Fraction Calculator With Every Step Shown

Entering a mixed number, and the one-fraction mode

Each fraction has three boxes: the whole number, the numerator and the denominator. Leave the whole box empty for a proper fraction such as 3/4, and fill it in for a mixed number such as 2 1/2. A minus sign in the whole box makes the whole mixed number negative, which is what −2 1/2 means — not minus two, plus a half.

Choose the operation from the list above the boxes. The last option takes a single fraction and simplifies it, converts it to a decimal and converts it to a percentage, which is what you want when the question is only asking you to write 18/24 in its simplest form.

Every box takes a whole number up to 1,000. The cap is deliberate: it keeps every step exact integer arithmetic, so nothing on the page has been rounded on the way to the answer.

What each line of the working is doing

Adding and subtracting need one shared denominator, so the tool takes the lowest common multiple of the two and rewrites both fractions over it. The LCM of 4 and 6 is 12, so 3/4 becomes 9/12 and 5/6 becomes 10/12, and only then do the numerators combine. The denominator does not move, because at that point you are counting pieces that are all the same size.

Multiplying needs no matching at all, so the working cancels common factors first — 4/9 × 3/8 becomes 1/3 × 1/2 — and multiplies the small numbers that are left. Dividing is turned into multiplying by the reciprocal before anything else happens, which is all that keep, change, flip means. The answer is then divided by the highest common factor of its numerator and denominator, and written as a mixed number if the numerator is the larger of the two.

The decimal comes from real long division, one digit at a time, remembering every remainder along the way. When a remainder turns up for the second time the decimal has begun repeating, and everything from that point on is marked with a bar. That is why 1/6 appears as 0.16 with a bar over the 6, rather than as 0.1667, and why 1/7 shows all six repeating digits.

The percentage is the same fraction multiplied by 100. When that recurs, the rounded figure is shown with the exact fraction beside it — 1/6 is 50/3%, not quite 16.67%.

What it will not do

It does not take decimals or algebra in the boxes. Enter 0.5 as 1 over 2. An algebraic fraction such as (x + 1)/3 is a different topic, and a calculator that returned a number for it would be teaching you the wrong thing.

It does not mark your work or know which method your teacher asked for. Where more than one valid route exists — cancelling before multiplying rather than simplifying at the very end — it shows the one that keeps the numbers smallest, and both reach the same answer.

It does not round the working. The only rounded figure anywhere on the page is the percentage when it recurs, and the exact value is printed next to it so you can see precisely what was rounded and by how much.

Where fractions go wrong in exams

Adding the denominators. 1/2 + 1/3 is not 2/5. Halves and thirds are different sized pieces and cannot be counted together until both are written in sixths, which is exactly the line the tool prints first.

Losing the whole number. Converting 2 1/2 by multiplying 2 by 2 and then forgetting to add the 1 gives 4/2 instead of 5/2, and every line after it inherits the mistake.

Flipping the wrong fraction. Keep the first, change the sign, flip the second: 3/4 ÷ 2/5 is 3/4 × 5/2, and flipping the 3/4 instead gives a number that is wrong in a way that looks tidy.

Writing 0.17 for 1/6. It is 0.1666… going on for ever, written with a bar or a dot over the 6. A rounded decimal costs the mark whenever the question asks for an exact value.

• 1/2 + 1/3 = 5/6, not 2/5
• 2 1/2 = 5/2, not 4/2
• 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8
• 1/6 = 0.16 recurring, not 0.17