Exact fraction calculator

Exact arithmetic first. A decimal only when useful.

Inputs are represented as integer numerator/denominator pairs. A decimal such as 0.125 becomes 125/1000, then reduces to 1/8. A mixed number such as −1 1/2 means −(1 + 1/2), or −3/2. Negative denominators and improper fractional parts in mixed numbers are rejected; enter a signed ordinary fraction instead.

For addition and subtraction, a/b ± c/d = (ad ± bc) / bd. Multiplication is ac/bd. Division is ad/bc, with c ≠ 0. The numerator and denominator are reduced by their greatest common divisor, and the sign stays on the numerator.

Example: 1 1/2 + 2/3 = 3/2 + 2/3 = (9 + 4)/6 = 13/6 = 2 1/6. The decimal, about 2.16666666667, is rounded to 12 significant digits. BigInt keeps the fraction exact within the documented input bounds; a repeating decimal is never claimed to terminate.