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Lesson 6.6 Name Add and Subtract Mixed Numbers Essential Question How can you add and subtract mixed numbers with unlike denominators? Number and Operations— Fractions—5.NF.A.1 Also 5.NF.A.2 MATHEMATICAL PRACTICES MP1, MP2, MP6 Unlock Unlock the the Problem Problem Denise mixed 1 4_5 ounces of blue paint with 1 2 __ 10 ounces of yellow paint. How many ounces of paint did Denise mix? • What operation should you use to solve the problem? • Do the fractions have the same denominator? 1 __ + 2___ Add. 14 5 10 To find the sum of mixed numbers with unlike denominators, you can use a common denominator. STEP 1 Estimate the sum. ___ STEP 2 Find a common denominator. Use the common denominator to write equivalent fractions with like denominators. © Houghton Mifflin Harcourt Publishing Company • Image Credits: (l) ©Andrew Paterson/Alamy STEP 3 Add the fractions. Then add the whole numbers. Write the answer in simplest form. So, Denise mixed _ ounces of paint. 1. MATHEMATICAL PRACTICE __ = 14 5 1 = + + 2 ___ 10 Math Talk MATHEMATICAL PRACTICES 2 Connect Symbols and Words Did you use the least common denominator? Explain. 1 Evaluate Reasonableness Explain how you know whether your answer is reasonable. 2. What other common denominator could you have used? Chapter 6 383 Example 5 − 23 __ Subtract. 4 __ 6 4 You can also use a common denominator to find the difference of mixed numbers with unlike denominators. STEP 1 Estimate the difference. __ STEP 2 Find a common denominator. Use the common denominator to write equivalent fractions with like denominators. STEP 3 3. __ = 45 6 __ = – – 23 4 Subtract the fractions. Subtract the whole numbers. Write the answer in simplest form. MATHEMATICAL PRACTICE 1 Evaluate Reasonableness Explain how you know whether your answer is reasonable. Share hhow Share and and Show Sh MATH M BOARD B 1. Use a common denominator to write equivalent fractions with like denominators and then find the sum. Write your answer in simplest form. __ = 72 5 __ = + + 43 Find the sum. Write your answer in simplest form. 3 2. 2 3_4 + 3 __ 10 384 3. 5 3_4 + 1 1_ 3 3 4. 3 4_ + 2 __ 5 10 © Houghton Mifflin Harcourt Publishing Company 4 Name Find the difference. Write your answer in simplest form. 5. 9 5_ − 2 1_ 6 6. 10 5_ − 9 1_ 3 9 7. 7 _2 − 3 1_ 6 3 Math Talk On On Your Your Own Own Find the sum or difference. Write your answer in simplest form. 3 + 22 _ 8. 1 __ 5 9. 8 1_ + 7 3_ 11. 12 3_4 − 6 1_ 6 12. 2 5_ − 1 1_4 10 6 6 MATHEMATICAL PRACTICES 6 Explain why you need to write equivalent fractions with common denominators to add 4 5_6 and 1 1_8 . 10. 2 1_ + 2 1_ 8 2 3 7 − 5 1_ 13. 14 __ 4 8 12 Practice: Copy and Solve Find the sum or difference. Write your answer in simplest form. 15. 8 1_ + 6 3_ 16. 2 1_ + 4 5_ 17. 3 5_ + __ 12 18. 3 2_ − 1 1_ 19. 5 6_7 − 1__2 3 20. 2 7_ − 1_2 7 − 12 _ 21. 4 __ 12 3 22. © Houghton Mifflin Harcourt Publishing Company 5 5 + 41 _ 14. 1 __ 23. 