Fraction Calculator

How to use

1. Enter two values in any form — 1/3, 0.75, 75% or 2 1/3.
2. Choose the operation (add, subtract, multiply or divide).
3. Read the simplified fraction, mixed number, decimal and percentage.
4. Use the comparison table to see all three notations for both inputs and the result.

How it works

Why fractions instead of decimals

This tool computes with rational numbers, not floats: a/b ± c/d is brought to a common denominator first; multiplication multiplies numerators and denominators; division multiplies by the reciprocal. For 1/3 + 1/6: common denominator 6 gives 2/6 + 1/6 = 3/6, which reduces to 1/2. Numerator and denominator are stored as integers (BigInt), so values like 1/3 that never terminate are never polluted by a 0.333333 float approximation.

What reducing and common denominators do

Reducing means dividing numerator and denominator by their greatest common divisor; a common denominator means unifying denominators to their least common multiple. Results are always given in lowest terms, plus a mixed number: 22/7 becomes 3 1/7 — more intuitive in kitchens and workshops than an improper fraction, though improper fractions are handier inside algebra.

Reading and writing repeating decimals

Decimals come in two kinds: if the denominator's prime factors are only 2s and 5s the decimal terminates (7/8 = 0.875, 3/4 = 0.75); otherwise a repeating block appears in parentheses: 1/3 = 0.(3), 5/6 = 0.8(3), 22/7 = 3.(142857). Parentheses mean the digits repeat forever — only the fraction is the exact value.

Calculation basis: fraction arithmetic follows the rules for rational numbers (common denominators for addition and subtraction, numerator × numerator over denominator × denominator for multiplication, multiply by the reciprocal for division); numerator and denominator are kept as integers (BigInt) and reduced to lowest terms. Repeating decimals are detected by tracking remainders in long division.

Code example

const gcd = (a, b) => b ? gcd(b, a % b) : Math.abs(a);

class Frac {
  constructor(n, d) {
    if (d < 0) { n = -n; d = -d; }
    const g = gcd(n, d) || 1;
    this.n = n / g; this.d = d / g;       // reduced on construction
  }
  add(o) { return new Frac(this.n * o.d + o.n * this.d, this.d * o.d); }
  mul(o) { return new Frac(this.n * o.n, this.d * o.d); }
  toString() { return this.n + "/" + this.d; }
}

new Frac(6, 8).toString();   // "3/4"

from fractions import Fraction

Fraction(6, 8)          # Fraction(3, 4) (reduced automatically)
Fraction(0.75)          # Fraction(3, 4)
Fraction("2 1/3")       # mixed-number strings are not supported; split them yourself

Fraction(1, 3) + Fraction(1, 6)   # Fraction(1, 2)
float(Fraction(1, 3))             # 0.333...

FAQ