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## 5-9

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**5-9**Dividing Fractions and Mixed Numbers Course 1 Warm Up Problem of the Day Lesson Presentation L-12 6.NS.1**21**1 1 1 3 1 1 1 11 1 __ __ __ __ __ _ __ __ __ __ 4 5 2 2 2 4 4 4 4 3 Warm Up Multiply. Write each answer in simplest form. 1.2 • 2 2. 1 • 3 3. 3 • 3 4. 2 • 1 5 or 5 10 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 cuts; yes, 14 in.**Vocabulary**reciprocal**Reciprocals can help you divide by fractions. Two numbers**are reciprocals if their product is 1. Copy to Notebook!**Think: of what number is 1?**• = 1 • 9 = 1 1 1 1 9 1 1 1 1 __ __ __ __ __ __ __ __ 9 9 9 9 9 1 9 9 Additional Example 1A: Finding Reciprocals Find the reciprocal. of is 1. The reciprocal of is 9.**• = 1**2 3 2 2 3 2 2 3 6 2 __ __ __ __ __ __ __ __ __ __ 3 3 2 3 3 3 6 3 2 2 Additional Example 1B: Finding Reciprocals Find the reciprocal. Think: of what number is 1? of is 1. • = = 1 The reciprocal of is .**1**16 16 80 16 5 1 5 16 16 5 __ __ __ __ __ __ __ __ __ __ __ 5 5 5 5 5 16 16 16 5 5 80 Additional Example 1C: Finding Reciprocals Find the reciprocal. 3 Write 3 as . • = 1 of is 1. • = = 1 The reciprocal of is .**Think: of what number is 1?**• 4 = 1 • = 1 4 1 1 1 1 1 1 __ __ __ __ __ __ __ 1 4 4 4 4 4 4 Check It Out: Example 1A Find the reciprocal. of is 1. The reciprocal of is 4.**• = 1**4 5 4 4 5 4 4 5 20 4 __ __ __ __ __ __ __ __ __ __ 5 5 4 5 5 5 20 5 4 4 Check It Out: Example 1B Find the reciprocal. Think: of what number is 1? of is 1. • = = 1 The reciprocal of is .**1**33 33 8 33 1 8 8 33 33 264 264 __ __ __ __ ___ __ __ __ __ __ __ 8 8 8 33 33 8 33 8 8 8 Check It Out: Example 1C Find the reciprocal. 4 Write 4 as . • = 1 of is 1. • = = 1 The reciprocal of is .**3**4 1 __ __ __ 4 3 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. 24 ÷ 4 = 6 24 • = 6 Copy to Notebook!**Rewrite as multiplication using the**reciprocal of 7, . 8 8 8 8 • 1 8 1 1 __ __ __ __ __ ____ __ 7 7 • 7 7 7 7 49 7 Additional Example 2A: Using Reciprocals to Divide Fractions and Mixed Numbers Divide. Write each answer in simplest form. ÷ 7 ÷ 7 = • = Multiply by the reciprocal. = The answer is in simplest form.**3**1 5 5 2 5 5 • 3 2 5 2 3 __ __ __ __ __ __ __ __ __ __ ____ 4 3 3 2 6 2 4 6 • 2 6 6 3 Additional Example 2B: Using Reciprocals to Divide Fractions and Mixed Numbers ÷ Rewrite as multiplication using the reciprocal of , . ÷ = • 1 = Simplify before multiplying. 2 Multiply. = You can write the answer as a mixed number. = 1**7**11 • 12 12 3 13 11 33 3 1 11 3 1 11 13 1 __ __ __ __ ______ __ __ __ __ __ __ __ __ __ __ 4 • 13 13 12 4 13 12 13 12 4 4 12 4 4 12 4 Additional Example 2C: Using Reciprocals to Divide Fractions and Mixed Numbers 2 ÷ 1 Write the mixed numbers as improper fractions. 2 = and 1 = 2 ÷ 1 = ÷ Rewrite as multiplication. = • 3 = Simplify before multiplying. 1 Multiply. = You can write the answer as a mixed number. = 2**Rewrite as multiplication using the**reciprocal of 3, . 2 2 2 2 • 1 2 1 1 __ __ __ __ __ ____ __ 3 3 • 3 3 3 3 9 3 Check It Out: Example 2A Divide. Write each answer in simplest form. ÷ 3 ÷ 3 = • = Multiply by the reciprocal. = The answer is in simplest form.**5**1 7 7 1 7 7 • 5 1 7 1 5 __ __ __ __ __ __ __ __ __ __ ____ 2 5 5 1 10 1 2 10 • 1 10 10 5 Check It Out: Example 2B ÷ Rewrite as multiplication using the reciprocal of , . ÷ = • 1 = Simplify before multiplying. 2 Multiply. = You can write the answer as a mixed number. = 3**3**11 • 9 9 2 10 11 33 2 1 11 2 1 11 10 1 __ __ __ __ ______ __ __ __ __ __ __ __ __ __ __ 3 • 10 10 9 3 10 9 10 9 3 3 9 3 3 9 3 Check It Out: Example 2C 3 ÷ 1 Write the mixed numbers as improper fractions. 3 = and 1 = . 3 ÷ 1 = ÷ Rewrite as multiplication. = • 3 = Simplify before multiplying. 1 Multiply. = You can write the answer as a mixed number. = 3**3**1 8 4 1 1 2 11 138 1 7 1 __ __ __ __ __ __ __ __ __ __ __ __ 7 11 2 13 2 5 1 4 5 35 4 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? , or 1 11 bags