Fractions Calculator
Fraction arithmetic is ordinary arithmetic with one extra step: the denominators have to agree before the numerators can be combined. Once that is handled, the four operations reduce to a handful of rules.
Result
5/6
- Decimal
- 0.833333
- Mixed number
- 5/6
- Simplified by
- already simplest
a/b + c/d, then divided by the greatest common divisor.
The formula this calculator uses
a/b + c/d = (a x d + c x b) / (b x d)
- a/b
- The first fraction, numerator over denominator
- c/d
- The second fraction
- b x d
- A common denominator that always works
How to check the result by hand
- 1
Work out the operation
Addition and subtraction need a common denominator. Multiplication and division do not.
- 2
Cross-multiply for addition or subtraction
The new denominator is b times d. The new numerator is a times d plus or minus c times b.
- 3
Multiply straight across for multiplication
Numerator times numerator and denominator times denominator, with no common denominator needed.
- 4
Flip and multiply for division
Dividing by c over d is the same as multiplying by d over c. Turn the second fraction upside down and multiply.
- 5
Simplify with the greatest common divisor
Find the largest number dividing both parts and divide them by it. Then convert an improper result to a mixed number if a whole-number form reads better.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate Fractions page.