Fraction Calculator

How fraction arithmetic works

To add or subtract fractions you first need a common denominator: a/b ± c/d = (a×d ± c×b) / (b×d). For example 1/2 + 3/4 = (1×4 + 3×2) / 8 = 10/8, which simplifies to 5/4 — the mixed number 1 1/4, or 1.25.

Multiplying and dividing

Multiplication is straightforward: multiply the numerators and the denominators, so 2/3 × 3/5 = 6/15 = 2/5. Division flips the second fraction and multiplies: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2.

Simplifying

Every answer is divided by the greatest common divisor of the numerator and denominator, so results always appear in lowest terms. Improper results also show the equivalent mixed number.