1. Dividing Fractions and Mixed Numbers

2. Learn to divide fractions and mixed numbers. Dividing Fractions and Mixed Numbers

3. Vocabulary reciprocal

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. 3 4 __ 4 3 24 ÷ 4 = 624 = 6 1 4 __ Reciprocal

5. 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

6. 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 __

7. 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 __

8. 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. =

9. 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 __

10. 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 __

11. 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. =

12. Lesson Quiz Find the reciprocal. 1. 2. Divide. Write each answer in simplest form. 3. ÷ 204. 3 ÷ 2 5. Rhonda put 2 pounds of pecans into a -pound bag. How many bags did Rhonda fill? 1 11 __ 8 13 __ 4 7 1 2 1 2 3 4 1 4 11 1 __ 13 8 __ 1 35 __ 7 5 2 5, or 1 11 bags