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Name 1-1 Date Use the fraction bar below for Exercises 1–4. 1 7 1. Label the first part of this fraction bar with the correct unit fraction. 2. Circle the first four parts of the bar. What fraction of the whole does this circled portion represent? 4 __ 7 3. Write your fraction from Exercise 2 as a sum of unit fractions. 4 = __ 1 + __ 1 + __ 1 + __ 1 __ 7 7 7 7 7 4. Represent the whole as the sum of the unit fractions. 1 + __ 1 + __ 1 + __ 1 + __ 1 + __ 1 + __ 1 = __ 7 = __ 1 7 7 7 7 7 7 7 7 5. Solve the problem below by circling parts of the fraction bar. Write the appropriate equation below the bar. © Houghton Mifflin Harcourt Publishing Company Brett is building a fence around his yard. He has worked on it 3 2 the first week and __ the for two weeks so far. He finished __ 8 8 second week. What fraction of the entire fence has he built? 5 __ 8 Eighths 2 8 + 3 8 = 5 8 6. Nena thinks that because 4 < 6, it must also be true that 1 < __ 1 __ . Explain to Nena why this is incorrect. 4 6 1 1 Possible answer: The 4 in __ means the whole is divided into 4 parts. __ is 4 4 1 means the whole is divided into 6 parts. one of those parts. The 6 in __ 6 1 __ is one of those parts. The more parts we divide a whole into the 6 1 < __ 1 . smaller each part will be, so __ 4 6 UNIT 1 LESSON 1 Introducing the Math Board 1 1-1 Name Date List all the factors of each number. 1. 16 1, 2, 4, 8, 16 2. 29 1, 29 3. 33 1, 3, 11, 33 4. 40 1, 2, 4, 5, 8, 10, 20, 40 List the first four multiples of each number. 5. 6 6, 12, 18, 24 6. 11 11, 22, 33, 44 7. 15 15, 30, 45, 60 8. 1 1, 2, 3, 4 Complete. 2 1 + __ 1 = __ 9. __ 3 3 3 1 6 – ___ 5 = ___ 11. ___ 10 10 10 2 4 – __ 2 = __ 13. __ 9 9 9 5 3 = __ 2 + __ 10. __ 7 7 7 6 4 + __ 2 = __ , or 1 12. __ 6 6 6 3 1 + ___ 1 + ___ 1 = ___ 14. ___ 10 10 10 10 Write an equation. Then solve the problem. Equations may vary. 15. Maggie has a ribbon 27 feet long. What is the length of the ribbon in yards? 16. Mañuel has 15 goldfish. This is 6 more than Quinn has. How many goldfish does Quinn have? Equation: 27 ÷ 3 = n Equation: n + 6 = 15 Answer: 9 yards Answer: 9 goldfish 18. Julie bought 19 beads at the craft store. Now she has 36 beads. How many beads did she have before she went to the craft store? Equation: 4 • 13 = n Equation: n + 19 = 36 Answer: 52 students Answer: 17 beads 19. Stretch Your Thinking Rashid bought some baseball cards. After giving 7 cards to his friend Grace, he arranged the remaining cards in 6 rows of 4. How many cards did he buy? Equation: n - 7 = 6 • 4 Answer: 31 cards 2 UNIT 1 LESSON 1 Introducing the MathBoard © Houghton Mifflin Harcourt Publishing Company 17. In their yearbook photo, students in the chorus stood in four rows with 13 students in each row. How many students are in the photo? Name 1-2 Date 1. Write a chain of equivalent fractions for the shaded parts. = 1 __ 2 = = 2 __ 4 = = 3 __ = 4 __ = 6 = 8 8 ___ 16 Use the number lines to complete Exercises 2–7. Fourths 0 — 4 1 — 4 2 — 4 3 — 4 4 — 4 0 — 8 2 — 8 4 — 8 6 — 8 8 — 8 0 — 12 3 — 12 6 — 12 9 — 12 12 — 12 Eighths © Houghton Mifflin Harcourt Publishing Company Twelfths 3 __ 2. What fraction is marked by the star? 3. What fraction is marked by the heart? 8 8 ___ 12 3 4. If you have __ cup of flour, how many eighths do you have? 4 6 __ 8 3 5. If you have ___ of an orange, how many fourths do you have? 12 1 __ 4 10 ___ 3 10 __ ___ 12 6. Which is greater, or ? 4 12 9 3 __ Possible answers: ___ 6 4 12 __ 7. Give two equivalent fractions for . 8 UNIT 1 LESSON 2 Explain Equivalent Fractions 3 Name 1-2 Date Add or subtract. 57,533 1. 4,560 + 52,973 = 3. 4,300,129 + 3,426 = 4,303,555 2. 581,002 + 26,596 = 607,598 4. 