Simplify Fractions Calculator

Use this free simplify fractions calculator to reduce any fraction to its lowest terms. Enter a numerator and denominator and it instantly divides both by their greatest common divisor (GCD), shows the GCD and the division steps, and converts improper fractions to mixed numbers — for example, 24/36 reduces to 2/3 and 7/3 becomes 2⅓.

How to use this calculator

The fastest way is to type the whole fraction in the top field — something like 24/36 or -7/2 — and the numerator and denominator fields fill in automatically. You can also type the numerator and denominator yourself, or edit them after entering the fraction. Everything updates instantly as you type.

Negative fractions work fine; put the minus sign anywhere (3/-8 means the same as -3/8), and the simplified result carries a single minus sign in front. If the numerator is zero, the answer is simply 0. If you enter a denominator of zero, the calculator tells you exactly what's wrong instead of guessing — a fraction with a zero denominator is undefined.

Improper fractions (where the numerator is larger than the denominator) are also converted to mixed numbers: 7/3 simplifies to 2⅓. Note this tool reduces fractions to lowest terms and keeps them as fractions — if you want the decimal value instead, use our fraction to decimal converter.

How it works

A fraction is in lowest terms when its numerator and denominator share no common factor larger than 1. To get there, the calculator finds the greatest common divisor (GCD) of the two numbers using the Euclidean algorithm: divide the larger number by the smaller, then replace the larger with the remainder and repeat until a remainder of 0 appears — the last non-zero remainder is the GCD.

For 24/36 the steps are: 36 = 24 × 1 + 12, then 24 = 12 × 2 + 0, so the GCD is 12. Next, divide both parts of the fraction by that GCD: 24 ÷ 12 = 2 and 36 ÷ 12 = 3. The simplified fraction is 2/3, which is already in lowest terms — dividing both parts by their GCD always guarantees that, because any remaining common factor would have divided the GCD too.

When the result is improper (the simplified numerator is larger than the denominator), the calculator also rewrites it as a mixed number by splitting off the whole part: 7/3 becomes 2⅓. A zero numerator short-circuits to 0 without any division, and a zero denominator is rejected outright since division by zero is undefined.

Assumptions: inputs must be whole numbers (integers); the denominator cannot be zero. Results are exact mathematical values, not estimates.