1. 5-6 Dividing Fractions and Mixed Numbers Learn to divide fractions and mixed numbers.

2. 5-6 Dividing Fractions and Mixed Numbers Vocabulary reciprocal multiplicative inverse

3. 5-6 Dividing Fractions and Mixed Numbers Reciprocals can help you divide by fractions. Two numbers are reciprocals if their product is 1.

4. 5-6 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 __

5. 5-6 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

6. 5-6 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

7. 5-6 Dividing Fractions and Mixed Numbers Check It Out: Example 1A Find the reciprocal. 1 4 __ 1 4 = 1 Think: of what number is 1? 1 4 __ 1 4 4 = 1 of is 1. 1 4 __ 4 1 The reciprocal of is 4. 1 4 __

8. 5-6 Dividing Fractions and Mixed Numbers Check It Out: Example 1B Find the reciprocal. 4 5 __ 4 5 = 1 Think: of what number is 1? 4 5 __ 5 4 4 5 = = 1 20 __ of is 1. 4 5 __ 5 4 The reciprocal of is. 4 5 __ 5 4

9. 5-6 Dividing Fractions and Mixed Numbers 1 8 __ 33 8 __ = 1 Write 4 as. 1 8 __ 8 33 __ 33 8 __ = = 1264 ___ of is 1. 33 8 __ 8 33 __ The reciprocal of is. 33 8 __ 8 33 __ 33 8 __ Check It Out: Example 1C Find the reciprocal. 4

10. 5-6 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 __

11. 5-6 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 __

12. 5-6 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!

13. 5-6 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 __

14. 5-6 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. =

15. 5-6 Dividing Fractions and Mixed Numbers Check It Out: Example 2A Divide. Write each answer in simplest form. ÷ 3 2 3 __ 2 3 ÷ 3 = Rewrite as multiplication using the reciprocal of 3,. 1 3 __ Multiply by the reciprocal. 2 3 __ 1 3 2 1 3 ____ = The answer is in simplest form. = 2 9 __

16. 5-6 Dividing Fractions and Mixed Numbers Check It Out: Example 2B ÷ 7 10 __ 7 10 __ ÷ = Rewrite as multiplication using the reciprocal of,. 5 1 __ Simplify before multiplying. 7 10 __ 5 1 7 5 10 1 ____ = You can write the answer as a mixed number. = 7 2 __ 1 5 1 5 1 5 1 2 Multiply. = 3 1 2 __

17. 5-6 Dividing Fractions and Mixed Numbers Check It Out: Example 2C 3 ÷ 1 2 3 __ Write the mixed numbers as improper fractions. 3 = and 1 =. 10 9 __ Rewrite as multiplication. 11 9 3 10 ______ = You can write the answer as a mixed number. = 33 10 __ 1 9 2 3 1 3 Simplify before multiplying. = 3 3 10 __ 3 ÷ 1 = ÷ 2 3 __ 1 9 11 3 __ 10 9 __ 11 3 __ 1 9 11 3 __ 9 10 __ Multiply. =