398,000 – 213,546 = 184,454 5. Solve the problem below by circling parts of the fraction bar. Write the appropriate equation below the bar. 2 of the Molly is driving across the country. She covered ___ 10 3 ___ on the second day. What distance on the first day and 10 fraction of the distance did she cover in the first two days? 5 ___ 10 2 — 10 3 — 10 + = 5 — 10 Complete. 1 + __ 1 + __ 1 + __ 1 = 6. __ 8 8 8 4 – __ 1 = 8. __ 5 1 __ 3 8 2 3 __ 5 2 = + __ 1 3 6 9 12. Stretch Your Thinking Alyssa said that __ and ___ are not 8 12 equivalent because there is no whole number you can 6 9 by to get ___ . Is she correct? Explain. multiply both parts of __ 8 12 She is not correct. Possible explanation: You can 3 6 by 2 to get __ and by 3 multiply both parts of __ 4 8 9 6 9 to get ___. Because both __ and ___ are equivalent 12 8 12 3 __ to , they are equivalent to each other. 4 4 UNIT 1 LESSON 2 Explain Equivalent Fractions © Houghton Mifflin Harcourt Publishing Company 10. 5 8 10 3 = ___ 7 + ___ , or 1 7. ___ 10 10 10 2 ___ 8 + =1 9. ___ 10 10 1 __ 3 = 11. 1 – __ 4 4 4 1 __ , or __ Name 1-3 Date 1. Write a chain of equivalent fractions for the shaded parts. = 2 __ = 3 __ = 4 6 = 1 __ = = 8 ___ = 2 16 = 4 __ 8 Write the multiplier or divisor for each pair of equivalent fractions. 6 2 = ___ 3. __ 4 = __ 1 2. ___ 12 3 5. Divisor = 9 4 56 5 5. Divisor = 9 4 © Houghton Mifflin Harcourt Publishing Company 56 6 6 10 = __ 1 10. ___ 45 60 5 6 7. Divisor = 10 5 = ___ 35 13. __ 7 6. Divisor = 42 7. Multiplier = 3 24 = __ 12. ___ 42 5. Multiplier = 7 6. Multiplier = 3 = ___ 18 11. __ 7 7 5 = ___ 25 9. __ 4 6 5 = ___ 30 7. __ 8 6. Divisor = 4 = __ 1 8. ___ 10 7. Divisor = 3 21 = __ 6. ___ 50 5. Multiplier = 16 60 3 6. Multiplier = 3 = ___ 15 5. ___ 10 6 = ___ 1 4. ___ 27 6 8 42 7 7. Multiplier = Complete each exercise about the pairs of fraction bars. 2 ___ __ , 4 5 10 14. What equivalent fractions are shown? 2 15. Identify the multiplier. 16. What equivalent fractions are shown? 17. Identify the divisor. 6 __ __ ,2 9 3 3 18. Write a chain with at least six equivalent fractions. 9 12 3 6 ___ ___ __ ___ = = = 15 20 5 10 = 15 ___ 25 = 18 ___ 30 Answers will vary. This is one possible answer. UNIT 1 LESSON 3 Equivalent Fractions and Multipliers 5 1-3 Name Date In Exercises 1–3, use this fraction bar. 1. Shade two of the equal parts. What fraction does the shaded portion model? 2 __ 3 2. Split each equal part (each unit fraction) into two equal parts. What fraction does the shaded portion model now? 4 _ 6 3. Fill in the boxes to show how you unsimplified the original fraction. 2× 2 4 _ = _ 3× 2 6 Show your work. Solve. 4. A restaurant has 60 plates. One night, 9 groups of 6 people ate dinner at the restaurant at the same time. How many plates were not used by these diners? 6 plates 2 plants 6. Stretch Your Thinking Carol’s bookshelf has 4 shelves with 6 books on each. Her brother Robert has 3 shelves with 7 books on each. They want to combine their books. If they put 9 books on a shelf, how many shelves will they need? 5 shelves 6 UNIT 1 LESSON 3 Equivalent Fractions and Multipliers © Houghton Mifflin Harcourt Publishing Company 5. Clara has a garden that is 7 feet wide and 4 feet long. She has 30 tomato plants to put in the garden. Each plant needs 1 square foot of space. How many leftover plants will Clara have? Name 1-4 Date Compare. 5 > __ 5 1. __ 1 < __ 1 2. __ 2 < __3 3. __ 6 > __2 4. __ 10 < ___ 11 5. ___ 3 < ___ 5 6. __ 5 < __4 7. ___ 1 < __ 4 8. __ 1 > __ 2 9. __ 1 1 10. ___ > ___ 7 < ___ 11 11. ___ 8 8 12 12 5 9 11 3 7 15 3 10 4 5 12 8 4 9 15 5 12 9 51 12 < ____ 12. ___ 25 100 Show your work. Solve. 