How do you simplify a ratio?
Find the largest number that divides every part exactly, and divide them all by it.
The working
12 : 16 Largest number dividing both: 4 12 ÷ 4 = 3, 16 ÷ 4 = 4 → 3 : 4
It works the same with three parts. 10:20:30 all divide by 10, giving 1:2:3. If no number above 1 divides them all, the ratio is already in its simplest form — 7:13 cannot be reduced.
What about decimals?
Multiply every part by 10, or 100, until they are whole numbers, then reduce as normal. A decimal ratio is perfectly ordinary and most calculators handle it badly.
The working
1.5 : 2 Multiply through by 10 → 15 : 20 Both divide by 5 → 3 : 4
How do you share an amount in a ratio?
- Add the parts to get the total number of sharesFor 2:3 that is 5 shares. This is the step people skip, and skipping it is why the answer comes out wrong.
- Divide the amount by the total shares£500 ÷ 5 = £100. That is what one share is worth.
- Multiply each part by the share value2 × £100 = £200 and 3 × £100 = £300. Every part gets multiplied, not just the one you care about — that is what keeps the proportions right.
- Check they add back up£200 + £300 = £500. If they do not, something went wrong at step one.
Splitting £100 three ways gives £33.33 each with a penny left over. The arithmetic is exact; real money is not divisible below a penny, so somebody has to take the odd one.
Finding a missing part
When two ratios are equal — a proportion — the diagonals multiply to the same thing. That lets you find any one of the four from the other three.
The working
3 : 4 = 9 : ? Cross-multiply: 3 × ? = 4 × 9 3 × ? = 36 ? = 12
This is the sum behind scaling a recipe, enlarging a drawing, or mixing anything to a specification.
Common questions
Does 2:3 mean two out of three?
No, and this is the misreading that catches most people. 2:3 means two parts to three parts — five parts in total, so two out of five, or 40%. "Two out of three" written as a ratio is 2:1.
How do I turn a ratio into a fraction?
For a two-part ratio a:b, the first part as a fraction of the whole is a/(a+b). So 3:4 is 3/7 of the total, not 3/4. The 3/4 figure is the ratio of one part to the other, which is a different question — it is also what you get if you divide 3 by 4 to express the ratio as the decimal 0.75.
Does the order matter?
Yes. A ratio is not a set — 2:3 and 3:2 are different answers, and swapping them swaps who gets more. Keep the order the question gave you.
Can a ratio have units?
The parts must be measured the same way, and the ratio itself then has no units. Two litres to three millilitres is not 2:3 — convert to the same unit first, and it turns out to be 2000:3.
Check this before you rely on it. A free guide to everyday arithmetic — not tax, accounting, financial, legal or medical advice. The working is shown above so you can verify it against your own figures. See our terms of use.