Ratio, proportion and rates of change is one of the main content areas of the GCSE Maths specification, and on Foundation tier it makes up a noticeably larger share of the marks than on Higher. Yet many students only revise ratio as 'sharing in a ratio' and are then surprised when it appears inside a question about recipes, exchange rates, similar shapes, speed or probability. This guide covers every type of ratio and proportion question you are likely to meet on Edexcel, AQA or OCR, the methods that work reliably, and the traps examiners set.
What a ratio actually tells you
A ratio compares quantities. If the ratio of boys to girls in a class is 2 : 3, then for every 2 boys there are 3 girls. That means there are 5 parts in total, boys make up 2/5 of the class and girls make up 3/5. Being able to move freely between ratios and fractions is the single most important skill in this topic, because Higher-tier questions very often give information as a fraction and expect you to turn it into a ratio, or the other way round.
Simplifying ratios
Simplify a ratio by dividing every part by the highest common factor, exactly as you would with a fraction. Before simplifying, make sure the units match: the ratio 50 cm : 2 m is 50 : 200, which simplifies to 1 : 4, not 25 : 1. You may also be asked to write a ratio in the form 1 : n, which means dividing both sides by the first number, even if n is a decimal. For example, 4 : 10 becomes 1 : 2.5.
Sharing an amount in a given ratio
This is the classic ratio question and it follows the same three steps every time.
- Add the parts of the ratio to find the total number of parts.
- Divide the amount by the total number of parts to find the value of one part.
- Multiply the value of one part by each number in the ratio.
For example, share £360 in the ratio 2 : 3 : 4. There are 9 parts, so one part is £40, and the shares are £80, £120 and £160. Always check that your shares add back up to the original total — it takes five seconds and catches most arithmetic slips.
When you are given the difference, not the total
Higher-tier and harder Foundation questions often give you something other than the total. 'Amir and Beth share sweets in the ratio 3 : 7. Beth gets 24 more than Amir. How many sweets are there?' Here the difference between the shares is 7 − 3 = 4 parts, and those 4 parts are worth 24, so one part is 6 and the total of 10 parts is 60. The same method — work out how many parts the given information represents — solves almost every variation.
A bar model is extremely helpful here. Draw a bar for each person split into equal boxes, label what you know, and the answer usually becomes obvious. Many of my students who 'cannot do ratio' find the topic straightforward as soon as they start drawing bars.
Combining two ratios
A common Higher-tier question gives two ratios with a shared quantity, such as a : b = 2 : 3 and b : c = 4 : 5, and asks for a : b : c. The trick is to make the shared quantity the same in both ratios. Here b is 3 in one and 4 in the other, so scale to make b equal to 12: a : b = 8 : 12 and b : c = 12 : 15, giving a : b : c = 8 : 12 : 15.
Direct proportion
Two quantities are in direct proportion when they increase at the same rate — double one, and the other doubles. Recipes, unit pricing and currency conversion are all direct proportion. The safest method is the unitary method: find the value of one unit, then multiply.
A recipe for 6 people uses 450 g of flour. How much is needed for 10 people? One person needs 450 ÷ 6 = 75 g, so 10 people need 750 g. If the numbers are awkward, you can also use a multiplier: 10/6 of 450 is 750 g.
Best buy questions
Best buy questions compare two or more offers. Calculate the cost per gram (or the grams per penny) for each option, keep the same unit throughout, and state clearly which is the better value. A final answer that just says 'the big one' without showing the comparison will not earn full marks — the working and a clear conclusion are both required.
Inverse proportion
Two quantities are in inverse proportion when one increases as the other decreases at the same rate — double one, and the other halves. The classic example is workers and time: if 4 builders take 6 days to build a wall, the total job is 4 × 6 = 24 builder-days. So 3 builders would take 24 ÷ 3 = 8 days. The key step is finding that total, which stays constant.
Algebraic proportion (Higher tier)
On Higher tier you need to express proportion algebraically. 'y is directly proportional to x' becomes y = kx. 'y is inversely proportional to the square of x' becomes y = k/x². The method is always the same.
- Write the proportion statement as an equation with a constant k.
- Substitute the given pair of values to find k.
- Rewrite the equation with the value of k.
- Use the equation to answer the question.
For example, y is directly proportional to the square root of x, and y = 12 when x = 9. Then y = k√x, so 12 = 3k and k = 4, giving y = 4√x. When x = 25, y = 20. You should also be able to recognise the shapes of proportion graphs: direct proportion is a straight line through the origin, and inverse proportion is a curve that approaches both axes without touching them.
Where ratio hides in other topics
Examiners like to test ratio indirectly, and these are the places it most often appears.
| Topic | How ratio appears |
|---|---|
| Similar shapes | Scale factors for length, area (squared) and volume (cubed) |
| Probability | Outcomes given as a ratio that must be converted to fractions |
| Speed, density, pressure | Compound measures are rates — a form of proportion |
| Maps and scale drawings | Scales such as 1 : 25 000 with unit conversions |
| Percentages | Percentage change as a multiplier, closely linked to proportion |
| Angles | Angles in a triangle or on a line given in a ratio, then shared from 180° or 360° |
The similar shapes link is worth extra attention on Higher tier. If the length scale factor is 3, the area scale factor is 9 and the volume scale factor is 27. Students who apply the length scale factor to an area or a volume lose every mark on the question.
Exam technique for ratio questions
- Write the total number of parts and the value of one part as separate, labelled lines — method marks are given for these steps.
- Check units before you start and convert so they match.
- Read whether the question wants one share, all the shares, the total or a difference.
- Use a bar model whenever you are unsure what the given information represents.
- Sense-check direct and inverse proportion answers before moving on.
- In best buy questions, compare like with like and write a clear concluding sentence.
How to revise ratio and proportion
Because ratio appears in so many contexts, mixed practice matters more than usual. Spend a session on each of the core skills — sharing, given difference, combining ratios, direct and inverse proportion and algebraic proportion — then move to mixed past paper questions where you are not told the topic in advance. That second stage is where real exam readiness comes from.
MathVault offers free GCSE practice organised by topic, which is ideal for the first stage. MathVault Premium adds full worked solutions and exam-style question sets, so you can check every step of your method rather than just the final answer.
Getting help with ratio and proportion
If ratio questions still feel like guesswork, the gap is often in fractions, multiplication or the meaning of 'parts' — skills from Key Stage 3 that were never fully secure. In one-to-one lessons I find exactly where the understanding breaks down and rebuild it, rather than repeating the same type of question. I am a QTS fully qualified teacher and Deputy Head of Maths, with over seven years of tutoring experience, and I teach GCSE students online and in London.
The short version
- Know the difference between part-to-part and part-to-whole.
- For sharing: total parts, value of one part, multiply.
- For differences: work out how many parts the given amount represents.
- Use the unitary method for direct proportion and a constant total for inverse proportion.
- On Higher, write proportion with k, find k, then use the equation.
- Expect ratio to appear inside similar shapes, probability and compound measures.