Fraction Calculator

Add, subtract, multiply, or divide two fractions, reduced to lowest terms.

First fraction
Second fraction
Result—

Enter your values and calculate to see the result.

Formula used

For fractions a/b and c/d:
  Add:       a/b + c/d = (a·d + c·b) / (b·d)
  Subtract:  a/b − c/d = (a·d − c·b) / (b·d)
  Multiply:  a/b × c/d = (a·c) / (b·d)
  Divide:    a/b ÷ c/d = (a·d) / (b·c)

Then divide numerator and denominator by gcd(numerator, denominator)
to reduce to lowest terms.
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Worked example

Problem: 1/2 + 3/4

Common denominator: (1×4 + 3×2) / (2×4) = (4 + 6) / 8 = 10/8

Reduce by gcd(10, 8) = 2: 10/8 = 5/4, or 1 1/4 as a mixed number.

Result: 5/4 (decimal 1.25)

Frequently asked questions

Does the result always come back in lowest terms?

Yes. After the operation the calculator divides the numerator and denominator by their greatest common divisor, so 6/8 is shown as 3/4. When the result is an improper fraction, a mixed-number form is also given.

What happens if I enter zero as a denominator?

A fraction with a zero denominator is undefined, so the calculator shows a validation message and does not compute a result until you enter a non-zero denominator.

Can it handle negative fractions?

Yes. Enter a negative sign on either the numerator or the denominator. The calculator normalises the sign onto the numerator, so the displayed result keeps a single, conventional sign.

How is division of fractions handled?

Dividing by a fraction multiplies by its reciprocal — a/b ÷ c/d becomes a/b × d/c. Dividing by zero (a zero second numerator) is rejected with a message.