Fraction Calculator

How it works

A fraction expresses a number as a numerator over a denominator (like 3/4). Operations on fractions follow simple rules but can be tedious by hand, especially when finding common denominators or simplifying results. This calculator handles addition, subtraction, multiplication, and division automatically and reduces every result to its simplest form.

Multiplication is the simplest operation: numerator times numerator over denominator times denominator, then simplify by dividing by the greatest common divisor. Division is multiplication by the reciprocal — flip the second fraction and multiply.

Addition and subtraction need a common denominator. The calculator uses the cross-multiplication shortcut: a/b + c/d = (a·d + b·c)/(b·d). It works for any two fractions but doesn't necessarily produce the simplest intermediate denominator. After computing, we divide both numerator and denominator by their GCD to get the canonical reduced form.

Fractions are exact in a way decimals are not — 1/3 has no clean decimal representation, but it stays exact as a fraction. For problems that require exact answers (algebra, probability ratios, recipe scaling), keep numbers as fractions until the final step. For numerical work, decimals are usually more convenient.

Watch out for sign conventions. We normalize results so the denominator is always positive — a negative fraction shows the minus sign on the numerator. Division by zero yields NaN; we don't crash but the result will display as undefined.

For mixed numbers (like 2 1/2), convert to an improper fraction first (2 1/2 = 5/2) before entering values. The result will also display as an improper fraction unless you convert back.