2. BELLWORK – 01OCT2013 Multiply. Tell whether each reciprocal is true or false. 1. 1/2 = 2/1 2. 2/3 = 4/6 3.1/5 = 3/15 4. 1/3 = 3/1 5.5/7 = 7/5

3. BELLWORK – 02OCT2013 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? 2 lengths

4. BELLWORK – 03OCT2013 Divide. Put each answer in simplest form. 1. 3/5  1/5 2. 7/9  3/1 3.1½  1/2

5. MA.6.A.1.2 We will multiply and divide fractions efficiently. MA.6.A.1.3 Sunshine State Standards Learning Goal

6. Vocabulary reciprocal multiplicative inverse

7. Reciprocals can help you divide by fractions. Two numbers are reciprocals or multiplicative inverses if their product is 1. A reciprocal is a “flipped fraction”. When you multiply by a reciprocal, the answer has to be 1!!!!

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

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

10. 1 5 16 5 __ = 1 Write 3 as. 1 5 __ 5 16 __ 16 5 __ = = 1 80 __ of is 1. 16 5 __ 5 16 __ The reciprocal of is. 16 5 __ 5 16 __ 16 5 __ Additional Example 1C: Finding Reciprocals Find the reciprocal. 3

11. RUBRIC FOR FINDING RECIPROCALS

12. Check It Out: Example 1A Find each reciprocal. 1 8 __ 4 4 1 8 = 33 8 __ ; 8 33 __

13. Check It Out: Example 1B Find each reciprocal. 5 5 = 5 1 __ ; 1 5

14. Check It Out: Example 1C Find each reciprocal. 1 4 __ 2 2 1 4 = 9 4 ; 4 9

15. RUBRIC FOR FINDING RECIPROCALS

16. 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 24 ÷ 4 = 624 = 6 1 4 __

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

18. 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!

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

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

21. RUBRIC FOR DIVIDING WITH RECIPROCALS

22. Check It Out: Example 2A Divide. Write each answer in simplest form. 7 10 __ 1 5 ÷ 7 10 __ 5 1. 35 10 __ 1 2 3

23. Check It Out: Example 2B Divide. Write each answer in simplest form. 3 4 __ 1 8 ÷ 7 4 8 1. 56 4 __ 14 1

24. Check It Out: Example 2C Divide. Write each answer in simplest form. 1 5 __ 1 2 ÷ 11 5 __ 33 2 __ 2 15 __ 216 ÷ 11 5 __ 2 33 __.

25. RUBRIC FOR DIVIDING FRACTIONS WITH RECIPROCALS

26. Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

27. Lesson Quiz Find the reciprocal. 1. 2. Divide. Write each answer in simplest form. 3. ÷ 204. 3 ÷ 2 5. Rhonda put 2 pounds of pecans into -pound bags. How many bags did Rhonda fill? 1 11 __ 8 13 __ 4 7 1 2 1 2 3 4 1 4 11 1 __ 13 8 __ 1 35 __ 7 5 2 5, or 1 11 bags

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

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

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

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

32. 5. In his 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 Lesson Quiz for Student Response Systems