NumberKS3 / GCSE

Reverse fractions of an amount - bar model

Find the whole amount when a fraction of it is known using equal parts in a bar model.

  • The denominator tells you how many equal parts make the whole.
  • Divide the known amount by the numerator to find one part.
  • Multiply one part by the denominator to find the whole.

Example 1

Find one part

of an amount is 24. Find the whole.

3 of 5 equal parts. Whole: 40. Selected amount: 24.Whole = 40888883 parts = 24
Divide to find one part, then multiply

Example 2

Use the same method

of an amount is 18. Find the whole.

2 of 7 equal parts. Whole: 63. Selected amount: 18.Whole = 6399999992 parts = 18
Divide to find one part, then multiply

Remember
For a reverse fraction, the known amount covers the numerator’s number of parts.

Your turn

Question 1

of an amount is 16. Find the whole amount.

2 of 3 equal parts. Whole: ?. Selected amount: 16.Whole = ?2 parts = 16
Check answer
2 of 3 equal parts. Whole: 24. Selected amount: 16.Whole = 248882 parts = 16
Question 2

of an amount is 39. Find the whole amount.

3 of 4 equal parts. Whole: ?. Selected amount: 39.Whole = ?3 parts = 39
Check answer
3 of 4 equal parts. Whole: 52. Selected amount: 39.Whole = 52131313133 parts = 39
Question 3

of an amount is 36. Find the whole amount.

4 of 7 equal parts. Whole: ?. Selected amount: 36.Whole = ?4 parts = 36
Check answer
4 of 7 equal parts. Whole: 63. Selected amount: 36.Whole = 6399999994 parts = 36
Question 4

of an amount is 45. Find the whole amount.

5 of 8 equal parts. Whole: ?. Selected amount: 45.Whole = ?5 parts = 45
Check answer
5 of 8 equal parts. Whole: 72. Selected amount: 45.Whole = 72999999995 parts = 45
Question 5

of an amount is 84. Find the whole amount.

7 of 10 equal parts. Whole: ?. Selected amount: 84.Whole = ?7 parts = 84
Check answer
7 of 10 equal parts. Whole: 120. Selected amount: 84.Whole = 120121212121212121212127 parts = 84
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