 — 20 4 — 20 5 — 20 6 — 20 7 — 20 8 — 20 9 — 20 10 — 20 11 — 20 12 — 20 13 — 20 14 — 20 15 — 20 16 — 20 17 — 20 18 — 20 19 — 20 20 — 20 1. Explain Tanith’s work so far to someone at home. 3 of each 2. Finish Tanith’s work by circling __ 4 circled fifth. How many 20ths did you circle altogether? 6 3 3 __ 2 ___ or ___ What is __ ⋅ ? 20 10 4 5 2 __ 3. Use the number line to find __ ⋅ 5. 3 6 Label all the parts above and below. 1 – 6 0 0 — 18 1 — 18 2 — 18 3 — 18 2 – 6 4 — 18 5 — 18 6 — 18 10 ___ 18 3 – 6 7 — 18 8 — 18 6 9 — 18 4 – 6 10 — 18 11 — 18 5 – 6 12 — 18 13 — 18 14 — 18 16 — 18 17 — 18 18 — 18 Show your work. Solve. © Houghton Mifflin Harcourt Publishing Company 15 — 18 1 3 of a bag of popcorn. 4. Four friends at a party popped __ 4 They ate half of what was popped. What fraction of the 3 __ popcorn in the bag did they eat? 8 7 5. Ashley brought __ gallon of lemonade to the party. 8 2 of it. How many gallons of Her friends drank __ 3 7 ___ gallon lemonade did they drink? 12 Multiply. You do not need to simplify. 2 ___ 2 __ 1 = 4 __ ⋅ 7. __ ⋅2= 6. __ 21 7 3 9 9 24 ___ 2 4 __ 9. __ ⋅ 12 = 10. __ ⋅2= 7 7 5 3 9 ___ 9 __ 5 1 = 12. ___ ⋅ 13. ___ ⋅3= 20 10 2 12 UNIT 3 LESSON 4 8 ___ 81 8 ___ 15 15 ___ 12 1 __ 8. __ ⋅5= 8 6 1 __ 11. __ ⋅3= 7 5 5 __ 14. __ ⋅1= 6 6 5 ___ 48 3 ___ 35 5 ___ 36 Multiply a Fraction by a Fraction 53 Name 3-4 Date Name the mixed number shown by the shaded parts. 1 5__ 2 1. 5 1__ 7 2. 1 1__ 3 3. Add. 81.46 5. 80.55 + 0.91= 454.65 4. 454 + 0.65 = 37.98 m 6. 31.78 m + 6.2 m = 1 7. Show __ of 7 on the number line. 3 0 1 2 3 4 5 6 7 7 __ 1 of 7 as a fraction. 8. Write __ 3 3 1 2__ 3 3 5 6 10. Stretch Your Thinking Solve for the unknown fraction. Then divide and shade an area model to show the 2 ⋅ = ___ ? 10 . equation. __ 5 2 5 30 5 __ 6 54 UNIT 3 LESSON 4 Multiply a Fraction by a Fraction © Houghton Mifflin Harcourt Publishing Company 1 9. Write __ of 7 as a mixed number. Name 3-5 Date Multiply. Simplify first if you can. 12 ___ 2 __ 1. __ ⋅6= 5 7 5 ___ 3. ___ ⋅ 8 = 3 24 15 3 1 1 5 35 1 12 3 9 6 1 1 7 __ 12. __ ⋅2= 21 49 7 25 5 __ 10. __ ⋅7= 2 ___ 2 1 816 15 7 ___ 11. __ ⋅ 6 = 3 1 1 ___ 1 4 ___ 9. ___ ⋅ 7 = 8 5 ___ 8. ___ ⋅ 2 5= 5 31 1 7 1 __ 1 1 5 __ 6. __ ⋅3= 25 3 ⋅ __ 2 = 7. ___ 5 10 17 9 ___ ⋅ 4 25 12 = ___ 82 2 __ 4. ___ ⋅8= 9 3 3 5. __ 9 1 __ 1 1 1 4 __ 2. __ ⋅1= 35 4 8 3 1 ___ 18 16 ___ 17 15 ___ 56 1 ___ 40 35 ___ 6 7 ___ 12 13. Which fraction is not equivalent to the others? 3 ___ 2 ___ 1 __ 9 ___ 10 ___ 6 ___ 7 ___ 100 ____ 15 10 5 45 50 40 35 500 Solve. Show your work © Houghton Mifflin Harcourt Publishing Company 3 of the animals are birds. Of the 14. In the town zoo, ___ 28 4 ___ are birds of prey. What fraction of the birds, 15 animals at the zoo are birds of prey? 1 ___ 35 5 15. Tuesday at the zoo, ___ of the visitors were adults. Of these 12 3 ___ were men. What fraction of the people who adults, 10 visited the zoo on Tuesday were men? 1 __ 8 14 16. On Tuesday, ___ of the souvenirs purchased at the zoo gift 25 shop were stuffed animals. Of the stuffed animals purchased, 10 ___ were bears. What fraction of the souvenirs purchased at 21 the zoo gift shop on Tuesday were stuffed bears? 