Exact fraction arithmetic
The core fraction operations use integer arithmetic rather than converting the fractions to ordinary floating-point decimals first. This preserves exact numerators and denominators for addition, subtraction, multiplication, division, and simplification.
How fractions are simplified
The numerator and denominator are divided by their greatest common divisor. A negative sign is normalized to the numerator and the denominator is kept positive, so equivalent forms such as 2/4 and −2/−4 reduce consistently.
Adding and subtracting fractions
Fractions with different denominators are cross-multiplied to a common denominator before the numerators are combined. The final result is then simplified automatically.
Decimal and percentage conversions
Conversion happens after the exact fraction is known. Terminating decimals are shown without unnecessary zeros. Repeating or longer decimals are limited to a practical number of places and marked with an ellipsis so a truncated decimal is not mistaken for an exact finite representation.
Input limits and zero denominators
Numerators and denominators must be whole integers. Zero is valid as a numerator but never as a denominator, and division by a zero fraction is rejected. Individual integer inputs are limited to 100 digits to keep browser calculations responsive.
Frequently asked questions
Can I enter negative fractions?
Yes. A negative numerator or denominator is accepted and the sign is normalized in the result.
Why are decimal inputs not accepted?
This page treats a fraction as an exact ratio of two whole integers. Use the decimal display to convert an exact fraction after calculation.