Fraction Calculator

Add, subtract, multiply or divide two fractions — result is automatically simplified.

Equation used
(a)/(b) ± (c)/(d) = (ad ± cb)/(bd); (a)/(b) × (c)/(d) = (ac)/(bd); (a)/(b) div (c)/(d) = (ad)/(bc) (then simplified by GCD)

Frequently Asked Questions

How is the result simplified?

After the arithmetic, the result's numerator and denominator are both divided by their greatest common divisor (GCD), so you always get the fraction in lowest terms.

Why does dividing by a fraction flip it?

Dividing by a/b is the same as multiplying by its reciprocal b/a, so a/b ÷ c/d is computed as a/b × d/c — that's why the calculator cross-multiplies (ad) over (bc).

What does the "Mixed number" result mean?

It only appears when the result is an improper fraction (numerator ≥ denominator). It shows the same value split into a whole number plus a proper fraction remainder, e.g. 7/2 becomes 3 1/2.