In short: To simplify a ratio, divide every part by the same number until they share no common factor bigger than 1. The quickest way is to find the highest common factor of the parts and divide by it once. For 18:24 the highest common factor is 6, so the ratio simplifies to 3:4.
Knowing how to simplify a ratio is a key GCSE Foundation skill, used in recipes, scale drawings, mixing quantities and sharing problems. Simplifying makes a ratio easier to read and compare, in the same way you simplify a fraction. This guide shows the reliable method using the highest common factor, with a worked example you can follow step by step.
The reliable method
A ratio is in its simplest form when the parts have no common factor other than 1.
- Check the parts are in the same units. If one part is in centimetres and another in metres, convert first so they match.
- Find a number that divides into every part. The most efficient choice is the highest common factor, the biggest number that goes into all the parts exactly.
- Divide each part by that number. Whatever you divide one part by, you must divide every part by.
- Check the result. If the new parts still share a common factor, divide again until they do not.
- Write the simplified ratio using the colon, keeping the parts in the original order.
If finding the highest common factor feels hard, you can divide by small numbers in steps, such as dividing by 2, then by 3, until nothing else divides in.
A worked example
Simplify the ratio 18:24 to its simplest form.
Both numbers are whole and in the same units, so we look for a common factor.
Find the highest common factor of 18 and 24:
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- The largest number in both lists is 6.
Divide each part by 6:
- 18 ÷ 6 = 3
- 24 ÷ 6 = 4
So 18:24 simplifies to 3:4. The parts 3 and 4 share no common factor other than 1, so this is fully simplified.
This works because dividing every part by the same number keeps the proportion identical — three parts to four parts is the same relationship as eighteen to twenty-four, just written with smaller, tidier numbers.
Common mistakes to avoid
- Trap: dividing only one part of the ratio. Halving the 18 but not the 24. Fix: whatever you do to one part, do to every part.
- Trap: stopping before it is fully simplified. Dividing 18:24 by 2 to get 9:12 and stopping. Fix: check whether the new parts still share a factor; 9 and 12 both divide by 3.
- Trap: changing the order of the parts. Writing 4:3 instead of 3:4. Fix: keep the parts in the same order as the question.
- Trap: adding instead of scaling. Treating a ratio as a difference rather than a multiplying relationship. Fix: see [ratio additive vs multiplicative explained](/misconceptions/ratio-additive-vs-multiplicative).
Frequently asked questions
How do you simplify a ratio to its simplest form? Divide every part of the ratio by the same number until the parts share no common factor other than 1. The fastest way is to divide by the highest common factor of the parts. For 18:24 the highest common factor is 6, giving 3:4.
What is 10:15 in its simplest form? The highest common factor of 10 and 15 is 5. Dividing both parts by 5 gives 2:3, which is fully simplified because 2 and 3 share no common factor other than 1.
How do you simplify a ratio with three parts? The same way as two parts: find a number that divides into all three, then divide each part by it. For 6:9:12, the highest common factor is 3, so it simplifies to 2:3:4.
Can you simplify a ratio with different units? Not until the units match. Convert everything to the same unit first. For 50 cm to 2 m, change 2 m into 200 cm, giving 50:200, which then simplifies to 1:4.
Is simplifying a ratio the same as simplifying a fraction? The idea is the same — divide all parts by a common factor — but a ratio compares parts to each other, while a fraction compares a part to a whole. Keep the colon notation for ratios.
Practise this
Find out which mistakes cost marks — [take the free diagnostic](/diagnostic). Related: [ratio additive vs multiplicative explained](/misconceptions/ratio-additive-vs-multiplicative).