Proportion
Two quantities are in direct proportion when one increases at the same rate as the other, so their ratio stays constant.
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Play with the controls to see the idea in action.
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Two quantities are in direct proportion when one increases at the same rate as the other, so their ratio stays constant.
- Direct proportion gives a straight line through the origin
- Inverse proportion means one rises as the other falls
- Use unit values to solve problems
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Proportion?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Proportion. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Proportion in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Proportion gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Proportion in detail
Two quantities are in direct proportion when they increase or decrease at the same rate, so doubling one doubles the other and their ratio stays constant. If 3 notebooks cost £6, then 9 notebooks cost £18. The unitary method, finding the value of one item first, solves many such problems.
In inverse proportion, one quantity increases as the other decreases so that their product stays constant: if 4 workers take 6 days, 8 workers take 3 days. Recognising which kind applies, and writing it as y = kx or y = k/x, is the key skill in proportion questions.
How the interactive helps you understand Proportion
Move the slope and y-intercept sliders. The line and its equation update, so you can see how the slope sets the steepness and the intercept sets where the line crosses the y-axis.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Proportion.
Real-life uses and examples
- Explain Proportion to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Proportion in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Proportion by estimating first, then working it out step by step.
Common mistakes to avoid
- Memorising the steps for Proportion without checking why they work.
- Forgetting units, signs or brackets when you apply Proportion.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Proportion
What is Proportion?
Two quantities are in direct proportion when one increases at the same rate as the other, so their ratio stays constant.
What are the most important points about Proportion?
The main points are: Direct proportion gives a straight line through the origin; Inverse proportion means one rises as the other falls; Use unit values to solve problems.
Why is Proportion useful?
Understanding Proportion gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Proportion?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Proportion?
Related topics in Mathematics include Laws of Indices, Standard Form, Significant Figures.