Leo+DadMade for Leo
Recognising & Simplifying Ratios
Rung 2 of 4 · The method

Simplifying a Ratio

Same idea as cancelling a fraction: divide both parts by the biggest number that goes into both. Let's make it automatic.


PractiseHit “new ratio”, simplify it, then check yourself.
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Simplifying a ratio means writing it with the smallest whole numbers that still describe the same mix. The whole job is two moves: find the highest common factor, then divide both parts by it.

The Two Moves

One — find the HCF. The highest common factor is the biggest number that divides both parts exactly. For 12 : 18, both divide by 6, and nothing bigger does, so the HCF is 6.

Two — divide both parts by it. 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so 12 : 18 = 2 : 3. You're finished when the two numbers share no factor bigger than 1.

A Worked One

Simplify 20 : 30. The HCF is 10. 20 ÷ 10 = 2, 30 ÷ 10 = 3, so the answer is 2 : 3. Notice that's the same simplest form as 12 : 18 — they were describing the same mix all along.

Handy shortcut: can't spot the HCF straight away? Keep dividing by any common factor you do see. 24 : 36 → halve both → 12 : 18 → divide by 3 → 4 : 6 → halve → 2 : 3. Slower, but you land in the same place.

It's Just Like Cancelling Fractions

If you can simplify 12/18 to 2/3, you can simplify the ratio 12 : 18 to 2 : 3 — it's the exact same skill with a colon instead of a fraction bar. Reuse what you already know.

Us, Thinking Out Loud

Could you teach me the two moves without looking?

How do you know when a ratio is fully simplified?