How to Simplify a Ratio

What a ratio is

A ratio compares two quantities, showing how much of one there is relative to the other. Written 2:3, it means two parts of the first to three of the second — a class with a 2:3 ratio of teachers to pupils, or a paint mix of 2 parts blue to 3 parts white. A ratio isn't tied to actual amounts, only the relationship: 2:3, 4:6 and 20:30 all describe the same proportion, which is exactly why simplifying is useful.

Simplifying by the GCD

Simplifying a ratio is like reducing a fraction: divide both numbers by their greatest common divisor. Take 12:18 — the largest number that divides both is 6, so dividing gives 2:3, the simplest form. If you spot a smaller common factor first, that's fine; just keep going. Halving 12:18 to 6:9, then dividing by 3 to 2:3, reaches the same place. You're done when no whole number divides both sides evenly.

Same units first

A ratio only makes sense when both sides are measured in the same unit, so convert before you simplify. Comparing 50 cm to 1 metre isn't 50:1 — turn the metre into 100 cm first, giving 50:100, which simplifies to 1:2. The same applies to minutes and hours, grams and kilograms, or any mixed units. Skip this step and the ratio is meaningless, no matter how neatly it reduces afterwards.

Comparing and scaling ratios

To compare two ratios, put them on common ground. One way is to turn each into a single number by dividing — 3:4 becomes 0.75, 5:8 becomes 0.625, so 3:4 is the larger proportion. Another is to scale both to share a value, like a common first term. Scaling is also how you use a ratio in practice: a 1:4 squash-to-water mix scaled up means 250 ml of squash to 1 litre of water. Keep the proportion fixed and you can grow or shrink any recipe or mixture.

Frequently asked questions

How do I simplify a ratio?

Divide both numbers by their greatest common divisor.

What is 12:18 simplified?

2:3.

How do I compare two ratios?

Scale them to a common value, or divide each into a single number.