Learn to divide fractions and mixed numbers .

1. Learn to divide fractions and mixed numbers.

2. Vocabulary reciprocal multiplicative inverse

3. Reciprocals can help you divide by fractions. Two numbers are reciprocals if their product is 1.

4. 1 __ 9 1 1 1 __ __ __ Think: of what number is 1? • = 1 9 9 9 1 9 1 __ __ __ • 9 = 1 9 1 9 1 __ 9 Additional Example 1A: Finding Reciprocals Find the reciprocal. of is 1. The reciprocal of is 9.

5. 2 __ 3 2 2 __ __ • = 1 3 3 2 3 3 2 6 __ __ __ __ __ 2 3 2 3 6 3 2 __ __ 2 3 Additional Example 1B: Finding Reciprocals Find the reciprocal. Think: of what number is 1? of is 1. • = = 1 The reciprocal of is .

6. 1 __ 5 1 16 __ __ 16 __ 5 5 5 16 5 5 16 80 __ __ __ __ __ 16 5 16 5 80 5 16 __ __ 5 16 Additional Example 1C: Finding Reciprocals Find the reciprocal. 3 Write 3 as . • = 1 of is 1. • = = 1 The reciprocal of is .

7. 1 __ 4 1 1 __ __ Think: of what number is 1? • = 1 4 4 1 4 1 __ __ __ • 4 = 1 4 1 4 1 __ 4 Check It Out: Example 1A Find the reciprocal. of is 1. The reciprocal of is 4.

8. 4 __ 5 4 4 __ __ • = 1 5 5 4 5 5 4 20 __ __ __ __ __ 4 5 4 5 20 5 4 __ __ 5 4 Check It Out: Example 1B Find the reciprocal. Think: of what number is 1? of is 1. • = = 1 The reciprocal of is .

9. 1 __ 8 1 33 __ __ 33 __ 8 8 8 33 8 8 33 264 264 __ __ __ __ ___ 33 8 33 8 33 8 __ __ 8 33 Check It Out: Example 1C Find the reciprocal. 4 Write 4 as . • = 1 of is 1. • = = 1 The reciprocal of is .

10. 4 3 __ __ 3 4 1 __ 4 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. 24 ÷ 4 = 6 24 • = 6

11. 8 __ 7 Rewrite as multiplication using the reciprocal of 7, . 8 8 1 __ __ __ 1 __ 7 7 7 7 8 • 1 ____ 7 • 7 8 __ 49 Additional Example 2A: Using Reciprocals to Divide Fractions and Mixed Numbers Divide. Write each answer in simplest form. ÷ 7 ÷ 7 = • = Multiply by the reciprocal. = The answer is in simplest form.

12. Caution! 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.

13. 2 5 __ __ 3 6 2 5 5 3 __ __ __ __ 3 2 __ __ 3 6 6 2 2 3 5 • 3 ____ 6 • 2 5 __ 4 1 __ 4 Additional Example 2B: Using Reciprocals to Divide Fractions and Mixed Numbers ÷ Rewrite as multiplication using the reciprocal of , . ÷ = • 1 = Simplify before multiplying. 2 Multiply. = You can write the answer as a mixed number. = 1

14. 1 3 __ __ 12 4 3 11 3 1 11 13 __ __ __ __ __ __ 4 4 4 12 4 12 1 13 __ __ 12 12 12 11 __ __ 13 4 11 • 12 ______ 4 • 13 33 __ 13 7 __ 13 Additional Example 2C: Using Reciprocals to Divide Fractions and Mixed Numbers 2 ÷ 1 Write the mixed numbers as improper fractions. 2 = and 1 = 2 ÷ 1 = ÷ Rewrite as multiplication. = • 3 = Simplify before multiplying. 1 Multiply. = You can write the answer as a mixed number. = 2

15. 2 __ 3 Rewrite as multiplication using the reciprocal of 3, . 2 2 1 __ __ __ 1 __ 3 3 3 3 2 • 1 ____ 3 • 3 2 __ 9 Check It Out: Example 2A Divide. Write each answer in simplest form. ÷ 3 ÷ 3 = • = Multiply by the reciprocal. = The answer is in simplest form.

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

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