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Percentage of amounts

Using 10%, 5% and 1% as building blocks, up to harder percentages such as 17.5%.

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Per cent means out of 100. 30% (say “thirty per cent”) means 30 out of every 100. Finding a percentage of an amount is finding a share of it, just as you found fractions of amounts in Lesson 3.5. In this lesson you will learn how to:

  • see what a percentage means on a hundred square
  • find the building blocks: 50%, 25%, 10%, 5% and 1%
  • build any percentage from the blocks, like 35% or 99%
  • find harder percentages such as 12.5% and 17.5%
  • use the reversible trick: 8% of 50 is the same as 50% of 8
Dark blue: whole numbers Blue: decimals, the parts of a whole Red dot: the decimal point

1. What per cent means

Key idea The whole amount is 100%. Split it into 100 equal parts: each part is 1%.

37 out of 100 is 37%

37 of the 100 squares are shaded, so 37% is shaded. The other 63 squares are 63%. 37% + 63% = 100%, the whole square.

Percentages to know by heart

  • 100% is all of it.
  • 50% is half of it.
  • 25% is a quarter of it.
  • 10% is a tenth of it.
  • 0% is none of it.

2. The building blocks

Key idea Five percentages are quick to find. Learn them, and you can build almost any other.

How to find each block

  1. 50%: halve it
    divide by 2
  2. 25%: halve it again
    half of 50%, or divide by 4
  3. 10%: divide by 10
    every digit moves one place to the right (Lesson 1.2)
  4. 5%: halve the 10%
    find 10% first, then halve it
  5. 1%: divide by 100
    or divide the 10% by 10

Example: the building blocks of 240

÷ 2÷ 2÷ 10÷ 2÷ 10100%24050%12010%2425%605%121%2.4

Every block comes from one above it. 10% of 240 is 24, so 5% is half of 24, which is 12.

Watch out 10% means divide by 10. 10% of 240 is 24, not 240 − 10.

3. Building any percentage

Key idea Split the percentage into blocks you know, find each block, then add them up. The blocks must add up to the percentage you want.

Example: 35% of 80

  1. Split it: 35% = 10% + 10% + 10% + 5%.10% of 80 = 8
  2. Three lots of 10%:8 × 3 = 24
  3. 5% is half of 10%:half of 8 = 4
  4. Add the blocks:24 + 4 = 28
Answer35% of 80 = 28

Take away a block: 99% of 300

99% is 1% less than the whole. 1% of 300 is 300 ÷ 100 = 3.

So 99% of 300 = 300 − 3 = 297.

Use 1% blocks: 12% of 50

12% = 10% + 1% + 1%. 10% of 50 is 5, and 1% of 50 is 0.5.

So 12% of 50 = 5 + 0.5 + 0.5 = 6.

Watch out Check that your blocks add up to the right percentage. 10% + 5% is only 15%, not 35%.

4. Harder percentages: 12.5% and 17.5%

Key idea Keep halving. Half of 5% is 2.5%. Half of 25% is 12.5%.

Example: 17.5% of 80

  1. Split it: 17.5% = 10% + 5% + 2.5%.10% of 80 = 8
  2. 5% is half of 10%:half of 8 = 4
  3. 2.5% is half of 5%:half of 4 = 2
  4. Add the blocks:8 + 4 + 2 = 14
Answer17.5% of 80 = 14

12.5% of 64

25% of 64 is 64 ÷ 4 = 16.

12.5% is half of 25%, so 12.5% of 64 = half of 16 = 8.

Money: 15% of £18

10% of £18 is £1.80, and 5% is half of that, £0.90.

So 15% of £18 = £1.80 + £0.90 = £2.70.

Watch out Money with pence has two decimal places. Write £2.70, not £2.7 or £2.07.

5. Key tip: percentages are reversible

Key tip You can swap the two numbers round. 8% of 50 is the same as 50% of 8. Pick whichever way round is easier.

Example: 8% of 50

8%of5050%of8

8% of 50 looks hard. Swap it round: 50% of 8 is half of 8, which is 4. So 8% of 50 = 4 as well.

Why it works: both mean “multiply the two numbers, then divide by 100”. 8 × 50 = 400, and 400 ÷ 100 = 4.

More swaps

  • 16% of 25 = 25% of 16 = a quarter of 16 = 4
  • 18% of 50 = 50% of 18 = half of 18 = 9
  • 4% of 75 = 75% of 4 = 3

Swap when the amount is a friendly percentage: 50, 25, 75, 10 or 20.

The mistakes that cost marks

  1. Taking away instead of dividing. Working out 10% of 240 as 240 − 10 = 230. 10% means divide by 10: 240 ÷ 10 = 24.
  2. Dividing by the percentage. Working out 5% of 80 as 80 ÷ 5 = 16. 80 ÷ 5 gives 20%. 5% is half of 10%: 10% of 80 is 8, so 5% is 4.
  3. Dividing by 10 for 1%. Giving 24 as 1% of 240. 1% means divide by 100: 240 ÷ 100 = 2.4.
  4. Blocks that do not add up. Working out 35% as 10% + 5%. 10% + 5% is only 15%. For 35% you need 10% + 10% + 10% + 5%.
  5. Stopping at one block. Giving 8 as 30% of 80. 8 is only 10%. 30% is three lots: 8 × 3 = 24.
  6. Money with one decimal place. Writing £2.7 for 15% of £18. write £2.70. Pence always take two places.

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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