How to work out a ratio — explanation and examples

How do you work out a ratio?

A ratio compares two quantities and says "for every so-many of the first there are so-many of the second". Like a fraction, a ratio can be simplified — 12 : 18 is exactly 2 : 3. Once that idea is clear, all the familiar questions open up: sharing an amount in a ratio, recipes, and the scale on a map.

The rule

Ratio a : b — for every a of the first kind there are b of the second · Simplify like a fraction

The ratio 2 : 3 — for every 2 purple circles there are 3 white ones. 4 : 6 and 12 : 18 both simplify to exactly the same ratio.

Worked examples, step by step

Finding and simplifying a ratio

A class has 12 boys and 18 girls. What is the ratio of boys to girls?

Write the ratio in the order the question gives: 12 : 18
Look for the highest common factor: 6
Simplify: 12 ÷ 6 = 2 and 18 ÷ 6 = 3
Answer: the ratio is 2 : 3 — for every 2 boys there are 3 girls

Sharing an amount in a ratio

Ronnie and Omar share £45 in the ratio 2 : 3. How much does each get?

Add the parts of the ratio: 2 + 3 = 5 parts
Work out what one part is worth: £45 ÷ 5 = £9
Ronnie: 2 × 9 = £18, and Omar: 3 × 9 = £27
Check: 18 + 27 = 45 — it all divides up exactly

A ratio in a recipe

A recipe uses 2 cups of flour for every 3 spoons of sugar. How many spoons of sugar are needed for 6 cups of flour?

Find how many times the flour has grown: 6 ÷ 2 = 3 (three times)
To keep the ratio, the sugar grows three times too
Calculate: 3 × 3 = 9
Answer: 9 spoons of sugar are needed

The scale of a map

A map has a scale of 1 : 50 000. The distance between two villages on the map is 4 cm. What is the real distance?

A scale of 1 : 50 000 means every 1 cm on the map is 50 000 cm in real life
Multiply: 4 × 50 000 = 200 000 cm
Convert to a sensible unit: 200 000 cm = 2000 m = 2 km
Answer: the real distance is 2 kilometres

Now try it yourself

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Ratio calculator

Simplify a ratio or share an amount — with the working shown at each step.

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Learn ratio and proportion

Ratio, fractions and proportion are close relatives — the full foundation is here.

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How to calculate percentages

The natural next step after ratio — the complete guide to percentages.

Frequently asked questions

What is the difference between a ratio and a fraction?

A fraction shows a part of a whole; a ratio compares two parts. If the ratio of boys to girls is 2 : 3, then the boys are 2 out of 5 — two fifths of the class, not two thirds.

How do you simplify a ratio?

Exactly like a fraction: divide both sides by the same number. 12 : 18 divided by 6 gives 2 : 3. A ratio in its simplest form has two sides with no common factor bigger than 1.

Does the order in a ratio matter?

Very much. A boys : girls ratio of 2 : 3 means there are more girls; 3 : 2 means exactly the opposite. Always read the ratio in the order of the quantities in the question.

What is a proportion?

An equality between two ratios — for example 2 : 3 = 8 : 12. In a proportion the product of the means equals the product of the extremes (3 × 8 = 2 × 12 = 24), and that is the quick way to find a missing quantity.

✍️ Written by the MathsUK teamChecked against the National Curriculum and GCSE specificationsLast updated: 13.09.2026