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Guide

How to Simplify and Solve Ratios

Understand what a ratio is, how to simplify one, and how to solve a proportion for a missing value.

Open the Ratio Calculator

A ratio compares two or more quantities. A ratio calculator simplifies a ratio to its lowest terms or solves a proportion (a : b = c : d) for a missing value.

What a ratio is

A ratio expresses the relative size of two quantities, written as a : b and read "a to b". A 2 : 3 ratio of boys to girls means for every 2 boys there are 3 girls. Ratios can be scaled: 2 : 3, 4 : 6, and 10 : 15 all represent the same relationship.

Simplifying a ratio

To simplify, divide both sides by their greatest common divisor (GCD). The ratio 12 : 18 has a GCD of 6, so it simplifies to 2 : 3. Simplified ratios are easier to compare and understand.

Solving a proportion

If a : b = c : d, then a × d = b × c

Given three values, solve for the fourth. If 3 : 4 = 9 : d, then 3 × d = 4 × 9, so d = 36 ÷ 3 = 12.

How to use the calculator

  1. To simplify: enter two numbers and read the reduced ratio.
  2. To solve a proportion: enter three of the four values and read the missing one.
  3. Check whether two ratios are equivalent by simplifying both and comparing.

Examples

A recipe for 4 uses 200g of flour; scaling to 6 people sets the proportion 4 : 200 = 6 : d, giving d = 300g. A map scale of 1 : 25,000 means 1cm on the map equals 25,000cm (250m) on the ground.

When a ratio calculator is useful

  • Scaling recipes, maps, and models.
  • Mixing ingredients, paint, or chemicals in set proportions.
  • Comparing financial or statistical figures.
  • Solving classroom ratio and proportion problems.

Put it into practice

Use the Ratio Calculator right now — free, in your browser, no sign-up required.

Try the Ratio Calculator

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