Ratio and proportion explained

Ratio vs proportion

A ratio compares two amounts, such as 3 : 4. A proportion is a statement that two ratios are equal, such as 3 : 4 = 9 : 12. Proportions are how we scale recipes, convert maps and work out prices.

How to solve a proportion

Write the proportion as two fractions, then cross-multiply. If A : B = C : D then A × D = B × C.

1. Write what you know as A : B = C : D, putting a letter such as x where the number is missing.
2. Multiply across the diagonals.
3. Divide to get the missing number by itself.
4. Check that both ratios simplify to the same thing.

Example 1: a recipe

Example 2: a map

Direct and inverse proportion

In a direct proportion, both amounts grow together: twice the flour needs twice the milk. In an inverse proportion, one grows while the other shrinks: twice as many workers finish the same job in half the time. The cross-multiplication method above is for direct proportions.

Common mistakes

• Putting the numbers in a different order on each side. If milk is on the bottom on the left, it must be on the bottom on the right.
• Mixing units between the two ratios.
• Forgetting to divide after cross-multiplying.

To check your work, use the proportion calculator, which shows every step. Or confirm two ratios match with the compare ratios calculator.

Frequently asked questions