Fractions and Mixed Numbers 5 9 Dividing Fractions

Fractions and Mixed Numbers 5 -9 Dividing Fractions and Mixed Numbers Warm Up Problem of the Day Lesson Presentation L-12 6. NS. 1 Course 11

5 -9 Dividing Fractions and Mixed Numbers Warm Up Multiply. Write each answer in simplest form. 1 1. 2 __ 2 1 2. 1 __ 2 • 2 5 • 1 3 __ 21 _ __ or 5 1 4 4 2 1 3. 3 __ • 3 3 4. Course 1 1 __ 25 • 1 __ 14 10 11 3 __ or 2 __ 4 4

5 -9 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 cuts; yes, 14 in. Course 1

5 -9 Dividing Fractions and Mixed Numbers Learn to divide fractions and mixed numbers. Course 1

5 -9 Dividing Fractions and Mixed Numbers Vocabulary reciprocal Course 1

5 -9 Dividing Fractions and Mixed Numbers Reciprocals can help you divide by fractions. Two numbers are reciprocals if their product is 1. Copy to Notebook! Course 1

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

5 -9 Dividing Fractions and Mixed Numbers Additional Example 1 B: Finding Reciprocals Find the reciprocal. 2 __ 3 2 __ • =1 3 3 2 __ 6 __ __ • = =1 3 2 6 2 __ Think: 3 of what number is 1? 2 3 __ of __ is 1. 3 2 __ __ The reciprocal of 3 is 2. Course 1

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

5 -9 Dividing Fractions and Mixed Numbers Check It Out: Example 1 A Find the reciprocal. 1 __ 4 1 __ • =1 4 1 __ • 4 =1 4 1 __ Think: 4 of what number is 1? 1 4 __ of __ is 1. 4 1 1 __ The reciprocal of 4 is 4. Course 1

5 -9 Dividing Fractions and Mixed Numbers Check It Out: Example 1 B Find the reciprocal. 4 __ 5 4 __ • =1 5 5 4 __ 20 __ • = __ = 1 5 4 20 4 __ Think: 5 of what number is 1? 4 5 __ of __ is 1. 5 4 __ __ The reciprocal of 5 is 4. Course 1

5 -9 Dividing Fractions and Mixed Numbers Check It Out: Example 1 C Find the reciprocal. 1 4 __ 8 33 __ • =1 8 8 33 264 __ • __ = ___ = 1 8 33 264 1 __. Write 4 __ as 33 8 __ of __ is 1. 8 33 33 8 __ __ The reciprocal of 8 is 33. Course 1 8

5 -9 Dividing Fractions and Mixed Numbers Look at the relationship between the 4 3 __ __ fractions 4 and 3. 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 Course 1 1 __ 24 • 4 = 6 Copy to Notebook!

5 -9 Dividing Fractions and Mixed Numbers Additional Example 2 A: Using Reciprocals to Divide Fractions and Mixed Numbers Divide. Write each answer in simplest form. 8 __ ÷ 7 7 8 8 1 __ ÷ 7 = __ • __ 7 7 7 Course 1 Rewrite as multiplication using the 1 __ reciprocal of 7, . 7 8 • 1 = ____ 7 • 7 Multiply by the reciprocal. 8 = __ 49 The answer is in simplest form.

5 -9 Dividing Fractions and Mixed Numbers Additional Example 2 B: Using Reciprocals to Divide Fractions and Mixed Numbers 5 __ 6 2 ÷ __ 3 2 5 __ 5 3 __ __ ÷ = • __ 3 6 6 2 1 5 • 3 = ____ 6 • 2 2 5 = __ 4 1 __ =1 4 Course 1 Rewrite as multiplication using the 3 2 __ __ reciprocal of 3 , 2. Simplify before multiplying. Multiply. You can write the answer as a mixed number.

5 -9 Dividing Fractions and Mixed Numbers Additional Example 2 C: Using Reciprocals to Divide Fractions and Mixed Numbers 3 2 __ 4 ÷ 1 __ 1 12 3 1 11 13 2 __ ÷ 1 __ = __ ÷ __ 4 12 11 = __ 4 12 • __ 13 3 11 • 12 ______ = 4 • 13 1 33 = __ 13 7 __ =2 13 Course 1 Write the mixed numbers as 3 = 11 __ improper fractions. 2 __ 4 4 1 13 __ __ and 1 = 12 12 Rewrite as multiplication. Simplify before multiplying. Multiply. You can write the answer as a mixed number.

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

5 -9 Dividing Fractions and Mixed Numbers Check It Out: Example 2 B 7 __ 10 1 ÷ __ 5 1 7 7 5 __ __ ÷ = • 5 10 10 1 1 7 • 5 = ____ 10 • 1 2 7 = __ 2 1 = 3 __ 2 Course 1 Rewrite as multiplication using the 5 1 __ __ reciprocal of 5 , 1. Simplify before multiplying. Multiply. You can write the answer as a mixed number.

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

5 -9 Dividing Fractions and Mixed Numbers Lesson Quiz Find the reciprocal. 1 11 __ __ 1. 11 1 8 __ 2. 13 13 __ 8 Divide. Write each answer in simplest form. 4 ÷ 20 3. __ 7 1 __ 35 2 1 __ 7 , or 1 __ 1 ÷ 2 __ 4. 3 __ 5 2 3 1 __ 5. Rhonda put 2 4 pounds of pecans into a __ -pound 4 bag. How many bags did Rhonda fill? 11 bags Course 1