4 ___ 15 UNIT 3 LESSON 5 Multiplication Strategies 55 Name 3-5 Date Add or subtract. 1 + __ 2. 5__ 35 4 + __ 1. 1__ 52 5 5 6 1 7__ 3 3 + __ 5 4. __ 4 2 3 1 1__ 9 5 4 2 - __ 1 3. 1__ 6 3 8 - __ 35 5. 7__ 9 9 3 1 __ 4 or 4__ 9 3 1 6. 6 - 4__ 8. 132.76 - 87.24 = 9. 968.29 - 217.5 = 2 1 1__ 2 Subtract. 7. 31,763 - 6.51 = 45.52 31,756.49 750.79 3 __ 10. Use the number line to find __ ⋅ 2 . Label all the parts 4 5 above and below. ⋅ __2 = 4 5 3 __ 6 ___ 20 1 5 0 1 20 2 20 3 20 4 20 5 20 6 20 7 20 8 20 1 9 20 10 20 11 20 12 20 13 20 14 20 15 20 16 20 17 20 18 20 19 20 20 20 11. Stretch Your Thinking Write a word problem that will 2 ___ ⋅ 8 = x in order to solve. Then use the equation __ 6 10 simplify and multiply to solve. 8 of the basketball team’s points in Possible answer: Jacob scored ___ 10 Saturday’s basketball game. Two sixths of the points Jacob scored were from free throws. What fraction of the team’s points did Jacob score 2 ___ 1 __ 4 from free throws? __ ⋅ 8 = __ ⋅ 4 = ___ 6 56 UNIT 3 LESSON 5 10 3 5 15 Multiplication Strategies © Houghton Mifflin Harcourt Publishing Company 0 20 2 5 Name 3-6 Date Find each product by first rewriting each mixed number as a fraction. 3 ⋅ 2__1 = 1. __ 7 2 2 3. 2__ ⋅ 4__1 = 5 3 3 __ 15 = ___ __ ⋅ 5 = ___ 11 7 2 2 5 3 7 2. 1___ ⋅5= 14 10 5 5 5 __ 7 __ ⋅ 7 = __ 9 5 1 7. 3__ ⋅ 3__1 = 14 8 ___ 56 = 1 __ ⋅ 21 = ___ 11__ 5 5. __ ⋅ 1__2 = 9 2 5 2 4 3 8 3 = 6. 12 ⋅ 2__ 9 4 49 = 7 __ 1 __ ⋅ 7 = ___ 12__ 2 1 __ 4. 5__ ⋅3= 4 9 = 1 8. __ ⋅ 3___ 9 10 Solve. 17 __ 17 = __ ___ ⋅ 5 = ___ 81 1 10 2 2 16 __ ___ ⋅3=2 3 8 12 ___ ___ ⋅ 11 = 33 1 4 13 1 ___ __ ⋅ 39 = ___ 9 10 30 Show your work. © Houghton Mifflin Harcourt Publishing Company 9. The bottom of Zeyda’s jewelry box is a rectangle with 3 1 inches and width 3__ inches. What is the area length 5__ 4 8 of the bottom of the jewelry box? 15 17___ square inches 32 10. The Patel family went apple picking. The number of 2 times the number of red apples they picked was 2__ 9 green apples they picked. If they picked 45 green apples, how many red apples did they pick? 100 red apples 1 11. The art museum is 8__ miles from Alison’s house. 2 2 of the way there so far. Alison has ridden her bike __ 3 How far has she gone? 2 miles 5__ 3 UNIT 3 LESSON 6 Multiply Mixed Numbers 57 Name 3-6 Date Add. 3 + __ 1 1. __ 8 3 1 + __ 2. __ 5 6 5 + __ 1 3. __ 4 6 8 13 ___ 19 ___ 23 ___ 24 20 24 1 + __ 2 4. __ 2 + __ 1 5. __ 7 3 3 4 + ___ 1 6. __ 5 9 10 13 ___ 7 __ 9 ___ 21 9 10 Use the Commutative Property to solve for n. 7. 55,207 + 87,331 = 87,331 + n n = 55,207 8. 48.76 + 20.08 = 20.08 + n n = 48.76 Multiply. Simplify first if you can. 1 __ 3 = 2 __ 7 __ ⋅ 10. ___ ⋅6= 9. __ 2 3 4 10 7 6 25 2 __ 1 __ ⋅4= 13. __ 5 2 7 5 2 __ 7 3 __ 11. __ ⋅5= 5 6 2 __ 14. __ ⋅3= 9 8 1 __ 2 1 ___ 12 15. Stretch Your Thinking Complete the mixed number equation that is represented by the area model. ⋅ 2 1 __ 58 2 1__ 3 = UNIT 3 LESSON 6 5 __ 6 Multiply Mixed Numbers © Houghton Mifflin Harcourt Publishing Company 5 ___ ⋅ 12 = 12. __ 3 __ 3-7 Name Date Solve. 