Fraction Calculator

Calculate with two integer fractions

Enter integer numerators and nonzero integer denominators, then choose addition, subtraction, multiplication, or division. The result is reduced to lowest terms and also shown as a mixed number and decimal.

Addition and subtraction

Fractions need a common denominator before their numerators can be combined. For a/b plus c/d, the unreduced result is (a×d + c×b)/(b×d). Subtraction uses a×d − c×b. The greatest common divisor then reduces numerator and denominator.

Multiplication and division

Multiplication uses (a×c)/(b×d). Division multiplies the first fraction by the reciprocal of the second: (a×d)/(b×c). A second numerator of zero makes division undefined because its reciprocal would have a zero denominator.

Worked example

For 3/4 + 5/6, a common denominator from direct cross multiplication is 24. The numerator is 3×6 + 5×4, or 38, so the result is 38/24. Dividing both parts by 2 gives 19/12, which is 1 7/12 or about 1.5833333333.

Signs and normalization

Negative numerators and denominators are accepted. The simplified result always moves the sign to the numerator and keeps the denominator positive. A zero result is displayed as 0 rather than 0 over another number.

Exact fraction versus decimal

The simplified fraction preserves the exact rational result for entered integers. The decimal is a rounded display and repeating values must be truncated. Use the fraction for exact follow-on arithmetic whenever possible.

Limitations and privacy

Inputs must be integers within JavaScript's safe-integer range. The tool does not parse typed forms such as “1 1/2”, solve equations, compare fractions, find a teaching-specific least common denominator, or support arbitrary-size integers. Values remain local.