13. During his first season on the school football team, Wade made 5 of the 9 field goals he tried. During his second season, he made 11 of the 15 field goals he tried. In which season did he make the greater fraction of the field goals he tried? during the second season 11 7 14. Mañuela bought ___ yard of polka dot fabric and __ yard 12 9 of flowered fabric. Which fabric did she buy more of? © Houghton Mifflin Harcourt Publishing Company the polka dot fabric 15. Of the 7 pens in Ms. Young’s desk, 3 are blue. Of the 9 pens in Mr. Fox’s desk, 5 are blue. Which teacher has a greater fraction of pens that are blue? Mr. Fox 16. Mr. Sommers spent 10 minutes of his 50-minute math period reviewing homework. Mr. Young spent 12 minutes of his 60-minute math period reviewing homework. Which teacher spent a greater fraction of his math period reviewing homework? 1 of the period Neither; both teachers spent __ 5 reviewing homework. UNIT 1 LESSON 4 Strategies for Comparing Fractions 7 Name 1-4 Date Complete. 3 __ 1 + __ 1 + __ 1 = 1. __ 4 4 4 + __ 1 = 3. __ 5 4 4 5 4 __ 8 – __ 4 = 2. __ 9 5 __ , or 1 3 + __ 3 = 4. __ 5 9 9 8 8 6 3 __ , or __ 4 8 Write the multiplier or divisor for each pair of equivalent fractions. 5 = ___ 10 5. __ 6 15 2 Multiplier = 5 4 5 Divisor = 4 ___ 5 = 12. __ 10 ___ 9 10 22 18 7 Multiplier = = 6 ___ = 15 ___ 15 27 = 8 ___ = 20 ___ 20 36 = 10 ___ = 25 ___ 25 45 6 11 = __ 1 10. ___ 28 Complete the chain of equivalent fractions. 5 24 Multiplier = 1 = ___ 7 9. __ 10 2 = 11. __ 4 3 Divisor = 25 = ___ 5 8. ___ 50 3 = ___ 18 7. __ 12 = __ 4 6. ___ 12 = 2 Divisor = 11 Answers may vary. Possible answers are given. 12 14 ___ ___ = = 30 30 ___ 54 35 = 35 ___ 63 Solve. He is not correct. The size of the whole was different for the two pizzas. Half of a large pizza is more than half of a small pizza because it is half of a larger amount. 8 UNIT 1 LESSON 4 Strategies for Comparing Fractions © Houghton Mifflin Harcourt Publishing Company 4 of a large pizza. Aidan 13. Stretch Your Thinking Harry ate __ 8 1 4 __ is equivalent ate of a small pizza. Harry said that since __ 2 8 1 __ to , he and Aidan ate the same amount of pizza. Is he 2 correct? Explain. Name 1-5 Date Name the mixed number shown by the shaded parts. 1 3__ 1. 2. 2 2 2__ 3 1__ 3. 3 7 Write the mixed number as a fraction. 7 __ 1 = 4. 2__ 2 = 5. 4__ 3 3 5 22 ___ 5 3 = 6. 3__ 15 ___ 9 = 10. __ 1 4__ 5 = 7. 1__ 4 4 8 13 ___ 8 Write the fraction as a mixed number. 1 1__ 7 = 8. __ 8 = 9. __ 6 6 3 2 2__ 3 10 = 11. ___ 2 2 7 3 1__ 7 Complete. Give the answer as a mixed number. 3 + __ 4 = 12. __ 5 5 8 = 2 + __ 14. __ 9 9 2 1__ 5 6 + __ 3 = 13. __ 1 2__ 2 = 15. 7 + __ 2 7__ 4 1 1__ 9 4 3 4 Show your work. Solve. © Houghton Mifflin Harcourt Publishing Company 3 6 7 16. Alicia walked __ mile on Saturday and __ mile on Sunday. 8 8 How far did she walk over the weekend? Give the answer as a mixed number. 5 1__ miles 8 5 17. The dark chain is ___ yard long. The light one is 12 9 ___ yard long. How long will they be if they are 12 joined? Give the answer as a mixed number. 2 yards 1___ 12 5 yd — 12 UNIT 1 LESSON 5 9 yd — 12 Fractions Greater Than One 9 Name 1-5 Date Solve. 5 of the way across the yard. How much 1. The dog has gone __ 8 farther does it have to go to reach the gate? 3 __ of the way 8 7 2. The cat has gone ___ of the way across the yard. How much 16 farther does it have to go to reach the gate? 9 ___ of the way 16 6 2 3. I cleaned __ of my room, and my friend cleaned __ of my 9 9 room. How much of my room do we still have to clean? 1 __ 9 8 4. Mrs. Spencer’s class is signing up to play sports. ___ of the 26 12 students want to play soccer and ___ want to play basketball. 26 The rest of the students want to play baseball. What fraction of the students wants to play baseball? 