3 __ ⋅1 1. __ 4 8 3 ___ 32 2 - __ 1 2. __ 2 4. __ ⋅ 12 7 24 = __ ___ 33 7 7 1 + __ 2 5. __ 5 __ 7. __ ⋅5 7 6 25 ___ 42 11 + 8. ___ 3 1 __ 10. __ ⋅1 3 8 1 ___ 24 3 1 + __ 1 3. ___ 9 10 5 __ 3 ___ 9 10 5 5 3 1 + __ 6. __ 4 3 8 5 __ 8 13 ___ 15 4 - __ 2 9. __ 12 9 11 3___ 9 2 __ 12 9 1 12. 10 - __ 9 89 = __ ___ 98 9 9 7 __ 11. __ ⋅3 8 4 21 ___ 32 Show your work. Solve. 7 gallon of water. It is 13. Rodrigo’s fish bowl holds __ 8 1 now __ full. How much water is in it? 2 7 ___ gallon 16 © Houghton Mifflin Harcourt Publishing Company 1 14. Kenya jumped 7__ feet. Janet jumped 6 How much farther did Kenya jump? 5 __ foot 6 1 6__ feet. 3 7 15. A group of hikers walked 8___ miles to Caribou Cave 10 1 __ and then 5 miles to Silver Stream. How far did they 5 walk altogether? 9 13___ miles 10 3 16. A recipe calls for __ cup of flour. Estevan wants to make 4 1 __ of the recipe. How much flour will he need? 3 1 __ cup 4 1 17. A truck was carrying 2__ tons of sand. When it arrived, 8 1 only 1__ tons of sand were left. How much sand was 2 lost along the way? 5 __ ton 8 UNIT 3 LESSON 7 Relate Fraction Operations 59 Name 3-7 Date Subtract. 3 - __ 1 1. __ 4 2 - ___ 1 2. __ 6 9 10 7 - __ 1 3. __ 4 8 7 ___ 11 ___ 5 __ 12 90 8 6 - __ 1 4. __ 7 4 - __ 2 5. __ 5 3 3 1 - __ 1 6. __ 2 8 11 ___ 2 ___ 3 __ 21 15 8 Sample estimates shown; accept reasonable estimates. 8. $44.25 - $21.76 $22 9. 14.6 + 2.4 17 Estimate each sum or difference. 7. 6.759 + 2.099 9 Find each product by first rewriting each mixed number as a fraction. 5 ___ 25 = ___ __ ⋅ 10 = ___ 21 5 1 = ⋅ 3__ 10. __ 8 3 12 12 8 3 3 11. 4__ ⋅5= 5 2 12. 1__ ⋅ 3__4 = 5 9 5 8 5 1 1 7 ___ 217 = ___ __ ⋅ 31 = ___ 4 37 5 9 45 45 © Houghton Mifflin Harcourt Publishing Company 1 __ 13. 6__ ⋅5= 23 __ 23 = ___ ⋅ 5 = ___ 23 31 __ 31 = __ ___ ⋅ 5 = ___ 37 5 8 8 8 14. Stretch Your Thinking Give an example that shows how to use the Distributive Property to multiply a number by a sum. All of the numbers you use should be mixed numbers or fractions. 5 = __ 2 1 + __ 1 + __ 2 __ Possible answer: __ ⋅ (2__ ) 2 ⋅ 2__ ⋅5= 4 4 3 6 3 3 6 3 + __ 5 = ___ 37 = ___ 2 __ 2 __ __ ⋅ 9 + __ ⋅ 5 = __ 21 3 4 3 6 2 9 18 18 60 UNIT 3 LESSON 7 Relate Fraction Operations Name 3-8 Date Complete each fraction box. 1. 3 7 __ and __ > + - ⋅ 8 3 6 7 > __ 7 > __ __ or __ 4 8 8 8 7 __ 8 7 __ 8 7 __ 8 2. 3 1 __ and __ 3 = __ 6 = ___ 13 = __ 7 + __ + __ 15 4 8 8 8 8 3 = __ 6 = __ 7 - __ 1 - __ 4 8 8 8 3 = ___ 21 ⋅ __ 4 32 5 2 4 > + - ⋅ 3 > __ 6 > ___ 5 1 __ or ___ 5 2 10 3 = ___ 5 + 1 + __ __ 5 2 10 3 - __ 6 1 = ___ __ 5 2 10 3 1 __ __ ⋅ 3 = ___ 2 5 10 10 6 = ___ 10 5 = ___ 10 11 = ___ ___ 11 10 1 ___ 10 10 Show your work. Solve. 7 ton of 3. The Eagle Trucking Company must deliver __ 8 5 __ cement blocks and ton of bricks to one place. 8 How much will this load weigh? 1 1__ tons 2 © Houghton Mifflin Harcourt Publishing Company 1 1 4. A truck carried 3__ tons of sand, but lost __ ton along 4 3 the way. How many tons of sand were delivered? 