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Fraction calculator

Add, subtract, multiply, or divide two fractions - exact whole-number arithmetic, fully reduced, with the working shown step by step.

Why exact fractions beat decimals

3/4 + 5/6 is exactly 19/12. As a decimal that's 1.58333... forever - and the moment you round it, you've introduced error that compounds through the rest of a calculation. This tool works in whole-number arithmetic throughout: common denominator for addition and subtraction, straight multiplication for the rest, then one reduction at the end using the greatest common divisor. The answer is exact, always fully simplified, and shown three ways - improper fraction, mixed number, and decimal.

The reduction step

A fraction is fully reduced when the numerator and denominator share no factor bigger than 1. The tool finds their greatest common divisor with Euclid's algorithm - the same method taught in school, just done instantly - and divides both by it. 38/24 becomes 19/12 because gcd(38, 24) = 2.

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