6 ___ 26 13 7 > ___ 7. ___ 2 > __ 1 5. __ 4 > ___ 4 6. __ 3 > __ 1 8. __ 6 4 = __ 9. __ 9 5 4 < __ 10. __ 3 > __ 4 12. __ 7 < __ 7 13. __ 6 5 6 3 3 7 < __ 11. ___ 12 4 9 6 5 10 9 12 5 9 24 6 8 14. Stretch Your Thinking Find two fractions that are 3 4 and __ . between __ 5 5 7 ___ Possible answers: ___ , 11 10 15 10 UNIT 1 LESSON 5 Fractions Greater Than One © Houghton Mifflin Harcourt Publishing Company Compare. Name 1-6 Date Add or subtract. 3 + __ 4 1. __ 6 + __ 3 2. __ 2 1__ 1 2__ 5 5 4 5 2 + __ 3. 4__ 27 4 9 7 4 7 + __ 4. 1__ 33 8 9 2 1 or 5__ 5__ 4 8 4 - __ 7. 6__ 32 5 6 - __ 6. 4__ 25 7 - __ 4 5. 1__ 8 5 2 3__ 7 9 3 1 1__ or 1__ 9 7 3 5 1 8. 25__ 10__ 8 1 + __ 9. 4__ 51 8 8 1 + __ 10. 3__ 21 7 7 2 2 5__ 1 + 1 12. 50__ 50__ 7 3 1 3__ 7 3 2 1__ 3 3 3 - __ 14. 5__ 27 8 1 - __ 15. 2__ 15 8 6 6 2 1 __ or __ 4 1 2__ or 2__ 8 2 6 3 Show your work. Solve. © Houghton Mifflin Harcourt Publishing Company 3 2 100__ 7 1 13. 2 - __ 2 10 2 5 + __ 11. 1__ 13 7 7 1 2__ 4 1 15__ or 15__ 5 9 5 7 inches long, but a section 1__ inches 16. I made a clay snake 9__ 8 8 long broke off. How long is the snake now? 6 3 7__ in. or 7__ in. 4 8 3 17. A group of campers hiked for 5__ hours today and 4 yesterday. How many hours did they hike in all? 2 1 hours or 12__ hours 12__ 4 2 3 6__ hours 4 1 2 18. Deacon had 12__ ounces of juice, but he drank 3__ ounces. 3 3 How much juice is left? 2 8__ oz 3 UNIT 1 LESSON 6 Add and Subtract Mixed Numbers 11 Name 1-6 Date Complete to form equivalent fractions. 1 = _____ 4 1. __ 2 24 6 = _____ 3. __ 12 = __ 4 2. _____ 5 15 8 7 28 Answers to Exercises 4–6 will vary. Possible answers are given. 6 4 = _____ 4. _____ 9 6 1 2 3 6. _____ = _____ 25 = _____ 5. ____ 100 8 4 12 Compare. 3 < __ 3 7. ___ 10 8 5 > ___ 19 10. __ 6 24 5 4 < __ 8. __ 5 > __ 2 9. __ 3 4 < ___ 11. ___ 1 > ___ 1 12. ___ 5 15 7 6 10 Solve. 49 3 50 Show your work. 13. Rosa got 5 out of 7 answers correct on her science quiz. Her older sister Ana got 4 answers out of 6 correct on her science quiz. Which sister answered a greater fraction of the questions correctly? Rosa © Houghton Mifflin Harcourt Publishing Company 85 14. The number 85% is equivalent to the fraction ____ . Pablo 100 spelled 21 out of 25 words correctly on his spelling test. Is this more or less than 85% of the words? less 3 15. Stretch Your Thinking Marla ate __ of a small pepperoni 8 3 2 __ of a pizza and of a small cheese pizza. Damien ate ___ 8 12 5 ___ of a small mushroom pizza. small veggie pizza and 12 Who ate a greater fraction of a whole pizza? Damien 12 UNIT 1 LESSON 6 Add and Subtract Mixed Numbers Name 1-7 Date Add. 1 + __ 1 1. __ 3 2 7 + __ 1 2. ___ 5 __ 9 4 18 1 + __ 2 5. __ 6 3 13 ___ 5 + __ 1 6. ___ 11 22 6 3 + __ 3 7. ___ 4 15 ___ 16 3 + __ 1 8. __ 7 2 21 ___ 5 __ 32 6 7 ___ 10 5 + __ 1 4. ___ 16 2 + __ 1 3. __ 9 ___ 6 32 5 10 3 5 + __ 3 9. ___ 16 ___ 21 Solve. 12 8 19 ___ 24 Show your work. 5 were 10. Of the people who attended the school play, ___ 12 1 __ students and were teachers. What fraction of the 8 total audience were students or teachers? 13 ___ 24 © Houghton Mifflin Harcourt Publishing Company 2 1 11. Mara bought __ yard of yellow ribbon and __ yard of blue 4 3 ribbon. How many yards of ribbon did she buy altogether? 11 ___ yard 12 5 12. For breakfast, Oliver drank ___ of a pitcher of juice. 16 3 __ His brother Joey drank of the pitcher of juice. 8 What fraction of a pitcher did they drink together? 11 ___ 16 3 1 13. A recipe calls for __ cup of brown sugar and __ cup of 4 3 white sugar. How much sugar is this altogether? 