1 3___ tons 12 2 5. The trucking company also needs to deliver 1__ tons of 3 7 ___ oak logs and 1 tons of maple logs. Which load 12 weighs more? oak logs 3 1 6. In a load of __ ton of steel rods, __ of them are bent. 4 8 How many tons of steel rods are bent? 3 ___ ton 32 3 7. The company delivered 1__ tons of bricks to one building site. 5 1 __ They delivered 2 times this much to a second site. What was 2 the weight of the load the company delivered to the second site? 4 tons UNIT 3 LESSON 8 Solve Real World Problems 61 Name 3-8 Date Multiply. 1. 2. 2,548 × __5 3. 945 12,740 4. 21 × 45 _ 5. 33 × _4 132 3,015 × __6 18,090 65 × 87 _ 6. 215 × __9 1,935 5,655 Find each product by first rewriting each mixed number as a fraction. 40 __ 320 = 23 ___ ⋅ 8 = ___ 11___ 4 2 = 7. 4__ ⋅ 2__ 9 3 27 27 9 3 5 9. 3__ 6 23 ___ 12 = ___ 6 ⋅ 13 1 8. 6__ ⋅ 10 = 13 5 5 46 = ___ 12 = ___ ⋅ ___ 37 13 31 ___ 62 = ___ ⋅ 10 = ___ 62 1 10. 5__ 13 3 16 ___ 3 = __ 3 ⋅5 1 1 3 = ___ 16 = __ ⋅ __ 31 5 5 5 Solve. 6 - __ 2 11. __ 7 7 4 __ 7 4 + __ 2 12. __ 9 3 1 1__ 9 2 ___ 13. __ ⋅ 9 3 10 3 __ 5 3 __ ⋅5 14. __ 1 15. 8 - __ 3 1 + __ 16. __ 5 7 8 6 55 = __ ___ 76 7 7 8 13 ___ 24 © Houghton Mifflin Harcourt Publishing Company 3 __ 8 17. Stretch Your Thinking Write and solve a word problem that requires multiplying two mixed numbers. 5 Possible answer: Taylor worked 6__ hours doing yard 6 work one weekend. The next weekend, he worked 1 1__ times as long as he did the previous weekend. 2 How many hours did Taylor work on the second 1 weekend? 10__ hours 4 62 UNIT 3 LESSON 8 Solve Real World Problems Name 3-9 Date Predict whether the product will be greater than, less than, or equal to the second factor. Then compute the product. Predictions may vary. 4 1. __ ⋅6=x 1 2. 1__ ⋅6=x 5 Predict: x < 6 4 4__ 5 Compute: x = 2 __ 4. __ ⋅5=x 2 10 3. ___ ⋅6=x 9 10 Predict: x > 6 2 6__ 3 Compute: x = 5 __ 5. __ ⋅5=x 6 6 5 Predict: x = __ 6 __ 5 Compute: x = 6 Compute: x = 6 Compute: x = 1 __ 6. 1__ ⋅5=x 6 Predict: x < Predict: x = 6 3 5 __ 6 ___ 25 36 6 5 Predict: x > __ 6 Compute: x = 1 1__ 9 Show your work. Solve. 3 times as tall as his brother. His brother 7. James is 1__ 7 1 __ is 3 feet tall. 2 1 feet? Is James’s height more or less than 3__ 2 © Houghton Mifflin Harcourt Publishing Company more How tall is James? 5 feet 8. South Middle School has 750 students. North Middle 13 times as many students as South. School has ___ 15 Does North Middle School have more or fewer than 750 students? fewer How many students attend North Middle School? 650 students UNIT 3 LESSON 9 Make Generalizations 63 Name Date Perry measured the foot length of four friends for a science fair experiment. Then, he made a bar graph to display his results. Foot length (in.) Foot Length 1. How much longer is Brennen’s foot than Clara’s foot? 0.7 inch 2. What is the difference between the longest foot and the shortest foot? 9 8.8 8.6 8.4 8.2 8 7.8 7.6 7.4 n a Ch Br en ne ar Cl ey 0.9 inch ne Ty e 0 en 3-9 Student Name Solve. 7 7 __ 3. __ ⋅ 4 ___ 8 9 18 1 3 4. 