Fraction Calculator — Add, Subtract, Multiply, Divide

Enter two values — a proper fraction like 3/4, a mixed number like 1 1/2, a whole number, or a decimal like 1.25 — pick an operation and get an exact answer, shown as a reduced fraction, an equivalent mixed number and a decimal, with the working laid out: the common denominator for addition and subtraction, multiplying across for a product, inverting the divisor for a quotient.

The arithmetic runs in arbitrary-precision integers, and reading a decimal as a fraction of its written digits is what makes that worth having. The string 0.1 becomes exactly one tenth here. Handed to a floating-point number it becomes 3602879701896397 / 36028797018963968, which is the nearest binary fraction and is not one tenth, which is why 0.1 + 0.2 famously misses 0.3 in almost every programming language. Adding thirds is the same story: a third has no finite decimal at all, so any calculator that converts to decimal first has already lost the answer before it starts.

Reduction uses the greatest common divisor, and the common denominator is the least common multiple rather than the product of the two denominators. Both give a correct answer; the second gives it with much larger numbers, so 1/12 + 1/18 comes out over 36 rather than over 216 and needs no cleanup afterwards.

A sign convention is worth stating because it catches people. A negative mixed number applies the minus to the whole quantity: -1 1/2 is negative three halves, not minus one plus a half. Written as an improper fraction it is -3/2, which is the unambiguous form to use if you are copying a value from somewhere else and are not certain how that source meant it. The decimal shown alongside each result is rounded for display — it is the fraction that is exact, and for a value like 1/3 the decimal can only ever be an approximation of it.