In short: To work out a percentage increase, turn the percentage into a multiplier and multiply the original amount by it. For a 15% increase the multiplier is 1.15; for a 15% decrease it is 0.85. Multiply once and you have the new amount in a single step.
Learning how to work out a percentage increase is essential for GCSE Foundation maths, because it appears in pay rises, price changes, interest and population questions. The quickest and most reliable approach is the multiplier method, which handles both increases and decreases with a single multiplication. This guide shows you the method step by step, with a worked example you can copy.
The reliable method
The multiplier method treats the original amount as 100% and adjusts from there.
- Start from 100%, which is the whole original amount. As a decimal, 100% is 1.
- For an increase, add the percentage on. A 15% increase means 100% + 15% = 115%, and 115% as a decimal multiplier is 1.15.
- For a decrease, take the percentage off. A 15% decrease means 100% − 15% = 85%, which gives a multiplier of 0.85.
- Multiply the original amount by the multiplier. This gives the new amount directly, with no separate adding step.
- Write the answer with the correct units.
To turn any percentage into a decimal multiplier, write the new total percentage and divide by 100. So 115% becomes 1.15 and 85% becomes 0.85.
A worked example
A monthly bus pass costs £40. The price goes up by 15%. What is the new price of the pass?
This is a 15% increase, so we use a multiplier.
Find the multiplier:
- An increase of 15% means the new price is 100% + 15% = 115% of the old price.
- 115% as a decimal is 115 ÷ 100 = 1.15.
Now multiply the original amount:
- New price = £40 × 1.15 = £46
So the new bus pass costs £46. (Check using building blocks: 10% of £40 is £4 and 5% is £2, so the increase is £6, and £40 + £6 = £46, which matches.)
This works because multiplying by 1.15 keeps the whole original amount (the "1") and adds the extra 15% (the "0.15") in the same step, so you never have to add the increase on separately.
Common mistakes to avoid
- Trap: multiplying by the percentage instead of the multiplier. Using 0.15 rather than 1.15, which gives only the increase, not the new total. Fix: for an increase, the multiplier is always bigger than 1.
- Trap: forgetting to add the increase back on. If you do find 15% separately, remember to add it to the original. Fix: the multiplier method avoids this by doing it in one step.
- Trap: using the wrong multiplier for a decrease. Subtracting from 100% incorrectly, such as writing 0.15 instead of 0.85. Fix: decrease multiplier = (100 − percentage) ÷ 100.
- Trap: chaining several changes by adding the percentages. Two 10% rises is not the same as one 20% rise, and reverse-percentage questions need a different approach. Fix: for multi-stage or reverse problems, see [percentage change explained](/misconceptions/percent-change-family).
Frequently asked questions
How do you calculate a percentage increase step by step? First add the percentage to 100 to get the new total percentage, for example 100 + 15 = 115. Divide by 100 to get the multiplier, so 115 becomes 1.15. Then multiply the original amount by 1.15 to get the increased amount in one step.
What is the multiplier for a 15% increase? It is 1.15. You start from 1, which represents the whole original amount, then add 0.15 for the extra 15%. Multiplying by 1.15 increases any number by 15%.
How do you work out a percentage decrease? Subtract the percentage from 100 and divide by 100 to get the multiplier. For a 20% decrease the multiplier is (100 − 20) ÷ 100 = 0.8. Multiply the original amount by 0.8; for example, £50 reduced by 20% is £50 × 0.8 = £40.
Why is the multiplier method better than finding the percentage first? It does the calculation in a single step, so there are fewer chances to make an error and nothing to add on afterwards. It is also the method examiners expect for harder questions like compound interest.
Does the multiplier method work without a calculator? Yes, although for awkward numbers it can be easier to find the percentage in chunks and add it on. For tidy values like £40 × 1.15, you can split it as £40 + (15% of £40) and reach the same answer.
Practise this
Find out which mistakes cost marks — [take the free diagnostic](/diagnostic). Related: [percentage change explained](/misconceptions/percent-change-family).