1. Division of Fractions Repeated Subtraction View
Created by Dr. Kien Lim

2. 1/3 of a cake makes 1 serving
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. x
4/5 ÷ 1/3 =

3. 1/3 of a cake makes 1 serving
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 5th grader.
4/5
1/3 ?
4/5 ÷ 1/3

4. 1/3 of a cake makes 1 serving
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 5th grader.
4/5
1/3
What does 4/5 ÷ 1/3 actually mean?
How many 1/3 are in 4/5?
4/5 ÷ 1/3

5. 1/3 of a cake makes 1 serving
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 5th grader.
4/5
1/3
How many 1/3 are in 4/5?
4/5 ÷ 1/3
More than 2 but less than 3.

6. 1/3 of a cake makes 1 serving
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 5th grader.
4/5
How do you find the exact answer?
1/3
How many 1/3 are in 4/5?
4/5 ÷ 1/3
Answer: 2 2 5

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

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

9. 1/3 of a cake makes 1 serving
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?
One cake
4/5
of a cake
1/3
How many 1/3 are in 4/5?
4/5 ÷ 1/3
Answer: 2 2 5 or 12 5

10. How many 1/3 of a cake are in 4/5 of a cake?
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?
One cake
How many 1/3 of a cake are in 4/5 of a cake?
4/5
of a cake
Can you see 12  5?
1/3
of a cake
How many 1/3 are in 4/5?
4/5 ÷ 1/3
Answer: 2 2 5 or 12 5

11. 1/3 of a cake makes 1 serving
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?
One cake
How many 5/15 of a cake are in 12/15 of a cake?
4/5
of a cake
How many 5 pieces are in 12 pieces?
1/3
of a cake
4/5 ÷ 1/3 12 5
Answer:
12  5 =

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

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