# 5-9

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## 5-9

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

2. 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

3. 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.

4. Learn to divide fractions and mixed numbers.

5. Vocabulary reciprocal

6. Reciprocals can help you divide by fractions. Two numbers are reciprocals if their product is 1. Copy to Notebook!

7. 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.

8. • = 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 .

9. 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 .

10. 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.

11. • = 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 .

12. 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 .

13. 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!

14. 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.

15. 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

16. 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

17. 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.

18. 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

19. 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

20. 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