Key ideas
Per cent
Per cent means out of 100.
37% = 37100
Building blocks
10% = 110: divide by 10
5% = half of 10%
25% = 14: divide by 4
50% = half
1% = 1100: divide by 100
Build any percentage
35% = 30% + 5%
12% = 10% + 1% + 1%
Choose the quickest blocks: 75% = 50% + 25%.
With a calculator
percentage100 × amount
17% of £84: 17100 × 84 = £14.28
Increase and decrease
Find the percentage, then add it (increase) or take it away (decrease).
As a percentage
Write it as a fraction, then make it out of 100.
1825 = 72100 = 72%
Percentages and hundredths
Write 310 as a percentage.(1 mark)
Make it out of 100.310 = 30100 × 10 top and bottom= 30%✓1
In plain EnglishPer cent means out of 100, so change the denominator to 100.
Multiples of 10%
Find 30% of £240.(2 marks)
Find 10%.10% = 24010 = £24✓1
In plain English10% is one tenth, so divide by 10.
Multiply by 3.30% = 3 × £24 = £72✓2
In plain English30% is three lots of 10%.
Multiples of 5% and 25%
Find 15% of 60 kg.(2 marks)
10% and 5%.10% = 6 kg5% = 3 kg half of 10%✓1
In plain EnglishFind 10% by dividing by 10. 5% is half of 10%.
Add.15% = 6 + 3 = 9 kg✓2
In plain English15% = 10% + 5%.
Find 75% of 48.(2 marks)
Find 25%.25% = 484 = 12✓1
In plain English25% is a quarter, so divide by 4.
Three lots.75% = 3 × 12 = 36✓2
In plain English75% is three lots of 25%, so multiply by 3.
Multiples of 1%
Find 3% of £700.(2 marks)
Find 1%.1% = 700100 = £7✓1
In plain English1% is one hundredth, so divide by 100.
Three lots.3% = 3 × £7 = £21✓2
In plain English3% is three lots of 1%, so multiply by 3.
Any percentage without a calculator
Find 36% of 450 without a calculator.(3 marks)
Break it up.36% = 10% + 10% + 10% + 5% + 1%✓1
In plain EnglishUse the blocks you know.
Find each block.10% = 45, so 30% = 1355% = 22.51% = 4.5✓2
In plain English10% is 450 ÷ 10. 5% is half of 10%, and 1% is 10% ÷ 10.
Add.135 + 22.5 + 4.5 = 162✓3
In plain EnglishAdd up all the blocks to make 36%.
Any percentage with a calculator
Find 17% of £84.(1 mark)
Out of 100.17100 × 84 = £14.28✓1
In plain EnglishOn the calculator: 17 ÷ 100 × 84.
Increasing and decreasing
A £60 jacket goes up in price by 20%. What is the new price?(2 marks)
Find 20%.10% = £6, so 20% = £12✓1
In plain EnglishFind 10% by dividing by 10, then double it to get 20%.
Increase: add.£60 + £12 = £72✓2
In plain EnglishThe price goes up, so add the 20% on to the original price.
A £45 game is reduced by 10% in a sale. Find the sale price.(2 marks)
Find 10%.10% = £4.50✓1
In plain EnglishDivide by 10 to find 10%.
Decrease: take away.£45 − £4.50 = £40.50✓2
In plain EnglishThe price goes down in the sale, so take the 10% away from the original price.
Expressing as a percentage
Amy scores 18 out of 25 in a test. What is her score as a percentage?(2 marks)
Write it as a fraction.1825✓1
In plain English18 out of 25 is the fraction 18/25.
Make it out of 100.1825 = 72100 × 4 top and bottom= 72%✓2
In plain English25 × 4 = 100, so multiply the top by 4 as well. With a calculator: 18 ÷ 25 × 100.
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