Show the Working

Fraction calculator

One box. Type 1/2 + 3/4 and you get the answer with the common denominator shown; type 3/4 on its own and you get it as a decimal, a percentage and a mixed number; type 0.375 and you get it back as a fraction.

This one runs on your own device. It is worked out in your browser, so there is nothing to send and nothing to log. Where a tool on this site does send something out, that page says so and names where it goes.

A fraction, a mixed number like 1 1/2, a decimal, or two of them with + − × ÷ between.

More options — decimal places, and how hard to look for a fraction

Neither is needed for the answers above. They are here because some people do need them.

Why adding fractions needs a common denominator

You cannot add halves to quarters any more than you can add feet to metres: they are different-sized pieces. So both are rewritten in pieces of the same size first, and the size that works is a multiple of both denominators. For 2 and 4 that is 4; for 3 and 5 it is 15.

The lowest common denominator is not required — multiplying the two denominators together always works — but it keeps the numbers small and usually means less cancelling afterwards. The reading above shows which one it used and what each fraction became.

Some fractions never finish as decimals

A third is 0.333… and it does not stop. Neither does a seventh, which repeats the six digits 142857 for ever. A decimal only terminates when the denominator's only prime factors are 2 and 5 — which is why halves, quarters, fifths and eighths come out neatly and thirds, sixths and sevenths do not.

Where a decimal repeats, the reading shows the repeating part in brackets rather than rounding it away and pretending the number stopped. The rounded version is given too, because that is usually the one you need.

Turning a decimal back into a fraction is a choice

Ask for 0.333333 as a fraction and there are two defensible answers: 333333/1000000, which is exactly what you typed, and 1/3, which is almost certainly what you meant. Neither is wrong and a calculator has to pick.

This one looks for the closest fraction whose bottom number is within the limit you set, and then says how far off it is. That is the part most converters leave out: 355/113 is a famously good stand-in for π, and knowing it is out by about a ten-millionth is the difference between using it and trusting it.

Where to go next

The same quantities, written differently:

What this does not do

Two terms at a time, one operator. Longer expressions need brackets and an order of operations, and a box that silently guesses where the brackets go in 1/2 + 3/4 × 2 is worse than a box that says it only does one step.

Denominators are limited to what ordinary arithmetic can hold exactly. Ask for something with more than fifteen digits in it and the answer stops being reliable, so the reading says so rather than printing a number it cannot stand behind.