1 cups 1___ 12 UNIT 1 LESSON 7 Add Unlike Fractions 13 Name 1-7 Date Solve for n or d. 1 = ___ n 1. __ 4 3 = ___ 15 2. __ 20 9 = __ 1 3. ___ 6 10 = __ n 4. ___ 5 3 = ___ 18 5. __ 42 3 = ___ n 6. __ 24 27 = __ n 7. ___ 3 14 = __ 2 8. ___ 7 5 = ___ n 9. __ 40 20 1 = ___ 10. __ 60 3 21 = __ 11. ___ 8 n 20 = __ 12. ___ 5 25 4 6 24 7 4 5 d 6 48 3 d 40 54 36 56 d 18 d 4 49 d 9 d Add or subtract. 2 3__ 1 + __ 21 13. 1__ 3 3 3 6 3 or 2__ 2__ 3 – __ 5 8 __ 4 16. 6 3 8 8 3 – __ 14. 3__ 11 5 5 2 2__ 5 3 + __ 15. 6__ 35 8 8 4 2 or 4__ 4__ 5 + __ 5 6 __ 3 17. 1 2 1 18. 7 – 5__ 7 > __ 2 20. ___ 3 1 < ___ 21. __ 19 < ___ 20 23. ___ 4 > __ 7 24. __ 6 6 10 4 3 1__ 4 Compare. 3 < __ 6 19. __ 4 7 15 6 > ____ 6 22. ____ 100 101 20 5 21 8 Solve. 5 20 9 Show your work. © Houghton Mifflin Harcourt Publishing Company 25. In a hockey game, Seth took 12 shots and scored 3 times. Zak took 10 shots and scored twice. Who scored on a greater fraction of his shots? Seth 7 26. Jia rode her bike 7__ miles in the morning and another 8 5 __ 6 miles in the afternoon. How many miles did she 8 ride altogether? 4 1 miles or 14__ miles 14__ 8 2 27. Stretch Your Thinking Last season, Jenny made 3 out of every 4 free throws she took. If she took 48 free throws, how many did she make? 36 free throws 14 UNIT 1 LESSON 7 Add Unlike Fractions Name 1-8 Date Subtract. 8 4 - ___ 2. __ 1 - __ 1 1. __ 7 3 5 15 4 ___ 4 ___ 21 15 61 - ___ 7 4. ____ 100 7 6 9 11 ___ 18 4 - __ 1 5. __ 25 5 - __ 2 3. __ 6 6 - __ 1 6. ___ 11 2 33 ___ 17 ___ 1 ___ 100 42 22 Circle the greater fraction. Then write and solve a subtraction problem to find the difference of the fractions. Common denominators in 9 = ___ 55 - ___ 54 = ___ subtraction problems may vary. 11 - ___ 1 9 11 ___ ___ 7. ___ 10 60 60 60 10 12 12 5 8. ___ 18 1 __ 3 5 = ___ 6 - ___ 5 = ___ 1 – ___ 1 __ 3 18 18 18 18 Show your work. © Houghton Mifflin Harcourt Publishing Company Solve. 9. Marly passes the library on her way to school. The 3 mile. distance from Marly’s house to the library is __ 8 4 mile. The distance from Marly’s house to the school is __ 5 How far is it from the library to Marly’s school? 17 ___ mile 40 1 7 10. Tim spends about __ of each weekday sleeping and about ___ 3 24 of each weekday in school. a. What fraction of a weekday does Tim spend either sleeping or in school? 15 5 ___ day or __ day 24 8 more 1 b. Is this more or less than __ a day? 2 3 1 ___ day or __ day 8 c. How much more or less? 24 UNIT 1 LESSON 8 Subtract Unlike Fractions 15 Name 1-8 Date Write each fraction as a mixed number. 1 2__ 11 = 1. ___ 3 1 57 = 9__ or 9__ 3. ___ 6 2 6 5 2__ 21 = 2. ___ 5 5 8 8 Write each mixed number as a fraction. 11 ___ 5 = 4. 1__ 6 35 ___ 2 = 5. 11__ 6 3 55 ___ 1 = 6. 6__ 3 9 9 Add or subtract. 3 + __ 2 7. __ 7 3 7 – ___ 8. ___ 7 10 5 __ 12 1 – __ 12. 5__ 12 12 12 3 + __ 13. 4__ 43 3 2 3 3 + __ 1 15. ___ 11 8 2 1 or 9__ 9__ 2 3 2 3__ 5 14. 4 – 3__ 4 4 10 6 1 or 4__ 4___ 6 4 7 ___ 5 10 11 – ___ 11. 6___ 25 6 5 10 4 2 ___ or __ 7 1 + __ 10. 2__ 35 6 3 + __ 2 9. ___ 10 3 3 __ 20 ___ 8 33 Show your work. Solve. © Houghton Mifflin Harcourt Publishing Company 16. Ayala and Sam were partners on a science project. Ayala 3 hours working on the project. Sam spent spent 2__ 4 3 __ 1 hours working on the project. How long did they 4 work altogether? 2 1 4__ hours or 4__ hours 4 2 17. Stretch Your Thinking Marti grouped all her CDs into 2 of my CDs are rock separate categories. She said, “__ 5 1 1 1 are country music.” music, __ are jazz, __ are hip hop, and __ 4 6 3 Explain why Marti’s statement cannot be correct. Possible answer: The sum should be 1 to represent 2 + __ 1 the whole collection, but it is greater than 1: __ 5 6 10 20 15 9 3 1 1 24 __ __ ___ ___ ___ ___ ___ ___ + + = + + + = 1 or 1 . 3 16 4 UNIT 1 LESSON 8 60 60 60 60 60 20 Subtract Unlike Fractions Name 1-9 Date Add or subtract. 1. 1 7__ 2 5 + 6__ 8 _ 2. 15 1 - 1__ 5 _ 5. 1 2___ 7. 