6 6 2 5 6 9 8 8 12 9 DEEPER Dakota makes a salad dressing by combining 6 1_3 fluid ounces of oil and 2 3_8 fluid ounces of vinegar in a jar. She then pours 2 1_4 fluid ounces of the dressing onto her salad. How much dressing remains in the jar? DEEPER This week, Maddie worked 2 1_2 hours on Monday, 2 2_3 hours on Tuesday, and 3 1_4 hours on Wednesday. How many more hours will Maddie need to work this week to make her goal of 10 1_2 hours a week? Chapter 6 • Lesson 6 385 MATHEMATICAL PRACTICES .0%&-t3&"40/tM",&4&/4& OqnakdlRnkuhmf¤@ookhb`shnmr OqnakdlRnkuhmf¤@ookhb`shnmr Use the table to solve 24–25. 24. 2 Reason Quantitatively Gavin plans to mix a batch 3 ounces of paint of Tangerine paint. He expects to have a total of 5 __ MATHEMATICAL PRACTICE 10 after he mixes the amounts of red and yellow. Explain how you can tell if Gavin’s expectation is reasonable. Paint Gavin Uses (in ounces) Red 25. SMARTER Gavin mixes the amount of red from one shade of paint with the amount of yellow from a different shade of paint. He mixes the batch so he will have the greatest possible amount of paint. What amounts of red and yellow from which shades are used in the mixture? Explain your answer. SMARTER 26. Yellow Shade 1 Sunrise Orange 3 Tangerine 5 Mango 28 5 34 3 10 9 28 5 56 56 Martin won first place in the 100-meter dash with a time of 23 7 __ 14 ___ 100 seconds. Samuel came in second place with a time of 15 10 seconds. 26a. A common denominator of the mixed numbers is 100. True False 26b. To find the difference between the runners’ times, Samuel’s time needs to be rewritten. True False 26c. Samuel’s time written with a denominator 70 of 100 is 15 ___ 100 . True False True False __ second. 26d. Martin beat Samuel by 21 25 386 © Houghton Mifflin Harcourt Publishing Company For 26a–26d, select True or False for each statement. Practice and Homework Name Lesson 6.6 Add and Subtract Mixed Numbers COMMON CORE STANDARD—5.NF.A.1 Use equivalent fractions as a strategy to add and subtract fractions. Find the sum or difference. Write your answer in simplest form. 1. 31_ − 11_ 2 2. 21_ + 13_ 5 3 _ 31 5 3__ _ −11 2 −1__ 2 8 3 4. 51_ + 61_ 3 6 10 5 10 3 2__ 10 __ 5. 2 1_ + 12_ 4 3. 41_ + 21_ 4 __ __ − 22 _ 6. 5 17 5 18 __ 3 __ __ 7. 6 3_ − 15_ 4 8 __ __ 8. 53_ − 21_ 7 5 __ Problem Problem Solving Solving 9. Jacobi bought 7 1_2 pounds of meatballs. He decided to cook 1 1_4 pounds and freeze the rest. How many pounds did he freeze? © Houghton Mifflin Harcourt Publishing Company _______ 11. WRITE 10. Jill walked 8 1_8 miles to a park and then 7 2_5 miles home. How many miles did she walk? _______ Math Write your own story problem using mixed numbers. Show the solution. Chapter 6 387 Lesson Check (5.NF.A.1) 1. Ming has a goal to jog 4 1_2 miles each day. On 9 miles. By how much did Monday she jogged 5 __ 16 she exceed her goal for that day? 2. At the deli, Ricardo ordered 3 1_5 pounds of cheddar cheese and 2 3_4 pounds of mozzarella cheese. How many pounds of cheese did he order all together? 3. The theater has 175 seats. There are 7 seats in each row. How many rows are there? 4. During the first 14 days, 2,744 people visited a new store. The same number of people visited the store each day. About how many people visited the store each day? 5. What number is 100 times as great as 0.3? 6. Mark said that the product of 0.02 and 0.7 is 14. Mark is wrong. What is the product? FOR MORE PRACTICE GO TO THE 388 Personal Math Trainer © Houghton Mifflin Harcourt Publishing Company Spiral Review (5.NBT.A.2, 5.NBT.A.3b, 5.NBT.B.6, 5.NBT.B.7)