Fraction Calculator

Operation

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How fraction arithmetic works

Adding or subtracting fractions requires a common denominator, so the calculator cross-multiplies (n1×d2 ± n2×d1 over d1×d2) to combine them. Multiplying fractions simply multiplies numerators and denominators directly; dividing multiplies by the reciprocal of the second fraction. Every result is then reduced to lowest terms by dividing both numerator and denominator by their greatest common divisor.

Frequently asked questions

Why is the result sometimes a whole number instead of a fraction? When the reduced denominator equals 1, the fraction simplifies exactly to a whole number — for example, 2/4 + 1/2 reduces to 1, shown simply as "1" rather than "1/1" or "4/4."

Can I enter negative numerators or denominators? Yes — the calculator normalizes the sign so a negative denominator is converted to a negative numerator with a positive denominator, keeping the reduced result in standard form.

Why does dividing by a fraction flip it (multiply by the reciprocal)? Dividing by a number is mathematically the same as multiplying by its reciprocal (1 divided by that number) — for fractions, the reciprocal is simply the fraction flipped upside down, which is why "divide by n2/d2" becomes "multiply by d2/n2."