5 8 Dividing Fractions and Mixed Numbers Warm

5 -8 Dividing Fractions and Mixed Numbers Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

5 -8 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. 1 __ 25 • 1 __ 14 10 11 3 __ or 2 __ 4 4

5 -8 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 lengths; yes, 14 in.

5 -8 Dividing Fractions and Mixed Numbers Sunshine State Standards MA. 6. A. 1. 2 Multiply and divide fractions…efficiently. Also MA. 6. A. 1. 3

5 -8 Dividing Fractions and Mixed Numbers Vocabulary reciprocal multiplicative inverse

5 -8 Dividing Fractions and Mixed Numbers Reciprocals can help you divide by fractions. Two numbers are reciprocals or multiplicative inverses if their product is 1.

5 -8 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.

5 -8 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.

5 -8 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 __. 5 16

5 -8 Dividing Fractions and Mixed Numbers Check It Out: Example 1 A Find each reciprocal. 1 4 __ 8 = 33 __ 8 ; __ 8 33

5 -8 Dividing Fractions and Mixed Numbers Check It Out: Example 1 B Find each reciprocal. 5 5 ; __ 5 = 1 1 __ 5

5 -8 Dividing Fractions and Mixed Numbers Check It Out: Example 1 C Find each reciprocal. 1 2 __ 4 = 9 __ 4 ; 4 __ 9

5 -8 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 1 __ 24 • 4 = 6

5 -8 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 Rewrite as multiplication using the 1 __ reciprocal of 7, . 7 • 1 ____ = 8 7 • 7 Multiply by the reciprocal. 8 = __ 49 The answer is in simplest form.

5 -8 Dividing Fractions and Mixed Numbers 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.

5 -8 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 • 3 ____ = 5 6 • 2 2 5 = __ 4 1 __ =1 4 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 -8 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 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 -8 Dividing Fractions and Mixed Numbers Check It Out: Example 2 A Divide. Write each answer in simplest form. 7 __ 10 ÷ 7 __ 10 . 35 __ 10 1 2 3 __ 1 __ 5 5 __ 1

5 -8 Dividing Fractions and Mixed Numbers Check It Out: Example 2 B Divide. Write each answer in simplest form. 3 1 __ 8 4 ÷ 7 __ 4 8. __ 56 __ 4 14 1

5 -8 Dividing Fractions and Mixed Numbers Check It Out: Example 2 C Divide. Write each answer in simplest form. 1 2 __ 5 ÷ 1 16 __ 2 11 __ 5 ÷ 33 __ 2 11 __ 5 . 2 __ 33 2 __ 15

5 -8 Dividing Fractions and Mixed Numbers Lesson Quizzes Standard Lesson Quiz for Student Response Systems

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

5 -8 Dividing Fractions and Mixed Numbers Lesson Quiz for Student Response Systems 1. Identify the reciprocal of . A. – 15 C. B. D. 15

5 -8 Dividing Fractions and Mixed Numbers Lesson Quiz for Student Response Systems 2. Identify the reciprocal of A. 15 C. B. 7 D. .

5 -8 Dividing Fractions and Mixed Numbers Lesson Quiz for Student Response Systems 3. Divide and identify the answer in the simplest form. A. C. B. D.

5 -8 Dividing Fractions and Mixed Numbers Lesson Quiz for Student Response Systems 4. Divide and identify the answer in the simplest form. A. C. B. D.

5 -8 Dividing Fractions and Mixed Numbers Lesson Quiz for Student Response Systems 5. In his pet care center, Nelson has pounds of cat food. He plans to feed a cat with of cat food. How many cats can he feed? A. 13 cats C. 11 cats B. 12 cats D. 10 cats pound