Ratios and Proportion

Understand ratios from scratch — what they mean, how to simplify them, how to share amounts in a ratio, and how to scale recipes. With real-life examples.

A ratio is just a way of comparing amounts. Think of a recipe: 2 parts flour to 1 part water. That's a ratio of 2:1.

What Is a Ratio?

If you mix orange squash with water in the ratio 1:4, that means for every 1 cup of squash, you add 4 cups of water. 5 cups total.

The order matters! 1:4 is NOT the same as 4:1.

Simplifying Ratios

Just like fractions — divide all parts by the same number.

Example: 12:8 → both divide by 4 → 3:2.

Sharing in a Ratio

This comes up all the time in exams: "Split £60 in the ratio 2:3."

Direct Proportion

If 3 pens cost £4.50, how much do 7 pens cost?

Scaling Recipes

A cake recipe for 8 people uses 200g flour, 100g sugar, 3 eggs. You want it for 12 people. The scale factor is 12 ÷ 8 = 1.5.

Map Scales

A map scale of 1:25,000 means 1 cm on the map = 25,000 cm in real life = 250 metres. So if two towns are 8 cm apart on the map, the real distance is 8 × 250 = 2,000 metres = 2 km.