About this calculator
Add, subtract, multiply or divide two fractions or mixed numbers and get the answer in its simplest form, as a mixed number and as a decimal, with each step of the working shown.
For a mixed number such as 1½, put 1 in the whole number box and 1 and 2 in the top and bottom boxes. Everything is calculated exactly using whole numbers, so there are no rounding errors in the fraction answer.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
1/2 + 1/3
- Answer
- 5/6
- As a decimal
- 0.833333 (rounded)
1/2 + 1/3 = 5/6.
Show the working
- Write both as fractions: 1/2 and 1/3.
- Give them a common bottom number (the lowest common multiple of 2 and 3 is 6): 3/6 and 2/6.
- Add the top numbers: 3 + 2 = 5, over 6.
3/4 − 5/6
- Answer
- -1/12
- As a decimal
- -0.083333 (rounded)
3/4 − 5/6 = -1/12.
Show the working
- Write both as fractions: 3/4 and 5/6.
- Give them a common bottom number (the lowest common multiple of 4 and 6 is 12): 9/12 and 10/12.
- Subtract the top numbers: 9 − 10 = -1, over 12.
2/3 × 3/4
- Answer
- 1/2
- As a decimal
- 0.5
2/3 × 3/4 = 1/2.
Show the working
- Write both as fractions: 2/3 and 3/4.
- Multiply the top numbers (2 × 3 = 6) and the bottom numbers (3 × 4 = 12).
- Simplify by dividing top and bottom by their greatest common factor, 6: 1/2.
1 1/2 ÷ 3/4
- Answer
- 2
3/2 ÷ 3/4 = 2.
Show the working
- Write both as fractions: 3/2 and 3/4.
- Dividing by a fraction means flipping it and multiplying: 3/2 × 4/3.
- Multiply across: 12 over 6.
- Simplify by dividing top and bottom by their greatest common factor, 6: 2.
How each operation works
- Adding and subtracting: the bottom numbers must match first. Find a common bottom number, convert both fractions, then add or subtract the top numbers. 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
- Multiplying: multiply the top numbers together and the bottom numbers together. 2/3 × 3/4 = 6/12 = 1/2.
- Dividing: flip the second fraction upside down and multiply. 3/2 ÷ 3/4 = 3/2 × 4/3 = 12/6 = 2.
Simplifying and mixed numbers
To simplify a fraction, divide the top and bottom by their greatest common factor. 12/18 divides by 6 to give 2/3. A fraction is in its simplest form when the top and bottom have nothing in common except 1.
A mixed number like 2½ is a whole number plus a fraction. To turn it into a top-heavy fraction, multiply the whole number by the bottom and add the top: 2 × 2 + 1 = 5, so 2½ = 5/2. For a negative mixed number, put the minus sign on the whole number only: −1½ means −(1 + ½) = −3/2.
The most common mistake
Adding the tops and adding the bottoms: 1/2 + 1/3 is not 2/5. Two fifths is smaller than a half, so that can't be right. The bottom number says the size of each piece, and pieces of different sizes can't be added until you cut them into matching pieces, which is exactly what the common bottom number does.
Frequently asked questions
How do I add fractions with different denominators?
Find a common denominator (the lowest common multiple of the bottom numbers), convert each fraction to it, add the top numbers and simplify. For 1/2 + 1/3 the common denominator is 6, giving 3/6 + 2/6 = 5/6.
How do I divide by a fraction?
Flip the second fraction and multiply. Dividing by 3/4 is the same as multiplying by 4/3.
How do I simplify a fraction?
Divide the top and bottom by their greatest common factor. The GCF & LCM calculator on this site can find it.
How do I enter a mixed number?
Put the whole number in the whole number box and the fractional part in the top and bottom boxes. For 2 3/4, use 2, 3 and 4.
Why does the decimal say “rounded”?
Many fractions, like 1/3, have decimals that never end. The fraction answer is exact, and the decimal is shortened to six places.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.