11 - __ 10__ 4 4 1 9 - ___ 5 __ 6. ___ 12 12 3 7 + __ 2 7. ___ 15 3 15 = __ 4 + ___ 7 ___ 5. __ 11 5 10 10 2 17 = ___ ___ 12 15 15 15 5 ___ ⋅ 9 ___ 8. __ 6 11 22 Complete each fraction box. 5 7 ___ and __ 12 4 2 __ and __ 6 5 + − ⋅ 6 12 12 5 10 7 __ + ___ = ___ + 6 12 12 5 - ___ 10 − 7 = ___ __ 6 12 12 5 35 7 __ ⋅ ___ = ___ 6 12 72 12 7 ___ = 12 7 = ___ 12 > 17 = ___ ___ 15 12 12 3 = __ 1 ___ 4 12 + − ⋅ 3 10 4 > __ 2 12 > ___ __ or ___ 5 15 3 4 + __ 2 = ___ 12 + __ 5 15 3 4 − __ 2 = ___ 12 − __ 5 15 3 8 4 __ __ ⋅ 2 = ___ 5 3 15 15 10 ___ = 15 10 = ___ 15 22 = ___ ___ 17 15 15 2 ___ 15 9. Stretch Your Thinking Write two multiplication equations using fractions and mixed numbers. Write one equation that will have a product greater than the first factor. Then write another equation that will have a product less than the first factor. 3 = ___ 25 = ___ 4 1 __ ⋅ 2__ 3 31 ; 3__ ⋅ 2 = ___ 21 Possible answer: 1__ 9 8 72 8 3 12 12 64 UNIT 3 LESSON 9 Making Generalizations © Houghton Mifflin Harcourt Publishing Company 5 > ___ 10 > ___ 7 7 > __ or ___ Name 3-10 Date Divide 5 __ 1. 5 ÷ 6 = 3. 33 ÷ 30 = 5. 3 ÷ 10 = 1 = 7. 100 ÷ __ 6 1 ÷ = 9. __ 8 5 1 ÷ = 11. __ 9 2 6 10 3 ___ 10 600 1 ___ 40 1 ___ 18 45 1 = 4. 8 ÷ __ 48 1 = 6. 4 ÷ __ 36 5 11 = ___ ___ 11 10 1 = 2. 9 ÷ __ 6 9 1 ___ 8. 1 ÷ 100 = 100 1 ___ 1 ÷ = 10. __ 7 56 8 1 ___ 1 ÷ = 12. __ 5 15 3 Show your work. Solve. 13. Alexander is dividing oranges into eighths. He has 5 oranges. How many eighths will he have? 40 eighths © Houghton Mifflin Harcourt Publishing Company 14. Carrie has 32 ounces of ice cream to divide equally among 10 people. How much ice cream will each person get? 1 3__ ounces 5 15. Nayati wants to swim 50 miles this school year. She plans to swim _1_ mile each day. How many days will it take her to 4 swim 50 miles? 200 days 1 16. Eric has __ of a watermelon to share equally with 3 friends. 3 How much will each person get? 1 ___ watermelon 12 17. A gardener needs to pack 16 pounds of beans into 20 bags. He wants all the bags to weigh about the same. About how much will each bag weigh? _4_ pound 5 UNIT 3 LESSON 10 When Dividing Is Also Multiplying 65 Name 3-10 Add or subtract. 3 1. 2__ Date 2. 4 5 - 1__ _8 1 1__ 5. 1 - 2__ _6 5 4__ 12 8. 5 6 __ and __ 7 6 7 10 2 14 > ___ > __ or ___ 7 35 35 10 2 14 __ ___ ___ + = + = 7 35 35 10 = 2 = ___ 14 − ___ − __ 7 35 35 2 = ___ 4 __ ⋅ 7 35 3 3 + 1__ _4 1 10___ 30 2 __ 5 2 __ 5 2 __ 5 2 __ 5 1 8__ 6. 7 8___ 5 ⋅ 10 5 5 + 4__ _6 Complete each fraction box. 7. 2 2 __ and __ − 7 6___ 2 3__ 6 + 2 6__ 2 4 - 3__ _5 9 7 > 1 3. 10__ 3 5 + 1__ _9 8 4. 2 4__ 6 > __ 5 36 > ___ 35 __ or ___ > 24 ___ 35 4 ___ 35 7 6 42 42 6 5 36 35 __ + __ = ___ + ___ = 7 6 42 42 6 − __ 5 = ___ 36 − ___ 35 = __ 7 6 42 42 6 5 30 5 __ ⋅ __ = ___ = __ 7 6 7 42 + − ⋅ 71 = ___ ___ 1 29 42 42 1 ___ 42 Predict whether the product will be greater than, less than, or equal to the second factor. Then compute the product. Predictions may vary. 3 2 1 ⋅5=x 10. __ ⋅5=x 11. 1__ ⋅5=x 9. __ 3 Compute: x = 1 3__ 3 6 Predict: x > 5 Predict: x = 5 Compute: x = 5 Compute: x = 5 5__ 6 12. Stretch Your Thinking Draw a diagram to show how many twelfths there are in 3. Describe a situation in which you would need to know how many twelfths there are in 3. 1 of a foot, so the Possible answer: An inch is ___ 12 number of inches in 3 feet is the number of twelfths in 3. 