Math calculators

Fraction calculator

Add, subtract, multiply and divide fractions and mixed numbers, simplify fractions and convert decimals to fractions.

Inputs

Fraction3/4, -1 1/2, 0.75 or 2+ Fraction

Results

Methodology

Conventions

Fractions are held exactly as integer numerator and denominator and reduced by their greatest common divisor.
Mixed numbers are written with a space: -1 1/2 means −(1 + 1/2).
Decimal to fraction uses continued fractions: the closest fraction whose denominator does not exceed the limit.

References

Khinchin, Continued Fractions (1964)

Formulas

Add: \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}
Divide: \frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}
Simplify: \frac{a}{b} = \frac{a / g}{b / g},\quad g = \gcd(a, b)