Fraction calculator
Simplify a fraction or add, subtract, multiply and divide two fractions.
Your inputs stay in your browser. Displayed fractions are exact, without rounding.
Method and assumptions
Method version 1.0.0 · Updated
Simplify
Formula: (n ÷ GCD) / (d ÷ GCD)
Integers only, with a nonzero denominator. The result is an exact reduced fraction with a positive denominator, without decimal rounding. Example: 12/18 = 2/3; zero becomes 0/1.
- numerator
- Numerator
- denominator
- Denominator
Operations
Formula: a/b ± c/d = (ad ± bc)/bd ; (a/b) × (c/d) = ac/bd ; (a/b) ÷ (c/d) = ad/bc
Each integer is limited to ±9,007,199,254,740,991. Denominators and the divisor fraction must be nonzero. Exact calculation and final reduction, even when products exceed that limit. Example: 1/2 + 1/3 = 5/6.
- numerator
- Numerator
- denominator
- Denominator
- operation
- Operation
- otherNumerator
- Second numerator
- otherDenominator
- Second denominator
Integers within the stated limits; exact fraction without rounding. Fields accept neither decimals nor thousands separators.
Calculate with code
These short examples use the same inputs and core calculation as this tool. Adapt validation and formatting to your application.
JavaScript
function gcd(a, b) { return b === 0 ? Math.abs(a) : gcd(b, a % b); }
const n = 12, d = 18, divisor = gcd(n, d);
console.log(`${n / divisor}/${d / divisor}`); // 2/3TypeScript
function gcd(a: number, b: number): number { return b === 0 ? Math.abs(a) : gcd(b, a % b); }
const divisor = gcd(12, 18);
console.log(`${12 / divisor}/${18 / divisor}`); // 2/3Python
from math import gcd
n, d = 12, 18
g = gcd(n, d)
print(f"{n // g}/{d // g}") # 2/3Java
int n = 12, d = 18;
int g = java.math.BigInteger.valueOf(n).gcd(java.math.BigInteger.valueOf(d)).intValue();
System.out.println((n / g) + "/" + (d / g)); // 2/3C#
int n = 12, d = 18;
int g = (int)System.Numerics.BigInteger.GreatestCommonDivisor(n, d);
Console.WriteLine($"{n / g}/{d / g}"); // 2/3