1 8__ 6 7 - 2___ 12 __ 7 5___ 12 5 9__ 6. 6 1 - 4__ _8 9 5 + 3__ _8 72 7 6__ 9. 9 2 - 4__ _3 9 3___ 14 2 - 1__ 7 __ 5 2___ 1 2__ 14 9 Show your work. Solve. © Houghton Mifflin Harcourt Publishing Company 1 1__ 53 4___ 24 8. 8 3 + 2__ _4 8 17 5___ 15 3 5__ 1 8__ 20 8 4 3___ 3. 5 1 + 5__ _4 17 7___ 1 14__ 4. 3 2__ 5 1 feet tall. This year it is 10___ 10. Last year my elm tree was 8__ 6 12 feet tall. How much did it grow in one year? 1 1__ feet 4 3 1 11. Luis rode his bicycle 2___ miles before lunch. He rode 1__ 4 10 miles after lunch. How far did Luis ride altogether? 11 3___ miles 20 1 1 12. Carrie spent 2__ hours trimming bushes and 1__ hours 4 2 weeding the garden. She is supposed to work in the yard for 5 hours. How much longer does she need to work? 1 1__ hours 4 UNIT 1 LESSON 9 Solve with Unlike Mixed Numbers 17 Name 1-9 Date Add or subtract. Try to do these in your head. 2 1 3 - __ 1 = 2__ or 2__ 2. 2__ 4 4 4 2 1 + __ 23 = 1. 3__ 6 6 - __ 4. 6__ 52 = 4 1__ 2 + __ 5. 8__ 12 = 3 + __ 7. 3__ 33 = 1 7__ 4 1 7 - __ 8. 7__ 3 3 = 4__ or 4__ 8 8 8 2 4 7 5 4 7 5 7 5 3 3 2 + __ 3. 3__ 44 = 1 8__ 6 - __ 6. 5__ 12 = 4 4__ 3 + __ 9. 5__ 35 = 9 5 1 10__ 3 5 5 7 7 7 8 8 Write the fractions in order from least to greatest. 1 __ 1 __ , 1 , __ ,1 10. __ 1 __ 1 __ __ , 1 , __ ,1 8 __ 4 __ 11. __ , 2 , __ ,1 2 __ 1 __ 12. __ , 3 , __ ,3 1 __ 2 __ __ , 3 , __ ,3 11 __ 2 ___ 13. ___ , 3 , __ , 19 9 3 6 2 3 5 2 4 9 6 3 2 1 __ 4 __ __ , 2 , __ ,8 9 9 9 9 9 9 9 9 2 5 3 4 3 ___ 2 ___ __ , 19 , __ , 11 5 30 3 15 15 5 3 30 List three fractions equivalent to the given fraction. Answers will vary. 1 14. __ 15 15. ___ 4 16. __ 9 17. ___ 5 18 7 12 Show your work. Solve. 1 cups of flour and 18. Ted is making a bread recipe that uses 3__ 4 3 a muffin recipe that uses 2__ cups of flour. 4 b. How much flour does Ted need for both recipes? 6 cups 19. Stretch Your Thinking Find the values of x and y in the drawing at the right. 7 4__ 8 inches x= 5 __ 8 _1_ in. 14 8 8 inches y= 6 _4_ in. 8 x 8 _1_ in. 8 3_2_ in. 8 y 18 UNIT 1 LESSON 9 Solve with Unlike Mixed Numbers © Houghton Mifflin Harcourt Publishing Company a. How much more flour is in the bread than in the muffins? 2 1 __ cup or __ cup 4 2 Name 1-10 Date Add or subtract. 1. 3 2. 2 - 1__ _5 5. 29 5___ 13 ___ 16 2 + __ 3 _ 23 1___ 48 5 7__ 9 2 - 3___ 15 __ 19 4___ 45 1 5__ 8 1 - 4__ _5 6. 79 4____ 100 9 + 5___ 10 __ 37 ___ 42 7. 3. 2 5 6 6 + __ _7 10 4 + 2__ 5 __ 1 5__ 3 1__ 5 4. 4__ 7 2___ 69 10___ 40 8. 1 8__ 4 9 - 3___ 20 __ 100 9. 8 7__ 9 7 + 9__ _8 55 17___ 4_4_ 72 5 © Houghton Mifflin Harcourt Publishing Company Solve. 1 cups of food each 10. The Taylors have four dogs. Molly eats 4__ 2 3 3 2 __ __ cup. day, Roscoe eats 3 cups, Milo eats 1 cups, and Fifi eats __ 4 4 3 How much do the Taylors’ dogs eat each day altogether? 2 10__ cups 3 11. Refer to Problem 10. How much more food does Molly eat each day than Roscoe? _5_ cup 6 12. The vet told the Taylors (from Problem 10) to decrease the 3 cup. After Molly’s food is adjusted, amount Molly eats by __ 4 will she eat more or less than Roscoe each day? How much more or less? 1 more; ___ cup 12 UNIT 1 LESSON 10 Practice with Unlike Mixed Numbers 19 Name 1-10 Date What mixed number is shown by each shaded part? 2. 1. 3 2__ 3. 1 1__ 4 1 3__ 2 3 Answer the questions about the bar graph. Give your answers as simple fractions. Cookies for the Bake Sale 4. How many cookies are there altogether? 45 15 10 8. Melanie baked 25 cookies. Did she bake more or less than half of the cookies? more Pe Bu an tt ut er l ea m at O oc Ch ola ip te 7. What fraction of the cookies are peanut butter? 