About the Fraction Calculator
This fraction calculator works out the sum, difference, product or quotient of two fractions and shows the result in simplest form, as a mixed number and as a decimal. The step-by-step solution shows how to find a common denominator, how to divide by multiplying by the reciprocal, and how to simplify at the end — handy for checking homework or revising the rules.
Decimals that never end, such as 1/3, are shown with the repeating part in brackets: 0.(3).
How to use
- Enter the numerator (top) and denominator (bottom) of the first fraction. For a mixed number, put the whole number in the box on the left.
- Choose an operation: + − × ÷.
- Enter the second fraction. The answer and the working appear instantly.
- To use a whole number, type it in the left box and leave the numerator and denominator empty.
How to add, subtract, multiply and divide fractions
| Operation | Method | Example |
|---|---|---|
| Add / subtract | Rewrite over the least common denominator, then combine the numerators | 1/2 + 1/3 = 3/6 + 2/6 = 5/6 |
| Multiply | Multiply numerators and denominators | 2/3 × 3/4 = 6/12 = 1/2 |
| Divide | Multiply by the reciprocal of the second fraction | 3/4 ÷ 3/8 = 3/4 × 8/3 = 2 |
| Simplify | Divide top and bottom by the greatest common factor | 6/12 → 1/2 (GCF 6) |
Mixed numbers and improper fractions
A mixed number combines a whole number and a proper fraction (e.g. 2 1/4). An improper fraction has a numerator greater than or equal to its denominator (e.g. 9/4). To convert a mixed number, use whole × denominator + numerator as the new numerator: 2 1/4 → (2 × 4 + 1)/4 = 9/4. To go back, divide the numerator by the denominator: the quotient is the whole number and the remainder is the new numerator.
Always convert mixed numbers to improper fractions before multiplying or dividing.
Converting fractions to decimals
If the denominator of a fraction in simplest form has no prime factors other than 2 and 5, the decimal terminates (3/8 = 0.375). Otherwise it repeats (1/6 = 0.1666…). The calculator puts the repeating block in brackets: 1/6 = 0.1(6), 1/7 = 0.(142857).
FAQ
How do I enter a negative fraction?
Put a minus sign in front of the whole number or the numerator. For example, −2 1/4 is entered as whole number -2, numerator 1, denominator 4 and is treated as −(2 + 1/4).
Why use the least common denominator?
Multiplying the two denominators also works, but the numbers get bigger and you have more simplifying to do. The least common denominator keeps the numbers as small as possible.
Can the answer be a whole number?
Yes. If the denominator becomes 1 after simplifying, the result is shown as a whole number, e.g. 3/4 ÷ 3/8 = 2.
Does it work with very large numbers?
Each box accepts up to 15 digits. The calculation uses exact integer arithmetic, so there are no rounding errors. Repeating decimals are shown when the repeating block is at most 60 digits long.