66 UNIT 3 LESSON 10 When Dividing Is Also Multiplying © Houghton Mifflin Harcourt Publishing Company Predict: x < 5 3 3-11 Name Date 1 ÷ 1. Consider the division problem __ 3. 2 Describe a situation this division could represent. Situations will vary. Draw a diagram to represent the division. Then find the solution. 1 __ ; Diagrams will vary. Check students’ work. 6 Write an equation. Then solve. Equations may vary. Show your work. 2. A rectangle has an area of 12 square feet and a length of 5 feet. What is its width? 2 5 ⋅ w = 12; 2__ feet 5 © Houghton Mifflin Harcourt Publishing Company 1 3. A tortoise must walk ___ mile to visit a friend. He plans to 12 break the journey into four equal parts with breaks in between. How long will each part of his journey be? 1 ÷ 1 4; ___ mile x = ___ 12 48 1 4. Harry worked 7 hours last week. This is __ as many hours as 3 Aidan worked. How many hours did Aidan work? 1 __ ⋅ a = 7; 21 hours 3 5. Lin is a camp counselor. She is making small bags of trail mix for campers to take on a hike. She has 2 pounds of raisins and 1 pound in each bag. How many bags can she fill is putting __ 8 before she runs out of raisins? 1 ; 16 bags x = 2 ÷ __ 8 1 6. Mr. Ramirez bought __ pounds of cashews. He divided the 4 cashews equally among his three children. How much did each child get? 1 ÷ 1 3; ___ pound x = __ 4 12 UNIT 3 LESSON 11 Solve Division Problems 67 Name 3-11 Date Add or subtract. 1. 1 1__ 2. 8 2 + 4__ _3 19 5___ 4. 1 6__ 3. 4 5 – 4__ _6 12 4 5. 7 11 + 5___ 14 __ 6. 2 – 2__ _5 3 1__ 5 1 11___ 14 3 8 + 7__ _9 2 17__ 5 1___ 24 2 5__ 1 9__ 9 5 6__ 8 1 + 3__ _2 1 10__ 8 Predict whether the product will be greater than, less than, or equal to the second factor. Then compute the product. Predictions may vary. 5 ⋅9=x 7. __ 7 8. __ ⋅9=x 5 Predict: x = 9 5 Predict: x < 9 9 Compute: x = 1 __ 10. 1__ ⋅4=x 2 3 9. 1__ ⋅9=x 8 7 7__ 8 Compute: x = 6 __ 11. __ ⋅4=x 5 6 4 Predict: x > __ 5 Compute: x = 1 1__ 5 Predict: x > 9 2 14__ 5 Compute: x = 2 __ 12. __ ⋅4=x 5 5 4 Predict: x = __ 5 Compute: x = 4 __ 5 5 4 Predict: x < __ 5 8 ___ 25 Compute: x = Divide. 4 1 = 16. 200 ÷ __ 4 24 800 14. 2 ÷ 3 = 1 ÷ = 17. __ 8 4 2 __ 3 1 ___ 32 15. 10 ÷ 3 = 1 ÷ = 18. __ 6 7 1 3__ 3 1 ___ 42 19. Stretch Your Thinking Harrison is playing a board game that 1 of the has a path of 100 spaces. After his first turn, he is __ 5 1 fewer way along the spaces. On his second turn, he moves __ 4 spaces than he moved on his first turn. On his third turn, he 1 times as many spaces than he moved on his first moves 1__ 4 turn. What space is he on after three turns? 60 68 UNIT 3 LESSON 11 Solve Division Problems © Houghton Mifflin Harcourt Publishing Company 1 = 13. 6 ÷ __ Name 3-12 Date Solve. 1 = 1. 5 ⋅ __ 3 1 ÷ = 3. __ 2 8 1 = 5. 5 ÷ ____ 100 3 ___ 7. __ ⋅ 10 = 5 27 1 ÷ 9. __ 10 = 5 1 11. __ ⋅ 14 = 8 5 __ 3 1 = 2. 5 ÷ __ 3 1 ___ 16 4. 27 ÷ 10 = 500 1 = 6. 12 ⋅ __ 2 __ 9 1 ___ 50 3 1__ 4 15 7 2___ 10 1 1__ 9 3 1 = 8. 16 ÷ __ 64 1 = 10. 10 ÷ __ 50 4 5 12. 18 ÷ 20 = Tell whether you need to multiply or divide. Then solve. Equations will vary. Possible equations are given. 