2 __ 9 5 Ch 5. What fraction of the cookies are chocolate chip? 4 __ 9 _1_ 3 6. What fraction of the cookies are oatmeal? Number 20 Flavor How do you know? © Houghton Mifflin Harcourt Publishing Company 1 Answers will vary. Half of 45 is 22__ ; 2 1 25 is greater than 22__ 2 9. Stretch Your Thinking Colby nailed together four wood 1 boards as shown at the right. All four boards are 5__ 2 inches wide. a. Find the perimeter of the outside rectangle. 88 inches b. Find the perimeter of the inside rectangle. 44 inches 20 UNIT 1 LESSON 10 Practice with Unlike Mixed Numbers Name 1-11 Date 1 Use benchmarks of 0, __ , and 1 to estimate the sum or difference. 2 Then find the actual sum or difference. 1 13 + __ 3. ___ 2 18 Estimate: 13 - ___ 3 2. ___ 2 + __ 4 1. __ 5 7 20 1 Estimate: 34 ___ Sum: 35 10 0 Estimate: 7 ___ 20 Difference: 1 2 1__ 9 Sum: Estimate the sum or difference by rounding each mixed number to the nearest whole number. Then find the actual sum or difference. 5 - __ 4. 3 __ 11 8 4 + ___ 5. 6__ 57 2 9 2 Estimate: 8 Sum: 15 18 12 Estimate: 1 2__ Difference: 11 - ___ 6. 7___ 41 12 Estimate: 1 12___ 36 Difference: 4 49 3___ 90 Tell whether the answer is reasonable or unreasonable. Explanations will vary. Explain how you decided. Possible explanations are given. 8 1 + __ 7. 2__ 5 1 = 7___ 5 9 7 - ___ 2 = ___ 8. __ 15 3 19 Reasonable; Using Unreasonable; Using rounding gives the benchmarks gives the estimate 2 + 5 = 7. estimate 1 - 0 = 1. 3 + __ 4 = ___ 7 9. __ 8 © Houghton Mifflin Harcourt Publishing Company 11 8 5 1 - __ 1 10. 4 __ 1 5 = 2__ 40 Unreasonable; Using benchmarks gives the 1 + = __ estimate __ 1 11. 2 2 3 6 2 Reasonable; Using rounding gives the estimate 4 - 2 = 2. Solve. 7 - __ 4 4 7 - ___ . 11. Estimate the difference 8 ___ 12 8 10 Explain how you found the answer. 1 7 Sample answer: Use the 0, __ , 1 benchmarks. 8 ___ is 2 12 1 __ 4 1 closer to 8 __ , 4 7 is closer to 5, and ___ is closer to __ ; 2 8 10 2 1 - - __ 8 __ 5 1=3 2 2 UNIT 1 LESSON 11 Reasonable Answers 21 Name 1-11 Date Add or subtract. Give your answer in simplest form. 1. 4 2. 7 - 3__ _8 3. 2 3 + 6__ _4 1 12__ 1 __ 6 __ 7 3 + __ _5 6. 8 7 - 1__ _8 1 8__ 16 1___ 10 5 - 1__ 6 __ 15 13 2___ 25 99 + 3____ 100 __ 51 6___ 2 35 1 3___ 4 1___ 4 3 5. 10__ 8 4. 1 5__ 100 Compare. 5 > __ 5 7. __ 7 9 6 > __ 4 10. ___ 11 9 99 < ____ 100 8. ____ 100 101 1 > ___ 1 11. ___ 21 22 9 7 > ___ 9. ___ 15 20 5 > __ 1 12. ___ Solve. 16 4 Show your work. 13. On the first math test, Octavia answered 24 out of 30 questions correctly. On the second math test, she answered 19 out of 25 questions correctly. On which test did she answer the greater fraction of the questions correctly? © Houghton Mifflin Harcourt Publishing Company the first test 14. Stretch Your Thinking Isidro is riding his bike 22 miles 1 miles and then took a to the art museum. He rode 7__ 2 7 mile. How break. Since his break, he has ridden 5___ 10 much farther does he have to ride to get to the museum? 4 8__ miles 5 22 UNIT 1 LESSON 11 Reasonable Answers Name 1-12 Date Solve. Explain why your answer is reasonable. Explanations may vary. Show your work. 1 feet long. She cut off a piece. Now the 1. Zoe had a board 5__ 4 5 __ board is 3 feet long. How long was the piece she cut off? 6 5 1___ feet 12 Answer: Why is the answer reasonable? 5 1 5__ rounds to 5. 3__ rounds to 4. The answer should 4 6 be about 5 - 4, or 1. 3 2. A rectangle has a length of 10___ inches and a width of 16 7 6__ inches. What is the perimeter of the rectangle? 8 1 34__ inches 8 Answer: Why is the answer reasonable? 3 7 10___ rounds to 10. 6__ rounds to 7. The answer 16 8 should be about 10 + 10 + 7 + 7 = 34. 2 3. Max is making trail mix. He combines __ pound of dried fruit 5 1 and __ pound of mixed nuts. He adds sunflower seeds to make 3 a total of 1 pound. What is the weight of the seeds? 