How to simplify fractions
Quick answer
Find the greatest common factor (GCF) of the numerator and denominator, then divide both by it. For example, the GCF of 18 and 24 is 6, so 18/24 simplifies to 3/4.
A simplified fraction is the same amount written with the smallest possible numbers. 18/24 and 3/4 are exactly equal; 3/4 is just easier to read.
Method 1: Divide by the greatest common factor
- List the factors of both numbers.
- 18: 1, 2, 3, 6, 9, 18
- 24: 1, 2, 3, 4, 6, 8, 12, 24
- The biggest number in both lists is 6.
- Divide top and bottom by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4, giving 3/4.
Method 2: Keep dividing by small numbers
If the GCF isn’t obvious, divide by any shared factor and repeat until you can’t anymore.
48/64 → 24/32 → 12/16 → 6/8 → 3/4
It takes more steps but you can’t get it wrong, as long as you keep going until no common factor is left.
Method 3: Prime factors
Break both numbers into primes and cancel what they share.
60/84 = (2 × 2 × 3 × 5) / (2 × 2 × 3 × 7) = 5/7
This is the most reliable way for large numbers.
Quick divisibility tricks
| A number is divisible by… | If… |
|---|---|
| 2 | It ends in 0, 2, 4, 6 or 8 |
| 3 | Its digits add up to a multiple of 3 |
| 5 | It ends in 0 or 5 |
| 9 | Its digits add up to a multiple of 9 |
| 10 | It ends in 0 |
So for 42/56, both are even (divide by 2 → 21/28), then both are multiples of 7 (→ 3/4).
Simplifying improper fractions
If the top is bigger than the bottom, simplify first, then turn it into a mixed number if needed. 34/8 simplifies to 17/4, which is 4¼ because 4 goes into 17 four times with 1 left over.
You’ll use this constantly when adding fractions with different denominators, since the answers often need reducing.
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