How to simplify fractions — step by step (with a worked example)
Simplifying a fraction means dividing the numerator and denominator by the same number without changing its value. The fastest route is the greatest common divisor (GCD). Worked example: 18/24 → 3/4 in a single step. Suitable for Grade 5–6 / Year 6–7.
Quick answer
To simplify a fraction, divide the numerator and denominator by their greatest common divisor (GCD). Example: 18/24 — the GCD is 6, so 18 ÷ 6 = 3 and 24 ÷ 6 = 4. The simplified fraction is 3/4.
At a glance
| Fraction | 18/24 |
|---|---|
| Method | Divide by the GCD |
| Steps | GCD(18, 24) = 6 |
| Result | 3/4 |
| Check | 3 and 4 are coprime ✓ |
| Grade level | Grade 6 (ages 11–12) |
Worked example: simplify 18/24
We find the GCD of 18 and 24 and divide both numbers by it.
The steps to simplify a fraction
These steps work for any fraction — including improper fractions like 100/35.
Step 1 · Start
18/24We reduce the fraction 18/24 to its simplest form.Step 2 · GCD
GCD(18, 24) = 6The largest number that divides both 18 and 24 with no remainder is 6.Step 3 · ÷ GCD
(18 ÷ 6) / (24 ÷ 6)Divide the numerator and denominator by the GCD 6.Step 4 · Result
= 3/43 and 4 are coprime — the fraction is fully reduced.
Why dividing by the GCD works
When you divide the numerator and denominator by the same number, that factor cancels out and the fraction still represents the same portion — so 18/24 and 3/4 are equivalent. By using exactly the greatest common divisor, you remove every shared factor in one move, and the fraction is immediately in lowest terms.