1. 3-11 Dividing Fractions and Mixed Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 3-11 Dividing Fractions and Mixed Numbers Warm Up Multiply. 1. 7979 · 3636 2. 9898 · 6565 3. 1515 2 · 7 4. 2 1212 · 1 1414 7 18 27 20 7 or 1 2 77 5 5 or 15 25 8 8 or 3 1

3. 3-11 Dividing Fractions and Mixed Numbers Problem of the Day The Jeffers family is putting in a new fence around their yard. The yard is in the shape of a square. If they put nine fence posts on each side of the square, how many posts will be used? 32

4. 3-11 Dividing Fractions and Mixed Numbers MA.7.A.3.2 …Divide…fractions…including solving problems in everyday contexts. Also MA.7.A.5.2 Sunshine State Standards

5. 3-11 Dividing Fractions and Mixed Numbers Vocabulary reciprocal multiplicative inverse

6. 3-11 Dividing Fractions and Mixed Numbers Reciprocals can help you divide by fractions. Two numbers are reciprocals or multiplicative inverses if their product is 1. The reciprocal of is 3 because 1313 1313 · 3 = 1313 · 3131 = 3333 = 1. Dividing by a number is the same as multiplying by its reciprocal.

7. 3-11 Dividing Fractions and Mixed Numbers Additional Example 1: Dividing Fractions Divide. Write each answer in simplest form. A. 3737 ÷ 2525 3737 ÷ 2525 = 3737 · 5252 = 3737 · 5 · 2 = 15 14 or 1 14 1 Multiply by the reciprocal of. 2525 B. 3838 ÷ 12 3838 ÷ = 3838 · 1 = 3838 · 1 1 4 = Multiply by the reciprocal of 12. 1 32 Simplify.

8. 3-11 Dividing Fractions and Mixed Numbers Check It Out: Example 1 Divide. Write the answer in simplest form. A. 3535 ÷ 1212 B. 4747 ÷ 20 3535 ÷ 1212 = 3535 · 2121 = 6565 = 1 5 1 4747 ÷ 20 = 4747 · 1 1 = 1 35 5

9. 3-11 Dividing Fractions and Mixed Numbers Divide. Write each answer in simplest form. A.5 2323 ÷ 1 1414 5 2323 ÷ 1 1414 = 17 3 ÷ 5454 = 17 3 · 4545 = 68 15 or 4 8 15 Write mixed numbers as improper fractions. Multiply by the reciprocal of 5454 B. 3434 ÷ 2 1212 3434 ÷ 2 1212 = 3434 ÷ 5252 = 3 4 · 2525 = 3·2 4·5 1 2 = 3 10 Write 2 as an improper fraction. 1212 Multiply by the reciprocal of. 5252 Simplify.. Additional Example 2: Dividing Mixed Numbers

10. 3-11 Dividing Fractions and Mixed Numbers Check It Out: Example 2A Divide. Write the answer in simplest form. 3535 ÷ 1 2525 3535 ÷ 1 2525 = 3535 ÷ 7575 = · = 3 7 1 3535 5757 1

11. 3-11 Dividing Fractions and Mixed Numbers Check It Out: Example 2B 1616 ÷ 3 1414 2 1616 ÷ 3 1414 2 = 19 6 ÷ 9494 19 6 = 4949 · 2 3 38 27 = = 11 27 1 Divide. Write the answer in simplest form.

12. 3-11 Dividing Fractions and Mixed Numbers Check It Out: Example 2C Divide. Write the answer in simplest form. 5 5858 ÷ 5959 45 8 ÷ 5959 = 45 8 · 9 5 1 5 5858 ÷ 5959 = = 81 8 = 1818 10 9

13. 3-11 Dividing Fractions and Mixed Numbers Check It Out: Example 2D Divide. Write the answer in simplest form. 4 2929 ÷ 2323 2 38 9 ÷ 8383 = 38 9 · 3 8 4 4 2929 ÷ 2323 = = 19 12 = 7 12 1 19 2 1 3

14. 3-11 Dividing Fractions and Mixed Numbers Additional Example 3: Consumer Application Anthony bought several pounds of fruit at the farmer’s market. He first purchased strawberries. Then he picked up 1 times as many pounds of bananas as strawberries. He finally selected 3 more pounds of apples than bananas. Anthony purchased 6 pounds of apples. How many pounds of strawberries did he buy? 1919 1313 Subtract the fractions then subtract the integers. The amount of bananas purchased is 2 lb. 7979 3434 Step 1: Find the amount of bananas Anthony purchased. 6 – 3 7979 1919 =5 – 3 7979 10 9 = 3939 2= 1313 2 1919 Regroup: 6 = 5 + + 9999 1919 Simplify. Work backward from the amount of apples Anthony purchased to the amount of strawberries.

15. 3-11 Dividing Fractions and Mixed Numbers Additional Example 3: Consumer Application Write mixed numbers as improper fractions. 1313 The amount of strawberries purchased is 1 lb. 2  1 3434 1313 =  7474 7373 or 1 1313 = 4343 7474 Multiply by the reciprocal of. Simplify. Step 2: Find the amount of strawberries purchased. The amount is times as much as the amount of bananas purchased, so divide the amount of bananas by. 3434 1 3434 1 =  4747 7373 =  4747 7373 1 1

16. 3-11 Dividing Fractions and Mixed Numbers Check It Out: Example 3 Hannah is putting her loose change into rolls. She has the most number of penny rolls. There are times as many dime rolls as penny rolls. There are times as many quarter rolls as dime rolls. If there are 15 quarter rolls, how many penny rolls does Hannah have? 5656 3 10 There are 15 quarter rolls. 10 3 50 1 There are 15 ÷ 3 10 = 15 1 · = 50 dime rolls 1 5 There are 50 ÷ 5 6 = · 6565 = 60 penny rolls 1 10

17. 3-11 Dividing Fractions and Mixed Numbers Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

18. 3-11 Dividing Fractions and Mixed Numbers Lesson Quiz 10 Divide. Write each answer in simplest form. 1. 2. 8 ÷ 4545 5959 ÷ 1818 3. 3535 ÷6 5. Roy cuts yard of silk from a roll. Susan then takes of the remaining silk on the roll. If there are 5 yards of silk after Susan’s cut, how much was on the roll before Roy’s cut? 1414 3434 4 4949 40 9 or 1 10 3 4. 2 1212 ÷ 1717 35 44 1414 7 yards 3434

19. 3-11 Dividing Fractions and Mixed Numbers 1. Divide. Write your answer in simplest form. 10 ÷ A. 6 B. 18 C. 12 D. 24 Lesson Quiz for Student Response Systems 5656

20. 3-11 Dividing Fractions and Mixed Numbers 2. Divide. Write your answer in simplest form. ÷ A. or 4 C. B.or 2D. Lesson Quiz for Student Response Systems 20 5 20 7 4 35 3 35 4747 1515 6767

21. 3-11 Dividing Fractions and Mixed Numbers 3. Divide. Write your answer in simplest form. ÷ 15 A. or 9C. B.24 D. or Lesson Quiz for Student Response Systems 75 8 1 24 3 15 5858 3838 1515

22. 3-11 Dividing Fractions and Mixed Numbers 4. Multiply. Write your answer in simplest form. 3 ÷ 5 A. C. or 1 B. D. 27 Lesson Quiz for Student Response Systems 50 81 23 27 81 50 1313 2525 31 50