Fraction Calculator

How the Fraction Calculator Works

This fraction calculator performs addition, subtraction, multiplication, and division on any two fractions. It automatically simplifies the final result using the greatest common divisor (GCD).

Formulas Used

• Addition: (a/b) + (c/d) = (ad + bc) / bd
• Subtraction: (a/b) − (c/d) = (ad − bc) / bd
• Multiplication: (a/b) × (c/d) = (ac) / (bd)
• Division: (a/b) ÷ (c/d) = (a × d) / (b × c)

Simplification Formula

To simplify a fraction, both the numerator and denominator are divided by their greatest common divisor:

Simplified Fraction = (n ÷ GCD(n, d)) / (d ÷ GCD(n, d))
  

Example

Add 1/4 + 1/6:

(1 × 6 + 1 × 4) / (4 × 6)
= (6 + 4) / 24
= 10 / 24
Simplified: 5 / 12