9 ___ 10 Show your work. 1 ounce. Jody has 1 pound 13. A dime weighs about ___ 12 (16 ounces) of dimes. About many dimes does she have? Divide; 192 dimes 1 14. Maddie has 180 coins. Of these coins, ___ are dimes. 12 About how many dimes does she have? © Houghton Mifflin Harcourt Publishing Company Multiply; 15 dimes 1 15. A rectangle has length 3 feet and width __ foot. What is the 4 area of the rectangle? 3 square foot Multiply; __ 4 1 16. A rectangle has area 3 square feet and width __ foot. 2 What is the length of the rectangle? Divide; 6 feet 17. Nisha wants to study 5 hours for the spelling bee. If she 1 hour per night, how many nights will she studies __ 3 have to study? Divide; 15 nights UNIT 3 LESSON 12 Distinguishing Multiplication from Division 69 Name 3-12 Date Multiply. 1. 134 ⋅ 5 = 670 4. 4,507 ⋅ 3 = 13,521 2. 44 ⋅ 21 = 924 3. 7 ⋅ 57 = 399 5. 36 ⋅ 76 = 2,736 6. 1,928 ⋅ 6 = 11,568 1 = 8. 100 ÷ __ 1 ÷ = 9. __ 4 Divide. 1 ÷ = 7. __ 2 9 10. 4 ÷ 5 = 1 ___ 18 4 __ 5 3 11. 12 ÷ 5 = 300 2 2__ 5 5 1 = 12. 8 ÷ __ 7 1 ___ 20 56 Show your work. Write an equation. Then solve. Equations may vary. 14. Stretch Your Thinking Using a whole number and a fraction as factors, write a multiplication equation with a product less than the whole number factor. Draw a picture to show how the product is less than the whole number factor. 9 7 Possible answer: ___ ⋅ 3 = 2___ 10 10 70 UNIT 3 LESSON 12 Distinguishing Multiplication from Division © Houghton Mifflin Harcourt Publishing Company 13. Marc is running 5 kilometers at track practice. He decides to break the run into 3 equal lengths. How long will each length be? 2 x = 5 ÷ 3; 1__ km 3 Name 3-13 Date Show your work. Solve. 1. Dan’s Ice Cream comes in cartons of two sizes. The large 3 1 pounds. The small carton holds 1__ pounds carton holds 4__ 4 2 less. How much ice cream does the small carton hold? 3 2__ pounds 4 2. Mac picked four baskets of blueberries. The weights of the berries in pounds are given below. Order the weights from lightest to heaviest. 5 __ 9 ___ 4 __ 13 ___ 4 10 5 20 13 __ 9 __ ___ , 4 , ___ ,5 20 5 10 4 1 3. Four cones of Dan’s Ice Cream hold __ pound. How much 2 ice cream does each cone hold? 1 __ pound 8 1 4. If a dish of ice cream holds __ pound, how many dishes can 4 1 __ you get from a 4 -pound carton of Dan’s Ice Cream? 18 dishes 2 © Houghton Mifflin Harcourt Publishing Company Solve. Give your answer in simplest form. 1 = 5. 3 ÷ __ 5 9 7. ___ ⋅ 2__1 = 14 3 = 1 + __ 9. __ 5 3 1 ÷ = 11. __ 4 8 5 - __ 13. 3__ 11 = 7 2 UNIT 3 LESSON 13 4 1 1__ 2 3 7 2___ 3 + ___ 11 = 6. 1__ 15 14 ___ 3 8. 2__ ⋅6= 6 1 ___ 9 2 - ___ 1 = 12. __ 32 5 3 2___ 14 3 15__ 5 5 5 + __ 8 = 10. __ 15 16 16 10 7 __ 14. __ ⋅2= 8 7 13 1___ 18 3 ___ 10 1 __ 4 Review Operations with Fractions 71 Name 3-13 Date 1 Use benchmarks of 0, __ , and 1 to estimate the sum or 2 difference. Then find the actual sum or difference. 5 + __ 4 1. ___ 10 13 – __ 3 2. ___ 14 9 1 Estimate: 85 17 ___ or ___ Sum: 90 18 1 __ Estimate: 2 1 __ 2 Difference: 8 – __ 7 3. __ 9 7 13 + __ 3 4. ___ 8 14 0 1 ___ Estimate: 2 Estimate: 72 Difference: 4 Sum: 19 1___ 28 Show your work. Write an equation. Then solve. Equations may vary. 5. A rectangle has an area of 20 square feet and a length of 6 feet. What is its width? 