Simplifying means writing a fraction with the smallest possible numbers while keeping the same value. Find the highest number that divides both the top and the bottom, 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 the top and the bottom by the same number. A fraction is in simplest form when no number bigger than 1 divides both parts — if it still can be divided, keep going.
Explore this idea with maths tools
Equal parts, equal wholes
2/4 = 4/8
Both bars are the same length. Find a division of the second bar that lines up exactly with the coloured edge.
Words to know
- simplify
- rewrite a fraction with the smallest whole numbers
- highest common factor
- the biggest number that divides both top and bottom
- 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 6/9
- 1.Highest common factor is 3.
- 2.6 ÷ 3 = 2 and 9 ÷ 3 = 3.
= 2/3
Simplify 10/15
- 1.Highest common factor is 5.
- 2.10 ÷ 5 = 2 and 15 ÷ 5 = 3.
= 2/3
For parents
Method: Divide the top and bottom by their highest common factor.
What to say: Ask 'can the top and bottom both still be divided?' If yes, keep dividing until they cannot.
Common mistakes:
- Halving once and stopping too early (8/12 → 4/6).
- Dividing the top and bottom by different numbers.