Math foundations

Fraction Simplifier

Reduce an integer numerator and nonzero integer denominator to lowest terms. Exact BigInt arithmetic preserves large integers beyond JavaScript’s safe Number range.

Enter values and select Calculate.

Formula and worked example

Find gcd(|numerator|, |denominator|), divide both components by that value, and move any negative sign to the numerator.

8/12 reduces to 2/3. The input 10/−15 normalizes to −2/3, while −10/−15 becomes 2/3.

Integer and sign policy

Numerator and denominator must be complete integers; malformed decimals are rejected.

The reduced denominator is always positive.

A zero numerator is displayed as 0 with the canonical reduced form 0/1.

Large integers and mixed numbers

Components may contain up to 200 digits and are simplified with integer-safe BigInt arithmetic.

An improper result also receives a mixed-number representation when it has a nonzero remainder.

This page reduces one fraction; it does not perform mixed-number arithmetic.

Conversion boundaries

Decimal to Fraction owns conversion from decimal notation.

Fraction to Decimal owns decimal expansion and repeating-cycle detection.

GCF Calculator owns general greatest-common-factor work, although the same mathematical operation supports fraction reduction.

Methodology and limits

This deterministic browser-local tool uses strict complete-value parsing and the displayed mathematical definition. It does not evaluate expressions, execute entered text, call a remote service, or silently cross its documented real-number or integer domain.