How to Simplify a Ratio

Simplifying a ratio works just like simplifying a fraction: divide both terms by their greatest common divisor. For example, 12:18 simplifies to 2:3, because the GCD of 12 and 18 is 6. The simplified ratio means the same thing as the original — it's just written in the cleanest possible whole numbers. You can simplify any ratio instantly with our free ratio calculator.

Divide both terms by the GCD

Find the largest number that divides both terms evenly, then divide each term by it. With 12:18, the GCD is 6, so 12 / 6 = 2 and 18 / 6 = 3, giving 2:3. If you don't spot the biggest factor at once, divide by any shared factor and repeat: 12:18 to 6:9 to 2:3 lands in the same place.

Equivalent ratios and scaling

A ratio describes a relationship, so you can scale it up or down and it stays equivalent. The ratio 2:3 is the same as all of these:

4:6 (multiply both terms by 2)
6:9 (multiply both terms by 3)
20:30 (multiply both terms by 10)

Each one reduces back to 2:3, which is exactly why simplifying is so useful — it gives every equivalent ratio one shared, recognizable form.

COSMIQ — Demo — Smart board lesson

Ratios with three or more parts

The same rule extends to longer ratios. For 4:6:8, the GCD of all three terms is 2, so divide each by 2 to get 2:3:4. Just make sure the common divisor you pick divides every term in the ratio, not only two of them.

Where ratios show up

Ratios appear in recipes, maps, model scales, mixing paint, and comparing quantities of almost any kind. If a recipe uses a 2:3 ratio of sugar to flour and you double it, you get 4:6 — still the same recipe, just bigger. Scaling cleanly is far easier when you start from the simplified ratio.

COSMIQ — Demo — Mini mock test

Simplify and scale with confidence

When you want a quick, correct answer, run your numbers through the ratio calculator, and since ratios and fractions are close cousins, the fraction calculator is handy too. To talk through a tricky scaling problem, COSMIQ's free voice tutor is free for every learner.

Related resources: ratio calculator · fraction calculator · free voice tutor