Simplifying a ratio means writing it with the smallest whole numbers while keeping the same comparison. Find the highest number that divides both terms, then divide both by it. For 8:12, the highest common factor is 4: 8 ÷ 4 = 2 and 12 ÷ 4 = 3, so 8:12 = 2:3. You must divide both terms by the same number — different divisors change the ratio. A ratio is fully simplified when no number bigger than 1 divides both terms; if both are still even, or share any factor, keep going.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- simplify
- rewrite a ratio with the smallest whole numbers
- highest common factor
- the biggest number that divides both terms
- simplest form
- no common factor greater than 1 remains
Worked examples
Simplify 8:12
- 1.Highest common factor is 4.
- 2.8 ÷ 4 = 2 and 12 ÷ 4 = 3.
= 2:3
Simplify 10:15
- 1.Highest common factor is 5.
- 2.10 ÷ 5 = 2 and 15 ÷ 5 = 3.
= 2:3
Simplify 9:6
- 1.Highest common factor is 3.
- 2.9 ÷ 3 = 3 and 6 ÷ 3 = 2.
= 3:2
For parents
Method: Divide both terms by their highest common factor.
What to say: Ask 'can both numbers still be divided by the same thing?' If yes, keep dividing.
Common mistakes:
- Halving once and stopping too early (8:12 → 4:6).
- Dividing the two terms by different numbers.