A ratio compares amounts — how much of one thing there is for every amount of another. We write it with a colon. If squash is mixed 1 : 4, that's 1 part juice for every 4 parts water. Recipes, mixing paint, map scales and mortar for bricks all rely on ratios.
Why this matters: a ratio keeps a mixture right no matter how much you make. Get the squash ratio wrong and it tastes horrible; get concrete's ratio wrong and a wall crumbles. The same idea scales a recipe for 4 up to a party of 40 without ruining it.
Squash 1 : 4 — 1 part juice for every 4 parts water
Reading a ratio
In a class with boys : girls = 3 : 5, for every 3 boys there are 5 girls. It does not mean exactly 3 boys and 5 girls — it's the proportion. The class could be 6 : 10, 9 : 15, and so on.
The order matters: 3 : 5 (boys to girls) is not the same as 5 : 3. Always match each number to the word in front of it.
Ratio, fraction and "for every"
Ratio 3 : 5 has 8 parts total → boys are 3/8, girls 5/8.
A ratio is close cousins with fractions. In the ratio 3 : 5 there are 3 + 5 = 8 parts in total, so boys are 3/8 of the class and girls are 5/8. This table shows the link:
Ratio (boys : girls)
Total parts
Boys as a fraction
Girls as a fraction
1 : 1
2
1/2
1/2
1 : 4
5
1/5
4/5
3 : 5
8
3/8
5/8
Simplifying a ratio
Just like a fraction, divide every part by the same number (their highest common factor) to reach the simplest form.
10 : 15 → both divide by 5 → 2 : 3.
Divide every part by the same number (their HCF).
The same works for three-part ratios: 9 : 6 : 12 → divide all by 3 → 3 : 2 : 4. Every part must be divided by the same number.
Same units first
Convert to one unit first, then simplify: 40p : 100p = 2 : 5.
Common mistake — mismatched units! To simplify 40p : £1 you must first make the units match: change £1 to 100p, giving 40p : 100p, then divide by 20 → 2 : 5. You can't compare pence with pounds, or centimetres with metres, directly — convert to one unit before simplifying.
Equivalent ratios
Multiplying or dividing every part by the same number gives an equivalent ratio — the proportion is unchanged: 2 : 3 = 4 : 6 = 20 : 30. This is how you fill in a missing value: to complete 3 : 5 = 9 : ?, notice 3 × 3 = 9, so the other part is 5 × 3 = 15.
In a nutshell: a ratio shows "for every", written a : b, and the order matters. Put both parts in the same unit, then simplify by dividing every part by a common factor — exactly like a fraction.