1. 5-8 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. 5-8 Dividing Fractions and Mixed Numbers Warm Up Multiply. Write each answer in simplest form. 1. 2 2 2. 1 3 3. 3 3 4. 2 1 5 or 5 10 1 5 __ 1 2 1 2 1 2 1 3 1 4 21 4 __ or 2 11 4 __ 3 4 1 4 _

3. 5-8 Dividing Fractions and Mixed Numbers Problem of the Day Rachel is building a doghouse. She needs to cut a 12-foot-long board into lengths of 65 in. How many lengths can she cut, and will there be any wood left? If so, how much? 2 lengths; yes, 14 in.

4. 5-8 Dividing Fractions and Mixed Numbers MA.6.A.1.2 Multiply and divide fractions…efficiently. Also MA.6.A.1.3 Sunshine State Standards

5. 5-8 Dividing Fractions and Mixed Numbers Vocabulary reciprocal multiplicative inverse

6. 5-8 Dividing Fractions and Mixed Numbers Reciprocals can help you divide by fractions. Two numbers are reciprocals or multiplicative inverses if their product is 1.

7. 5-8 Dividing Fractions and Mixed Numbers Additional Example 1A: Finding Reciprocals Find the reciprocal. 1 9 __ 1 9 = 1 Think: of what number is 1? 1 9 __ 1 9 1 9 9 = 1 of is 1. 1 9 __ 9 1 The reciprocal of is 9. 1 9 __

8. 5-8 Dividing Fractions and Mixed Numbers Additional Example 1B: Finding Reciprocals Find the reciprocal. 2 3 __ 2 3 = 1 Think: of what number is 1? 2 3 __ 3 2 2 3 = = 1 6 6 __ of is 1. 2 3 __ 3 2 The reciprocal of is. 2 3 __ 3 2

9. 5-8 Dividing Fractions and Mixed Numbers 1 5 __ 16 5 __ = 1 Write 3 as. 1 5 __ 5 16 __ 16 5 __ = = 1 80 __ of is 1. 16 5 __ 5 16 __ The reciprocal of is. 16 5 __ 5 16 __ 16 5 __ Additional Example 1C: Finding Reciprocals Find the reciprocal. 3

10. 5-8 Dividing Fractions and Mixed Numbers Check It Out: Example 1A Find each reciprocal. 1 8 __ 4 4 1 8 = 33 8 __ ; 8 33 __

11. 5-8 Dividing Fractions and Mixed Numbers Check It Out: Example 1B Find each reciprocal. 5 5 = 5 1 __ ; 1 5

12. 5-8 Dividing Fractions and Mixed Numbers Check It Out: Example 1C Find each reciprocal. 1 4 __ 2 2 1 4 = 9 4 ; 4 9

13. 5-8 Dividing Fractions and Mixed Numbers Look at the relationship between the fractions and. If you switch the numerator and denominator of a fraction, you will find its reciprocal. Dividing by a number is the same as multiplying by its reciprocal. 3 4 __ 4 3 24 ÷ 4 = 624 = 6 1 4 __

14. 5-8 Dividing Fractions and Mixed Numbers Additional Example 2A: Using Reciprocals to Divide Fractions and Mixed Numbers Divide. Write each answer in simplest form. ÷ 7 8 7 __ 8 7 ÷ 7 = Rewrite as multiplication using the reciprocal of 7,. 1 7 __ Multiply by the reciprocal. 8 7 __ 1 7 8 1 7 ____ = The answer is in simplest form. = 8 49 __

15. 5-8 Dividing Fractions and Mixed Numbers When you divide by a proper fraction, the quotient will be greater than the dividend. For example, since there are 8 halves in 4, 4  ½ = 8. Caution!

16. 5-8 Dividing Fractions and Mixed Numbers Additional Example 2B: Using Reciprocals to Divide Fractions and Mixed Numbers ÷ 5 6 __ 5 6 ÷ = Rewrite as multiplication using the reciprocal of,. 3 2 __ Simplify before multiplying. 5 6 __ 3 2 5 3 6 2 ____ = You can write the answer as a mixed number. = 5 4 __ 2 3 2 3 2 3 1 2 Multiply. = 1 1 4 __

17. 5-8 Dividing Fractions and Mixed Numbers Additional Example 2C: Using Reciprocals to Divide Fractions and Mixed Numbers 2 ÷ 1 3 4 __ Write the mixed numbers as improper fractions. 2 = and 1 = 13 12 __ Rewrite as multiplication. 11 12 4 13 ______ = You can write the answer as a mixed number. = 33 13 __ 1 12 __ 3 4 1 3 Simplify before multiplying. = 2 7 13 __ 2 ÷ 1 = ÷ 3 4 __ 1 12 __ 11 4 __ 13 12 __ 11 4 __ 1 12 __ 11 4 __ 12 13 __ Multiply. =

18. 5-8 Dividing Fractions and Mixed Numbers Check It Out: Example 2A Divide. Write each answer in simplest form. 7 10 __ 1 5 ÷ 7 10 __ 5 1. 35 10 __ 1 2 3

19. 5-8 Dividing Fractions and Mixed Numbers Check It Out: Example 2B Divide. Write each answer in simplest form. 3 4 __ 1 8 ÷ 7 4 8 1. 56 4 __ 14 1

20. 5-8 Dividing Fractions and Mixed Numbers Check It Out: Example 2C Divide. Write each answer in simplest form. 1 5 __ 1 2 ÷ 11 5 __ 33 2 __ 2 15 __ 216 ÷ 11 5 __ 2 33 __.