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Fractions of amounts

Unit and non-unit fractions, and working backwards: if 3/5 of a number is 27, what is the number?.

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A fraction of an amount is a share of it. 14 of 20 sweets means: share the 20 sweets into 4 equal groups and take 1 group. In this lesson you will learn how to:

  • find a unit fraction of an amount, like 14 of 20
  • find a non-unit fraction of an amount, like 34 of 20
  • draw a bar model to see the parts
  • find fractions of an hour and of money
  • work backwards: if 35 of a number is 27, what is the number?

1. Unit fractions of amounts

Key idea A unit fraction has 1 on top: 12, 13, 14… To find one, divide by the bottom number.

Example: 14 of 20

Share 20 into 4 equal groups: 20 ÷ 4 = 5. So 14 of 20 is 5.

Watch out Divide by the bottom number. 14 of 20 is 20 ÷ 4, not 20 × 4.

2. Non-unit fractions and the bar model

Key idea Divide by the bottom to find one part, then multiply by the top to find that many parts. The bottom says how many equal parts; the top says how many you take.

Example: 34 of 20

20555515
  1. One part: divide by the bottom.20 ÷ 4 = 5
  2. Three parts: multiply by the top.5 × 3 = 15
Answer34 of 20 = 15

3. Fractions of an hour and of money

Key idea Change to a unit that shares exactly: 1 hour = 60 minutes and £1 = 100p. Then divide by the bottom and multiply by the top as usual.

34 of an hour

121234567891011

60 ÷ 4 = 15 minutes, and 15 × 3 = 45 minutes.

Money

  • 25 of £1: 100p ÷ 5 = 20p, and 20p × 2 = 40p.
  • 38 of £24: £24 ÷ 8 = £3, and £3 × 3 = £9.
Watch out Write the unit in your answer: 45 minutes, 40p, £9.

4. Working backwards

Key idea When you know a fraction of the number and need the whole: divide by the top to find one part, then multiply by the bottom to find all the parts.

Example: 35 of a number is 27. What is the number?

?9999927
  1. 3 parts are 27, so one part is27 ÷ 3 = 9
  2. The whole is 5 parts.9 × 5 = 45
Answer45

Check forwards: 35 of 45 is 45 ÷ 5 × 3 = 27.

What is left over

Ali spends 25 of his money. He has £18 left. How much did he have to start with?

  • He spent 25, so 35 is left: 3 parts are £18.
  • One part: £18 ÷ 3 = £6. All 5 parts: £6 × 5 = £30.

The mistakes that cost marks

  1. Dividing by the top number. Working out 34 of 20 as 20 ÷ 3. divide by the bottom (20 ÷ 4 = 5), then multiply by the top (5 × 3 = 15).
  2. Stopping at one part. Giving 5 as 34 of 20. 5 is only 14. Multiply by the top to get 3 parts: 15.
  3. Working forwards when you should work backwards. “35 of a number is 27”, answered with 35 of 27. 27 is the part. Divide by the top (27 ÷ 3 = 9) and multiply by the bottom (9 × 5 = 45).
  4. Answering the wrong part. Giving the amount spent when the question asks how much is left. read the question again. Left over = the whole minus the part used.
  5. Using 100 minutes in an hour. Working out 34 of an hour as 75 minutes. an hour is 60 minutes: 60 ÷ 4 × 3 = 45 minutes.
  6. Forgetting the unit. Writing 40 for 25 of £1. write 40p. The unit is part of the answer.

Quick checklist

Tick each one when you can do it without help.

Download

Print these and work through them away from the screen.

Year 4 practice paper PDF · 11+ style, with answer sheet and answers Year 5 practice paper PDF · 11+ style, with answer sheet and answers Year 6 practice paper PDF · 11+ style, with answer sheet and answers

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