Last updated 23 August 2026
How fraction arithmetic works
- Adding / subtracting — cross-multiply to a common denominator first: a/b ± c/d = (ad ± bc) / bd.
- Multiplying — straightforward: multiply the numerators together and the denominators together.
- Dividing — flip the second fraction and multiply: a/b ÷ c/d = a/b × d/c.
Every result is reduced to its simplest form by dividing both the numerator and denominator by their greatest common divisor, so 6/8 comes back as 3/4, never left unreduced.
Common questions
How do you add fractions with different denominators?
Cross-multiply so both fractions share a common denominator, add the numerators, then simplify. For a/b + c/d, that's (ad + bc) / (bd), reduced by dividing both parts by their greatest common divisor.
Why does the result get automatically simplified?
6/8 and 3/4 are the same value, but 3/4 is the form anyone would expect as an answer. The calculator divides both numerator and denominator by their greatest common divisor so the result is always in its simplest form.
What does the mixed-number result mean?
It's the same value written as a whole number plus a fraction, such as 7/4 shown as 1 3/4. It only appears when the result is greater than one whole.