Chapter 1 · RatioYear 7 · FS Level 1

Writing and simplifying ratios

A ratio compares parts of a whole. 2 : 3 means for every 2 of the first, there are 3 of the second. The order matters.

Add the parts to find the whole. In 2 : 3 there are 5 parts, so the first is 25 of the whole and the second is 35.

So in the class of 30: 5 parts, 30 ÷ 5 = 6 in each part, and the girls are 3 × 6 = 18.

Chapter 2 · RatioYear 7–9 · FS Level 1–2 · GCSE

Sharing in a ratio

To share an amount in a ratio: add the parts, divide to find one part, then multiply.

Sometimes you are told the difference or one share instead of the total. Work out how many parts that amount is, then find one part.

Check: the shares should add up to the total and simplify back to the ratio.

Chapter 3 · ProportionYear 8 · FS Level 2

Scaling and best buys

Things in proportion scale by multiplying. A recipe for 4 people made for 6 needs everything × 64 = × 1.5.

The unitary method finds the amount for one first: for 4 people 300 g, for 1 person 75 g, for 6 people 450 g.

For a best buy, compare the price of the same amount, such as the cost per 100 g.

Chapter 4 · RatioGCSE Foundation and Higher

Ratios, fractions and combining

To write a ratio in the form 1 : n, divide both sides by the first number: 4 : 10 = 1 : 2.5.

To combine two ratios that share a quantity, make that quantity’s numbers match by multiplying up to their LCM.

Fractions and ratios swap easily: if 38 of a bag is red, red : not red = 3 : 5.

Chapter 5 · RatioAll levels

Ratio in one go

A checklist for any ratio question:

For recipes and best buys, multiply by the same number, or find the amount for one.