How to Simplify Ratios and Solve Proportions (Recipes, Maps and Scaling)

A ratio compares two quantities. A proportion says two ratios are equal. Both appear in recipes, maps, mixing paint and sharing money.

Quick answer

• To simplify a ratio, divide every part by their greatest common factor: 12 : 18 = 2 : 3.
• To solve a proportion a : b = c : x, use x = (b × c) ÷ a.

Simplifying

12 : 18 → the GCF is 6 → 2 : 3. As percentages: 2 ÷ 5 = 40 percent and 3 ÷ 5 = 60 percent.

Solving a proportion

If 3 cups of rice serve 5 people, how many cups for 12 people?

3 : 5 = x : 12 → x = 3 × 12 ÷ 5 = 7.2 cups.

Examples

• Maps: a scale of 1 : 50,000 means 1 cm on the map is 500 m on the ground.
• Mixing: a 1 : 4 concentrate to water ratio means 250 ml of concentrate in 1 litre of mix (one part in five).
• Sharing money: divide 90,000 in the ratio 2 : 3 → 36,000 and 54,000.

Steps

1. Choose Simplify or Solve.
2. Enter the numbers.
3. Read the result and percentages.

Common mistakes

• Using different units in the same ratio (cm and m).
• Forgetting that a ratio of 1 : 4 has 5 parts in total.
• Mixing up the order: a : b is not b : a.