Fraction Calculator
Add, subtract, multiply or divide two fractions and reduce the answer to simplest form. Enter whole-number numerators and nonzero denominators.
Simplified fraction
Integer inputs only. Denominators cannot be zero. Division by a zero fraction is undefined.
Formula checked · NumberSwift · Review process
How this calculator works
Addition and subtraction first put both fractions over a common denominator. Multiplication multiplies numerators and denominators directly. Division multiplies by the reciprocal of the second fraction. The result is reduced by its greatest common divisor. A zero denominator or division by a zero fraction is undefined.
Formula
Addition: a/b + c/d = (ad + bc)/bd. Subtraction: (ad − bc)/bd. Multiplication: ac/bd. Division: ad/bc. Divide numerator and denominator by their greatest common divisor to simplify.
Assumptions & limitations
Integer inputs only. Denominators cannot be zero. Division by a zero fraction is undefined.
Worked example
For 1/2 + 1/3, use a common denominator of 6: 3/6 + 2/6 = 5/6. For division, 1/2 ÷ 1/3 = 1/2 × 3/1 = 3/2. Both results are already in simplest form.
To express your simplified answer in decimal notation, use the Fraction to Decimal Calculator; keep the fraction when exact arithmetic matters.
Our approach to calculations ↗Common questions
Why is the answer reduced?
Dividing numerator and denominator by their greatest common divisor gives the equivalent fraction in simplest form.
Can the result be negative?
Yes. Subtracting a larger fraction from a smaller one produces a negative numerator.
Why can I not divide by a zero fraction?
Division multiplies by the reciprocal, which would require a zero denominator. That operation is undefined.