1 6 ⋅ w = 20; 3 __ feet 3 6. Bailey attends gymnastics practice for 8 hours each week. 1 the number of hours that the gym is open for This is __ 4 practice. How many hours is the gym open for practice? 1 __ ⋅ a = 8; 32 hours 4 Solve. 1 ÷ = 7. __ 3 4 1 ___ 12 1 8. __ ⋅3= 4 3 __ 4 1 = 9. 14 ⋅ __ 6 1 2 __ 3 © Houghton Mifflin Harcourt Publishing Company 1 ÷ 5 different 10. Stretch Your Thinking How is solving __ 8 1 from solving __ ⋅ 5? 8 1 ÷ 1 5, multiply __ by Possible answer: To solve __ 8 8 1 __ 1. 1 the reciprocal of 5: __ ⋅ 1 = ___ To solve __ ⋅ 5, first 8 5 40 8 5. rewrite 5 as __ Then, multiply the two fractions: 1 5. 1 __ __ ⋅ 5 = __ 8 1 8 72 UNIT 3 LESSON 13 Review Operations with Fractions Name 3-14 Date These graphs show the instruments in two different high school marching bands. Carter School Marching Band Reagan School Marching Band 1 – 3 1 – 3 percussion 2 – 5 brass 1 – 6 percussion woodwind 1 – 2 brass 4 — 15 woodwind Show your work. Solve. Use the circle graphs. 1. The Reagan School Marching Band has three percussion musicians. How many musicians altogether are in the band? 18 musicians 2. There are 30 musicians in the Carter School Marching Band. How many of them play brass instruments? © Houghton Mifflin Harcourt Publishing Company 12 musicians Suppose both bands decide to combine and perform as one band. 3. What fraction of the band members will play a brass instrument? 7 ___ 16 4. What fraction of the band members will play a percussion instrument? 13 ___ 48 5. What fraction of the band members will play a woodwind instrument? 7 ___ 24 UNIT 3 LESSON 14 Focus on Mathematical Practices 73 Name 3-14 Date Show your work. Solve. Explain how you know your answer is reasonable. Explanations may vary. 1 feet and a width 1. James’s garden has a length of 12__ 4 2 of 9__ feet. What length of fencing will he need to 3 surround his garden? 5 feet 43__ 6 Answer: Why is the answer reasonable? 1 2 12__ rounds to 12. 9__ rounds to 10. The answer 4 3 should be about 12 + 12 + 10 + 10, or 44 Solve. 1 ÷ = 2. ___ 3 11 1 ÷ = 5. ___ 5 12 1 ___ 33 1 ___ 60 1 = 3. 6 ÷ __ 3 1 = 6. 7 ⋅ __ 8 18 7 __ 8 2 __ 4. __ ⋅5= 3 7 1 7. __ ⋅ 12 = 5 10 ___ 21 2 2__ 5 Show your work. Solve. 1 pound altogether. What 8. Kayla packs 4 boxes that weigh __ 6 does each box weigh? 1 ___ pound 24 © Houghton Mifflin Harcourt Publishing Company 2 9. Mrs. Blackwell put 4__ grams on the scale during a lab in 3 5 grams to the scale. How science class. Then, she added 2__ 6 many grams are on the scale in all? 1 7__ grams 2 10. Stretch Your Thinking If you start with 1 and repeatedly 1 , will you reach 0? Explain why or why not. multiply by __ 2 No. Possible explanation: Each fraction has twice the denominator as the fraction preceding 1 __ 1 ___ , 1 , __ , 1 , . . . The fraction will get closer it: 1, __ 2 4 8 16 and closer to zero without ever reaching zero. 74 UNIT 3 LESSON 14 Focus on Mathematical Practices