Keep the fraction exact until the end

A decimal like 0.333333 is only an approximation of one third. This tool reads whole-number numerators and denominators and uses integer arithmetic for the fraction operations. It reduces the final numerator and denominator by their greatest common divisor, then separately calculates a decimal for convenience. The exact fraction is the reference when the decimal repeats or rounds.

Denominators and signs matter

To add or subtract fractions, express both over a common denominator. Multiplication combines numerators and denominators directly. Division multiplies by the reciprocal of the second fraction. A zero denominator is never valid, and dividing by a fraction with a zero numerator is also invalid. A negative denominator is moved into the numerator so the result has a consistent sign convention.

An improper fraction is still a useful result

If the reduced numerator is larger than the denominator, the tool keeps an improper fraction such as 7/3 rather than silently converting it into a mixed number. A denominator of 1 is displayed as a whole number. Inputs are limited to 12-digit integers per field. The decimal display uses normal browser number precision and is not an additional exact representation.

Worked examples

Operation	Exact result	Decimal (approx.)
1/2 + 1/3	5/6	0.83333333
3/4 ÷ 1/2	3/2	1.5

Good questions.

Can I enter a mixed number?

Convert it to an improper fraction first: 1 1/2 becomes 3/2.

Why is the decimal labelled approximate?

Many fractions do not have a finite decimal expansion, and the display is rounded.

Can a denominator be negative?

Yes, except zero. The result moves the negative sign to the numerator.

Updated 5 November 2026 · Methods & corrections

Fraction calculator