Add, subtract, multiply and divide fractions — and see the working step by step. Free, nothing to install, no sign-up.
This calculator adds, subtracts, multiplies and divides fractions, and it does not just give you the answer: it shows the working step by step, including the common denominator and the simplifying, so you can copy it into your notebook and see which line you went wrong on. It runs inside your browser and downloads as a PDF.
The bottom one, the denominator, says how many pieces you cut the thing into. The top one, the numerator, says how many of those pieces you have. In three quarters you cut into four and you have three. So the bottom number is the SIZE of the piece and the top one is the NUMBER of pieces — which is exactly why you cannot treat them the same way.
You can only put together pieces of the same size. If the denominators already match, add the top numbers and leave the bottom alone: 2/5 + 1/5 = 3/5. If they do not match, first find a number both denominators go into — the lowest common multiple — and convert both fractions. One third plus one sixth: 3 and 6 both go into 6, so 1/3 becomes 2/6, and 2/6 + 1/6 = 3/6, which simplifies to 1/2.
Adding the bottom numbers too. Half plus half would give two quarters, and two quarters is a half; but half an apple plus half an apple is a whole apple, not half. The sum contradicts reality, so the sum is wrong. You never add denominators, because a denominator is not an amount: it is the size of the piece.
To multiply you need no common denominator at all: top times top, bottom times bottom. 2/3 × 3/4 = 6/12, which simplifies to 1/2. And dividing is multiplying with one trick: flip the second fraction over and multiply. 1/2 ÷ 1/4 becomes 1/2 × 4/1 = 4/2 = 2. Which makes sense, because there are two quarters in a half.
Turn the fractions into decimals and do the sum again on an ordinary calculator: 1/3 is 0.333 and 1/6 is 0.166, and together they make 0.5, which is exactly 1/2. If the decimal does not match, the slip is almost always in converting to the common denominator. And in an addition the answer has to be bigger than both starting fractions: if it comes out smaller, you either subtracted or added the bottoms.
Because a denominator is not an amount, it is the size of the piece. Half plus half is one whole, and adding the bottoms would give 2/4, which is a half. The sum would contradict reality.
It is the lowest common multiple of the two denominators: the smallest number they both go into. For 3 and 6 it is 6; for 4 and 6 it is 12. If you cannot see it, multiplying the two denominators always works — you just have more simplifying to do afterwards.
If you can, yes — that is what gets asked for in class. You simplify by dividing top and bottom by the same number until nothing goes into both any more. The calculator does it and shows you what it divided by.
Yes. The sign goes on the numerator and the calculator carries it through. And an improper fraction — top bigger than bottom, like 4/2 — works the same way; the answer comes back reduced.
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