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Fraction Calculator

Enter two fractions and pick an operation. The answer comes back in lowest terms, with the working, the mixed number and the decimal beside it.

Your fractions

Type a fraction (3/4), a mixed number (2 3/4), a whole number or a decimal.
Operation
Common denominator
12
3/4 + 1/3
13/12
Working
3/4 + 1/3 = 9/12 + 4/12 = 13/12
As a mixed number
1 1/12
As a decimal
1.08(3)
As a percentage
108.3333%

How to use this calculator

  1. Type the first fraction as 3/4. A mixed number like 2 3/4, a whole number like 5 and a decimal like 0.75 are all accepted.
  2. Choose the operation: add, subtract, multiply or divide.
  3. Type the second fraction the same way.
  4. Read the answer in lowest terms, and check the working line for the intermediate step — the common denominator for a sum, or the flipped fraction for a division.

The three figures beside the answer are the same number in the forms people usually need next: as a mixed number, as a decimal, and as a percentage. A repeating decimal is shown with the repeating block in brackets, so 1/3 reads 0.(3) rather than a row of threes that has to stop somewhere.

How to calculate with fractions

Multiplying is the easy one: multiply straight across. Adding and subtracting need the two fractions to be counting the same thing first, which is what a common denominator does.

a/b + c/d = (a × d + c × b) / (b × d)
  • a/b — the first fraction, e.g. 3/4
  • c/d — the second fraction, e.g. 1/3
  • b × d — a denominator both fractions divide into, e.g. 12

Multiplying the denominators always gives a common denominator, though not always the lowest one. The calculator uses the lowest common multiple, so 1/4 + 1/6 goes over 12 rather than 24 and the answer needs less reducing at the end.

Division is multiplication by the reciprocal — the second fraction turned upside down. That is why 1/2 ÷ 3/5 and 1/2 × 5/3 give the same 5/6.

Worked examples

The four operations, worked through
SumMiddle stepAnswer
3/5 + 1/5same denominator, add the tops4/5
3/4 + 1/39/12 + 4/1213/12 = 1 1/12
2/3 × 5/6(2 × 5) / (3 × 6)10/18 = 5/9
1/2 ÷ 3/51/2 × 5/35/6
2 3/4 − 1/211/4 − 2/49/4 = 2 1/4

The last row shows a mixed number entering the sum: 2 3/4 becomes 11/4 first, because2 × 4 + 3 = 11. Everything after that is ordinary fraction arithmetic.

Frequently asked questions

How do I add fractions with different denominators?

Rewrite both over a common denominator, then add the numerators and leave the denominator alone. For 3/4 + 1/3 the common denominator is 12, giving 9/12 + 4/12 = 13/12. The calculator shows that middle step, because it is the one that gets skipped.

How do I multiply and divide fractions?

To multiply, multiply the numerators together and the denominators together: 2/3 × 5/6 = 10/18, which reduces to 5/9. To divide, flip the second fraction and multiply instead: 1/2 ÷ 3/5 becomes 1/2 × 5/3 = 5/6. Neither needs a common denominator.

Can I enter mixed numbers and whole numbers?

Yes. Type a mixed number with a space, as in 2 3/4, and a whole number on its own. A whole number is treated as itself over 1, which is why 3 × 5/7 works out as 3/1 × 5/7 = 15/7.

Why is my answer shown as a different fraction from the one I expected?

Because it is reduced to lowest terms. 10/18 and 5/9 are the same number, and the calculator always shows the simplest form. The working line keeps the unreduced version so you can see where the answer came from.

Are the results exact?

Yes. The sum is done in whole numbers, not decimals, so 1/3 + 1/6 comes out as exactly 1/2. Floating-point arithmetic cannot represent a third, which is why a fraction calculator has to work this way rather than converting first.

What happens if I divide by zero?

The result reads "—" and the working line says "Cannot divide by zero". Dividing by zero has no answer, and a calculator that returned a number there would be wrong rather than helpful. Enter a non-zero second fraction and the answer reappears.