Fraction Calculator
How it works
Adding and subtracting cross the two denominators to get a common one, then combine the numerators over it. Multiplying just multiplies straight across, numerator by numerator and denominator by denominator. Dividing multiplies by the second fraction flipped upside down. Whatever the operation, the raw result is then reduced by its greatest common divisor, so it always comes back in the smallest whole-number form.
Frequently asked questions
How does simplifying a fraction work?
Simplifying divides both the numerator and the denominator by their greatest common divisor (GCD) — the largest number that goes into both evenly. It's the same idea as reducing 4/8 down to 1/2: both are the same value, but 1/2 is the smallest whole-number way to write it, so every result here is shown that way rather than left unreduced.
Why is the denominator always shown as positive?
A fraction like -3/-4 is the same value as 3/4 — the two negatives cancel out — so showing a negative denominator would just be a confusing way to write a positive result. Any negative sign is normalized onto the numerator instead, so a negative result reads as, say, -3/4 rather than 3/-4.
What happens if I divide by a fraction of zero, like 5/0 or dividing by 0/3?
Dividing by a fraction whose numerator is zero is rejected, for the same reason ordinary division by zero is: there is no number that, multiplied by zero, gives back the original fraction. Rather than silently producing Infinity, this tool tells you the operation is undefined. A fraction with a denominator of zero isn't a valid fraction at all, so that is rejected too, on either side of the operation.