Fraction Simplifier

Reduce fractions to their lowest terms. Enter a fraction and see the step-by-step simplification using the greatest common divisor (GCD).

How It Works

Greatest Common Divisor (GCD)

A fraction is simplified by dividing both the numerator and denominator by their greatest common divisor. The GCD is the largest number that divides both values evenly. This tool uses the Euclidean algorithm to find the GCD efficiently.

1. Find the GCD of the numerator and denominator
2. Divide both by the GCD
3. The result is the fraction in lowest terms

Example: 12/18 → GCD(12, 18) = 6 → 12÷6 / 18÷6 = 2/3

The Euclidean Algorithm

The Euclidean algorithm finds the GCD by repeatedly dividing and taking remainders. Starting with two numbers, divide the larger by the smaller and replace the larger with the remainder. Repeat until the remainder is zero; the last non-zero remainder is the GCD.

Example: GCD(48, 18): 48 = 2×18 + 12, then 18 = 1×12 + 6, then 12 = 2×6 + 0. GCD = 6

Negative Fractions

When simplifying negative fractions, the sign is normalized so the negative sign appears only on the numerator. For example, 4/(−6) becomes −2/3.