Fraction Calculator
Add, subtract, multiply or divide two fractions - the answer appears simplified, as a mixed number and as a decimal, with every step shown.
The left box on each fraction is an optional whole number, for mixed numbers like 1 3/4.
How fraction arithmetic works
Every operation on two fractions reduces to a couple of integer sums. For addition and subtraction you first put both fractions over a common denominator (the product of the two denominators always works), then add or subtract the numerators. Multiplication is the easy one: multiply the tops together and the bottoms together. Division is multiplication in disguise - flip the second fraction and multiply.
- Add / subtract -
a/b +/- c/d = (a x d +/- c x b) / (b x d) - Multiply -
a/b x c/d = (a x c) / (b x d) - Divide -
a/b / c/d = (a x d) / (b x c)
Whatever the operation, the raw answer is then reduced by dividing top and bottom by their greatest common divisor, so 6/8 always comes back as 3/4.
A worked example
Take 2/3 + 1/4. The common denominator is 3 x 4 = 12, giving 8/12 + 3/12 = 11/12. Since 11 and 12 share no factors, that is already in lowest terms and, being smaller than one, has no mixed-number form. As a decimal it is roughly 0.9167. Now try 5/2 x 4/3: multiply across to get 20/6, reduce by 2 to reach 10/3, which is the mixed number 3 1/3, or 3.3333 as a decimal.
Pitfalls to watch
A denominator can never be zero, and you cannot divide by a fraction whose numerator is zero - both are flagged above rather than returning a silent wrong answer. When you enter a mixed number, the sign lives on the whole-number box: -1 1/2 means minus one and a half, not minus one plus a half. For percentages and decimals of these results, the percentage calculator picks up where this leaves off, the unit converter is handy when the fractions are measurements, and the aspect ratio calculator uses the same simplifying step on width and height.