How to Simplify Fractions Fast (Using the GCD)

To simplify a fraction, divide the numerator and denominator by their Greatest Common Divisor (GCD). For 18/24, the GCD is 6, so it reduces to 3/4 in a single step.

Here's the fast method, why it works, and the mistakes that trip students up.

The one-step method

Find gcd(numerator, denominator), then divide both by it. Because you used the greatest common divisor, the result is already in lowest terms — no repeated halving needed. The Fraction Simplifier shows each step.

Worked example: 45/60

gcd(45, 60) = 15. So 45 ÷ 15 = 3 and 60 ÷ 15 = 4, giving 3/4. Both equal 0.75 — the value never changes.

Why dividing by the GCD works

Dividing the top and bottom by the same number is the same as multiplying by 1 (like 15/15), so the fraction's value is untouched. The GCD just gets you there in one move instead of several.

Common mistakes

• Dividing by a common factor that isn't the greatest (you'll need to repeat).
• Forgetting to divide both numbers.
• Stopping before the GCD reaches 1 between the new numerator and denominator.