GCSE Maths · Maths
Percentages: a clear study guide
Percentages describe parts of a whole or changes relative to an original amount. Decide whether the question asks for a percentage of a value, a change, or the original value before choosing a multiplier.
Multipliers
An increase of p percent uses the multiplier 1 + p/100. A decrease of p percent uses 1 - p/100. Multiply the original amount by the multiplier and keep the units in the final answer.
For example, a 15 percent increase uses 1.15, while a 15 percent decrease uses 0.85.
- 10 percent = 0.10 as a decimal.
- Increase by 25 percent: multiply by 1.25.
- Decrease by 25 percent: multiply by 0.75.
Reverse percentages
If a final value is known after a percentage change, divide by the multiplier to find the original. Do not subtract the percentage from the final value, because the percentage was calculated from the original amount.
For repeated changes, apply each multiplier in sequence. A 10 percent increase followed by a 10 percent decrease does not return to the starting value.
Check the context
Estimate the result before calculating. A discount should reduce the price, a growth multiplier should be greater than one and a probability or proportion should stay within the range the question allows.
Quick check
What multiplier represents a 20 percent decrease?
Answer: 0.80.
How do you undo a 30 percent increase?
Answer: Divide the final amount by 1.30.
Common questions
Why is a 10 percent increase followed by a 10 percent decrease not the original value?
The second 10 percent is calculated from the increased amount, so the two multipliers are 1.10 and 0.90, whose product is 0.99.
How do I find a percentage change?
Calculate the change, divide by the original amount and multiply by 100. State whether it is an increase or a decrease.