How this fraction calculator works
A fraction is just a numerator over a denominator — a way of writing part of a whole. This calculator works with whole numbers internally, so the answers are exact: there is no floating-point rounding hiding in the fraction itself. You can also add a whole-number part to either fraction to enter a mixed number such as 1 1/2.
For addition and subtraction it puts both fractions over a common denominator, combines the numerators, then reduces. For multiplication it multiplies numerators and denominators directly; for division it multiplies by the reciprocal of the second fraction. In every case the final step is to divide the numerator and denominator by their greatest common divisor (GCD) so the result is in lowest terms, and to express it as a mixed number and a decimal.
Reference note: a denominator of 0 is undefined, so the calculator reports an error instead of a number. Dividing by a fraction whose numerator is 0 is likewise undefined and handled the same way. Negative numerators or whole parts are allowed and the sign is normalised onto the numerator.
Common fraction ↔ decimal equivalents
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | ≈0.333 | ≈33.3% |
| 2/3 | ≈0.667 | ≈66.7% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.1 | 10% |
Frequently asked questions
- How do I add fractions?
- Give both fractions the same denominator, add the numerators, then keep that common denominator. For example 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6. Finally reduce to lowest terms if possible.
- How do I multiply or divide fractions?
- To multiply, multiply the numerators together and the denominators together: 2/3 × 3/4 = 6/12 = 1/2. To divide, flip the second fraction and multiply: 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3.
- How do I simplify a fraction?
- Divide the numerator and denominator by their greatest common divisor (GCD). For example 6/8 has a GCD of 2, so dividing both by 2 gives 3/4, which is in lowest terms.
- How do I convert a decimal to a fraction?
- Write the decimal over a power of ten matching its decimal places, then reduce. For example 0.75 = 75/100 = 3/4. The converter above does this automatically.
- What is a mixed number?
- A mixed number combines a whole number and a proper fraction, such as 1 1/2. It equals an improper fraction — 1 1/2 is the same as 3/2 — and this calculator accepts and returns both forms.
- How do I subtract fractions with different denominators?
- Convert both fractions to a common denominator, subtract the numerators, then reduce. For example 3/4 − 1/6 becomes 9/12 − 2/12 = 7/12, already in lowest terms.