Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Multiply. Write each answer in simplest form. Warm Up Multiply. Write each answer in simplest form. 1. 2 • 2 2. 1 • 3 3. 3 • 3 4. 2 • 1 1 2 __ 5 1 2 __ 1 2 __ 21 4 __ 1 4 _ or 5 1 3 __ 10 1 5 __ 1 4 __ 11 4 __ 3 4 __ or 2

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.

Learn to divide fractions and mixed numbers.

Vocabulary reciprocal multiplicative inverse

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

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

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

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

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

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

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

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 __ 1 4 __ 24 ÷ 4 = 6 24 • = 6

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

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!

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

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

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

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

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

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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

Lesson Quiz for Student Response Systems 1. Identify the reciprocal of . A. –15 C. B. D. 15

Lesson Quiz for Student Response Systems 2. Identify the reciprocal of . A. 15 C. B. 7 D.

Lesson Quiz for Student Response Systems 3. Divide and identify the answer in the simplest form. A. C. B. D.

Lesson Quiz for Student Response Systems 4. Divide and identify the answer in the simplest form. A. C. B. D.

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