Fiducia TogetherRatio and proportion
Comparing quantities, sharing amounts, and quantities that vary together.
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 ratio compares parts, written 3:2. Direct proportion means one quantity rises as another does at a constant rate; inverse proportion means one rises as the other falls.
Where it applies
Both tiers, and one of the largest sources of marks on a GCSE paper.
How it works
Ratio problems usually reduce to finding the value of one part. Direct proportion is y = kx; inverse is y = k/x, and the exam skill is finding k first from given values.
Compound measures — speed, density, pressure, rates of pay — are proportion in disguise.
How to use it in your work
Ratio questions are heavily worded, so write down what one part is worth before doing anything else.
Watch whether a ratio is part-to-part or part-to-whole. 3:2 means five parts, not three.
For "best buy" questions, get both options to the same unit before comparing.
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.