Fraction Calculator

Add, subtract, multiply, or divide fractions

Enter a numerator and denominator for each fraction, then choose the operation. The result is reduced using the greatest common divisor and may also be displayed as a decimal.

Operation rules

Addition and subtraction require a common denominator: a/b + c/d = (ad + bc)/bd. Multiplication uses ac/bd. Division multiplies by the reciprocal, so a/b ÷ c/d = ad/bc.

Common errors

A denominator cannot be zero, and the second fraction cannot be zero when dividing. Keep negative signs consistent and reduce only after completing the operation. Decimal output may be rounded when the fraction has a repeating decimal expansion.

How fraction operations are checked

For addition and subtraction, the calculator converts both fractions to a common denominator before combining the numerators. Multiplication multiplies numerator by numerator and denominator by denominator, while division multiplies the first fraction by the reciprocal of the second. The final numerator and denominator are reduced by their greatest common divisor.

A denominator can never be zero, and division by a zero-valued fraction is undefined. Mixed numbers should first be converted to improper fractions: multiply the whole number by the denominator, add the numerator, and retain the denominator. Decimal output is an approximation when the fraction has a repeating expansion, so the reduced fraction remains the exact result.