Working with fractions
A fraction shows a part of a whole as a numerator over a denominator. This calculator adds, subtracts, multiplies and divides fractions, mixed numbers and decimals, and always returns the answer in lowest terms with the mixed-number and decimal forms alongside.
It also shows the working, which is useful for homework: how the common denominator was found and how the final fraction was simplified.
How it is calculated
a/b + c/d = (ad + bc) ÷ bd
a/b × c/d = ac ÷ bd
a/b ÷ c/d = a/b × d/c
Worked example
1/2 + 1/3
- Common denominator
- 6
- Rewrite
- 3/6 + 2/6
- Add the tops
- 5/6
- As a decimal
- 0.8(3) repeating
- As a mixed number
- 5/6
Handy rules to remember
- To add or subtract, the denominators must match, so find a common denominator first.
- To multiply, multiply straight across. To divide, flip the second fraction and multiply.
- Simplify by dividing top and bottom by their greatest common factor.
- A mixed number such as 1 3/4 equals the improper fraction 7/4.
Converting a mixed number
To turn 1 3/4 into an improper fraction by hand: multiply the whole number by the denominator and add the numerator (1 × 4 + 3 = 7), keeping the same denominator — 7/4. This calculator accepts either form directly, so you don't need to convert first.