4 ___ pounds 15 Answer: © Houghton Mifflin Harcourt Publishing Company Why is the answer reasonable? 2 1 1 __ and __ are each a little less than __ , so their sum is 5 3 2 a little less than 1. It would take a small fraction, close to 0, to make a total of 1. 4. At the start of party, a bowl contains 16 pints of punch. 1 1 pints. Then the host adds another 7__ pints Guests drink 10__ 4 2 to the bowl. How much punch is in the bowl now? 1 pints 13__ 4 Answer: Why is the answer reasonable? 1 10__ rounds to 10, so about 6 pints are left and then 4 1 1 7__ are added, so the answer should be about 13__ . 2 2 UNIT 1 LESSON 12 Real World Problems 23 Name 1-12 Date Tell whether the answer is reasonable or unreasonable. Explain how you decided. Explanations may vary. 8 + ___ 39 1 = ___ 1. __ 9 10 37 1 - __ 2. 5__ 4 2 = 2___ 90 6 8 Unreasonable; __ is very close to 9 39 1 1, but ___ isn’t even __ . 90 8 42 the estimate 5 - 4 = 1. 2 5 + __ 1 4. 5__ 1 3 = 5___ 11 - __ 7 = ___ 1 3. ___ 12 7 Unreasonable; Rounding gives 24 6 4 12 Reasonable; Using benchmarks Unreasonable; Using rounding gives the estimate 1 - 1 = 0. gives the estimate 6 + 2 = 8. Add or subtract. 5 = 7 + __ 5. __ 8 8 3 = 7 - ___ 7. ___ 15 10 4 - __ 9. 5__ 21 = 5 3 4 1 1__ or 1__ 8 2 21 7 3 3 - ___ 5 = 8. __ 4 12 5 + ___ 10. 7__ 2 11 = 6 12 5 1 ___ or __ 30 7 3___ 15 5 1___ 4 + __ 2= 6. __ 6 4 1 ___ or __ 12 3 9 3 or 10__ 10___ 4 12 Compare. 5 5 > __ 11. __ 9 8 7 12. 1___ < 1__2 3 5 > __ 13. __ 7 9 1 1 > ___ 14. ___ 90 89 2 5 > __ 15. ___ 9 18 55 65 > ___ 16. ___ 56 66 12 3 © Houghton Mifflin Harcourt Publishing Company Solve. 17. Stretch Your Thinking Find two mixed numbers such that when you estimate their sum by rounding to the nearest whole number you get a different estimate than when you round to the nearest half. Demonstrate that your numbers satisfy this condition. 5 5 Possible answer: 2__ and 3__ . When you round to 8 8 the nearest whole number, the estimated sum is 3 + 4 = 7. When you round to the nearest half, 1 + __ the sum is 2__ 3 1 = 6. 2 24 UNIT 1 LESSON 12 2 Real World Problems 1-13 Name Date In the space below, design and sketch a bird hotel. Assume your design will be made from wood, and includes these characteristics. 1 -inch ‣ Walls not exposed to weathering are __ 4 thick. 1 -inch thick. ‣ Walls exposed to weathering are __ 2 ‣ The rooms are identical. © Houghton Mifflin Harcourt Publishing Company State the number of birds your design will accommodate, and the dimensions of one room. Then use the dimensions to compute the overall length, width, and height of your hotel. UNIT 1 LESSON 13 Focus on Mathematical Practices 25 Name 1-13 Date Add or subtract. Give your answer in simplest form. 1. 1 7__ 2. 4 5 - 4__ 6 _ 9 1___ 5 2___ 12 4. 3. 10 9 + 1___ 10 __ 6 - 1__ _7 1 2__ 7 4 3__ 5 7 ___ 5. 10 11 + 1___ 12 __ 37 2___ 4 4__ 6. 5 7 - 1__ _8 37 2___ 60 4 5 3___ 12 2 + 1__ 3 __ 1 5___ 40 12 Compare. 1 < ___ 1 7. ___ 57 47 5 > __ 2 10. __ 6 3 5 < __ 4 8. __ 7 15 14 < ___ 9. ___ 5 15 3 < 7 11. 15__ 15___ 8 10 16 9 1 > 12. 14___ 13___ 10 10 Show your work. Solve. 3 1 of a movie on Friday, __ of the movie 13. Blake watched __ 5 6 on Saturday, and the rest on Sunday. What fraction of the movie did he watch on Sunday? 7 ___ 30 a. What is the sum of the three fractions? 3 1__ 7 b. Why does it make sense for the sum to be greater than 1 whole? Some students have a sister and a brother. Because the three parts overlap, the total is more than 1 whole. 26 UNIT 1 LESSON 13 Focus on Mathematical Practices © Houghton Mifflin Harcourt Publishing Company 14. Stretch Your Thinking Marshall surveyed his classmates 5 3 1 have a sister, __ have a brother, and ___ and found that __ 7 14 2 don’t have any siblings.