Fiducia TogetherPercentages
Parts per hundred: increases, decreases, reverse percentages and compound change.
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.
What it is
A percentage is a fraction out of 100. Percentage change is the change divided by the original, times 100.
Where it applies
Both tiers, and in business, science and everyday life.
How it works
A multiplier is the efficient method: a 15% increase is × 1.15, a 15% decrease is × 0.85. Repeated change compounds — three years at 5% is × 1.05³, not × 1.15.
A reverse percentage works backwards from the new value: divide by the multiplier, do not subtract the percentage.
How to use it in your work
The reverse percentage is the most commonly failed question on the paper. If a price is £60 after a 20% discount, the original is 60 ÷ 0.8 = £75, not £72.
Always divide by the ORIGINAL when finding percentage change.
Where to get help
Your teacher, your board's specification for what is on your paper, and Bitesize for worked examples. The maths song runs the topics in order.
Revise this with a song
These are ours. We write revision songs because a lot of people remember a tune when they cannot remember a page, and because revising out loud in the kitchen beats staring at a highlighter.
- The Maths Song The GCSE maths topics, in order.
Where to read more
Last reviewed 2026-08-28 by Fiducia Together · Next review due 2027-08-28
Please note: This page explains a word or a process in education. It is general information about the system, the law and the guidance in England — not advice about your child, your school or your exam. If a decision is going against you, get advice from one of the free services we link to before you agree to anything or miss a deadline. If you are revising, check your own exam board's specification: boards word things differently and yours is the one that marks you.