Ratio & Proportion: Complete Guide
Ratio and proportion appear all over GCSE Maths, from recipes to best-buy problems. Learn to simplify ratios, share amounts and work with direct and inverse proportion.
Simplifying ratios
Divide all parts of a ratio by their highest common factor, just like simplifying a fraction.
Simplify 12 : 18
Sharing in a ratio
Share £40 in the ratio 3 : 5
Direct and inverse proportion
Direct proportion: as one quantity increases, the other increases at the same rate (y = kx). Double one, double the other.
Inverse proportion: as one increases, the other decreases (y = k ÷ x). For example, more workers means less time for a fixed job.
- Forgetting to add the ratio parts before dividing
- Mixing up the order of the ratio
- Treating inverse proportion as if it were direct
Frequently asked questions
How do I simplify a ratio?
Divide every part of the ratio by their highest common factor, the same way you simplify a fraction.
How do I share an amount in a ratio?
Add the ratio parts to get the total number of parts, divide the amount by that total to find one part, then multiply by each part of the ratio.
What is the difference between direct and inverse proportion?
In direct proportion both quantities increase together (y = kx). In inverse proportion one increases as the other decreases (y = k/x).
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