1. 2. 1/3 of a cake makes 1 serving. How many servings can we get from 4/5 of a cake? (a)Write an equation to represent the problem. Let x be the answer. 4/5 ÷ 1/3 = x

2. 2. 1/3 of a cake makes 1 serving. How many servings can we get from 4/5 of a cake? (b)Solve this problem in a way such that it is meaningful for a 5 th grader. 1/3 4/5 4/5 ÷ 1/3 ?

3. 2. 1/3 of a cake makes 1 serving. How many servings can we get from 4/5 of a cake? (b)Solve this problem in a way such that it is meaningful for a 5 th grader. 1/3 4/5 4/5 ÷ 1/3 What does 4/5 ÷ 1/3 actually mean? How many 1/3 are in 4/5?

4. 2. 1/3 of a cake makes 1 serving. How many servings can we get from 4/5 of a cake? (b)Solve this problem in a way such that it is meaningful for a 5 th grader. 1/3 4/5 4/5 ÷ 1/3 How many 1/3 are in 4/5? More than 2 but less than 3.

5. 2. 1/3 of a cake makes 1 serving. How many servings can we get from 4/5 of a cake? (b)Solve this problem in a way such that it is meaningful for a 5 th grader. 1/3 4/5 4/5 ÷ 1/3 How many 1/3 are in 4/5? How do you find the exact answer? Answer: 2 2525

6. 1/3 4/5 4/5 ÷ 1/3 How many 1/3 are in 4/5? We have seen why the answer is 2 2 / 5. Answer: 2 2525 or 12 5 Can you see 12/5 in these pictures?

7. How many 1/3 are in 4/5? We have seen why the answer is 2 2 / 5. Answer: 2 2525 or 12 5 Can you see 12/5 in these pictures? 1/3 4/5 4/5 ÷ 1/3

8. 2. 1/3 of a cake makes 1 serving. How many servings can we get from 4/5 of a cake? (c)What is the referent whole for the dividend 4/5? 1/3 4/5 4/5 ÷ 1/3 How many 1/3 are in 4/5? Answer: 2 2525 One cake of a cake or 12 5

9. 2. 1/3 of a cake makes 1 serving. How many servings can we get from 4/5 of a cake? (d)What is the referent whole for the divisor 1/3? 1/3 4/5 4/5 ÷ 1/3 How many 1/3 are in 4/5? Answer: 2 2525 One cake of a cake or 12 5 How many 1/3 of a cake are in 4/5 of a cake? Can you see 12  5?

10. 2. 1/3 of a cake makes 1 serving. How many servings can we get from 4/5 of a cake? (d)What is the referent whole for the divisor 1/3? 1/3 4/5 4/5 ÷ 1/3 Answer: One cake of a cake 12 5 How many 5/15 of a cake are in 12/15 of a cake? How many 5 pieces are in 12 pieces? 12  5 =

11. 2. 1/3 of a cake makes 1 serving. How many servings can we get from 4/5 of a cake? 1/3 4/5 4/5 ÷ 1/3 How many 1/3 are in 4/5? Answer: 2 2525 1/3 of a cake of a cake (e)What is the referent whole for the quotient 2 ? 2525 of 1/3 cake is equal to 4/5 cake. 2 2525 2  = 2 1 4 5 3 5 or 12 5 ÷ = 2 4 1 2 5 3 5

12. 2  = 2 1 4 5 3 5 ÷ = 2 4 1 2 5 3 5 2 2 / 5 is a fraction of another fraction. Its referent whole is the multiplicand. The referent whole for the quotient is the divisor. In repeated-subtraction view of division, the referent whole for the dividend and divisor are by default 1 unit. In fractional part of a quantity view of multiplication, the referent whole for the multiplicand and the product is by default 1 unit. In summary, what is the referent whole for each of these numbers?