How fraction arithmetic works
Adding or subtracting fractions requires a common denominator, found here by multiplying the two denominators together. Multiplying fractions multiplies straight across; dividing multiplies by the reciprocal of the second fraction. Every result is then simplified by dividing both parts by their greatest common divisor (GCD).
- a/b — first fraction (numerator 1 / denominator 1)
- c/d — second fraction (numerator 2 / denominator 2)
More detail
Why the answer gets reduced
Fraction arithmetic on raw numerators and denominators often produces a fraction that isn't in lowest terms — for example 1/2 + 1/3 works out to 5/6 directly, but many combinations leave a common factor in both parts. Dividing numerator and denominator by their greatest common divisor (GCD) shrinks the fraction to its simplest equivalent without changing its value.
Watch the sign. If a denominator is entered as negative, the result's sign is normalized onto the numerator (e.g. 3/−4 becomes −3/4) so the denominator you see is always positive.
Frequently asked questions
What is 1/2 + 1/3?
Using a common denominator: (1×3 + 1×2) / (2×3) = 5/6. Enter numerator 1 = 1, denominator 1 = 2, operation = Add, numerator 2 = 1, denominator 2 = 3 above to see it computed live.
How do you subtract fractions?
Cross-multiply onto a common denominator, then subtract: a/b − c/d = (ad − bc) / bd. For example 1/2 − 1/3 = (1×3 − 1×2) / (2×3) = 1/6.
How do you divide two fractions?
Multiply the first fraction by the reciprocal of the second: a/b ÷ c/d = ad / bc. For example 1/2 ÷ 1/3 = (1×3) / (2×1) = 3/2 = 1.5.
Why does the calculator show “—”?
Three cases. A denominator of 0 makes a fraction undefined; dividing by a fraction whose numerator is 0 is dividing by zero; and leaving any of the four boxes empty stops the calculation, because treating a blank as 0 would produce an answer for a value you never typed. Enter 0 explicitly when you actually mean zero.
How is the result reduced to lowest terms?
The calculator finds the greatest common divisor (GCD) of the resulting numerator and denominator (via the Euclidean algorithm) and divides both by it. If the reduced denominator is 1, only the whole number is shown.