Appears in: Functional Skills Level 1 · Functional Skills Level 2 · GCSE foundation
How to work out percentages
Percentages are on every Functional Skills and GCSE foundation paper, usually several times, and they're the topic most resit learners have never quite fixed. There are two things you need to be able to do: find a percentage of an amount, and write one number as a percentage of another. Both come down to a couple of moves.
Two methods for a percentage of an amount
- The 10% method (no calculator): 10% is the amount divided by 10. 1% is the amount divided by 100. 5% is half of 10%. Build the percentage you need from those pieces and add them up.
- The multiplier method (calculator): turn the percentage into a decimal by dividing by 100, then multiply. 35% of something is that something × 0.35.
- To write one number as a percentage of another: divide the part by the whole, then multiply by 100. The whole is whatever the question says 'out of'.
Worked examples
Example 1
Work out 35% of £240 without a calculator.
- 10% of £240 = £24.
- 30% = 3 × £24 = £72.
- 5% = half of £24 = £12.
- 35% = £72 + £12 = £84.
Example 2
Work out 17.5% of 80 kg.
- 10% of 80 = 8. 5% = 4. 2.5% = 2.
- 17.5% = 8 + 4 + 2 = 14 kg.
- Check with the multiplier: 80 × 0.175 = 14.
Example 3
A learner scores 45 out of 60 on a test. What is that as a percentage?
- Part ÷ whole: 45 ÷ 60 = 0.75.
- × 100: 0.75 × 100 = 75%.
Where the marks go missing
- Dividing the wrong way round when writing a score as a percentage: it's always part ÷ whole, so 45 ÷ 60, not 60 ÷ 45.
- Turning 5% into 0.5 instead of 0.05. Divide by 100, so move the decimal point two places.
- Forgetting that 'of' means multiply. 20% of 50 is 0.2 × 50, not 50 ÷ 20.
Frequently asked questions
How do I work out a percentage without a calculator?
Find 10% by dividing by 10, 1% by dividing by 100 and 5% by halving 10%, then add the pieces you need. 35% is three lots of 10% plus one 5%.
How do I work out what percentage one number is of another?
Divide the first number by the second and multiply by 100. 18 out of 24 is 18 ÷ 24 = 0.75, so 75%.