How to simplify a ratio and solve proportions

Updated 2026-11-13

Quick answer

To simplify a ratio, divide both numbers by their greatest common divisor. For 12 : 18 that divisor is 6, so the ratio is 2 : 3. To find a missing number in A : B = C : D, use D = C × B ÷ A, which gives 15 when C is 10.

Steps

Write the ratio, for example 12 : 18.
Find the greatest number that divides both exactly. For 12 and 18 it is 6.
Divide both by it: 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so the ratio is 2 : 3.
To solve 12 : 18 = 10 : D, cross-multiply: D = 10 × 18 ÷ 12 = 15.
Or enter A, B and C in the ratio calculator and read the simplest ratio and D.

More examples, including decimals

The ratio 3 : 4 is already in its simplest form, and 3 : 4 = 15 : D gives D = 15 × 4 ÷ 3 = 20. A ratio with decimals, such as 2.5 : 10, is simplified by scaling to whole numbers first: it is 1 : 4. Then 2.5 : 10 = 4 : D gives D = 16.

A ratio can also be written as a decimal. 12 : 18 is 12 ÷ 18 = 0.6667, which is the same as 2 : 3.

Splitting an amount in a ratio

To share ₹500 in the ratio 2 : 3, add the parts, 2 + 3 = 5, divide the total by that sum, 500 ÷ 5 = 100, and multiply by each part. One person gets ₹200 and the other gets ₹300. The same method works for dividing profits, ingredients or costs between people.

Scaling a recipe or a map

A ratio keeps its meaning when both sides are multiplied or divided by the same number. If a recipe uses flour and sugar in the ratio 3 : 1 and you want 15 parts of flour, you need 5 parts of sugar. On a map, a scale of 1 : 50,000 means 1 cm on the map is 50,000 cm, or 500 m, on the ground.

Common questions

What is a ratio?

A comparison of two quantities, written A : B, such as 2 : 3.

What is a proportion?

A statement that two ratios are equal, such as 12 : 18 = 10 : 15.

How do I cross-multiply?

In A : B = C : D, A × D = B × C. Solve for the missing number by dividing.

Can ratios have more than two parts?

Yes, such as 2 : 3 : 5. Add all the parts to split an amount between them.