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Published byMarshall Hutchinson Modified over 6 years ago
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Division of Fractions Repeated Subtraction View
Created by Dr. Kien Lim
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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 =
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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
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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
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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.
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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
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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
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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
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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
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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
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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 =
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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
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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.
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