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

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

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

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 of is __ 9 1 The reciprocal of is __

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 __ = = __ of is __ 3 2 The reciprocal of is. 2 3 __ 3 2

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 __ 5 16 __ The reciprocal of is __ 5 16 __ 16 5 __ Additional Example 1C: Finding Reciprocals Find the reciprocal. 3

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 of is __ 4 1 The reciprocal of is __

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 __ = = 1 20 __ of is __ 5 4 The reciprocal of is. 4 5 __ 5 4

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

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 = 624 = __

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. ÷ __ 8 7 ÷ 7 = Rewrite as multiplication using the reciprocal of 7,. 1 7 __ Multiply by the reciprocal. 8 7 __ ____ = The answer is in simplest form. = 8 49 __

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!

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 __ ____ = You can write the answer as a mixed number. = 5 4 __ Multiply. = __

5-6 Dividing Fractions and Mixed Numbers Additional Example 2C: Using Reciprocals to Divide Fractions and Mixed Numbers 2 ÷ __ Write the mixed numbers as improper fractions. 2 = and 1 = __ Rewrite as multiplication ______ = You can write the answer as a mixed number. = __ 1 12 __ Simplify before multiplying. = __ 2 ÷ 1 = ÷ 3 4 __ 1 12 __ 11 4 __ __ 11 4 __ 1 12 __ 11 4 __ __ Multiply. =

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

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 __ ____ = You can write the answer as a mixed number. = 7 2 __ Multiply. = __

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