Fraction Calculator

A complete fraction calculator that can add, subtract, multiply, divide, simplify, and convert fractions automatically.

Fraction A

/

Fraction B

/
Addition: 1/1
A/B + C/D = (AD + BC) / BD
Subtraction: 1/1
A/B − C/D = (AD − BC) / BD
Multiplication: 1/1
A/B × C/D = (A×C) / (B×D)
Division: 1/1
A/B ÷ C/D = (A×D) / (B×C)

Simplify Fraction A

Result: 1/2
A/B simplified = (A ÷ gcd) / (B ÷ gcd)

Improper to Mixed Number

Fraction A → 1 1/2
Mixed = floor(A/B) remainder (A mod B)/B

Mixed to Improper Fraction

/ = 3/2
Improper = whole×den + num / den

How the Fraction Calculator Works

This calculator performs all fraction operations using exact arithmetic. Fractions are simplified using the greatest common divisor (GCD) method.

Addition Formula

A/B + C/D = (AD + BC) / (BD)

Subtraction Formula

A/B − C/D = (AD − BC) / (BD)

Multiplication & Division

Multiplication: A/B × C/D = (A×C)/(B×D)
Division: A/B ÷ C/D = (A×D)/(B×C)

Simplification Formula

A/B simplified = (A ÷ gcd(A,B)) / (B ÷ gcd(A,B))

Mixed Number Conversion

Improper → Mixed:

whole = floor(A/B)
remainder = A mod B

Mixed → Improper:

(whole×den + num) / den

Examples

  • 1/2 + 1/3 = 5/6
  • 3/4 × 2/5 = 6/20 = 3/10
  • 7/3 = 2 1/3 (mixed number)

Input Rules

  • Denominators cannot be zero.
  • Fractions simplify automatically.
  • Negative values are supported.
  • Mixed numbers must have denominator > 0.

Frequently Asked Questions

Yes, all results are simplified using the GCD method.
Yes, negative numerators or denominators are allowed.
Yes, improper → mixed and mixed → improper are both supported.