Fraction Calculator
Add, subtract, multiply or divide two fractions, including mixed numbers such as 1 1/2. The answer is always reduced to lowest terms and also given as a mixed number, a decimal and a percentage, with the working shown.
Optional, for a mixed number
Optional, for a mixed number
Result
Enter both fractions to see the result.
The calculation runs in this browser tab. Nothing you enter is uploaded, saved or logged.
What is a fraction?
A fraction a/b represents a parts out of b equal parts of a whole: the numerator a counts the parts and the denominator b says how many make a whole. 3/4 is three quarters. A fraction whose numerator is larger than its denominator (7/4) is improper, and can be written as a mixed number, a whole number plus a proper fraction: 1 3/4.
Fractions can be exact where decimals cannot: 1/3 has no finite decimal form (0.333… forever) but is perfectly exact as a fraction. The calculator therefore works on the fractions themselves and converts to a decimal only for display.
How to use the Fraction Calculator
- Enter the first fraction: a numerator and a denominator. For a mixed number, also fill in the whole number (1 1/2 is whole 1, numerator 1, denominator 2).
- Choose the operation: add, subtract, multiply or divide.
- Enter the second fraction.
- Read the result in lowest terms, with the mixed number, decimal, percentage and working. Copy result copies the fraction.
Formula
- Add or subtract
- a/b ± c/d = (a × d ± c × b) ÷ (b × d), then reduce; or use the least common denominator
- Multiply
- a/b × c/d = (a × c) ÷ (b × d)
- Divide
- a/b ÷ c/d = a/b × d/c = (a × d) ÷ (b × c)
- Mixed number to fraction
- w n/d = (w × d + n) ÷ d
To add or subtract, the calculator rewrites both fractions over the least common multiple of the denominators, which keeps the numbers small. The working line shows this step.
Every result is reduced by dividing the numerator and denominator by their greatest common divisor.
Worked example
Adding 3/4 and 5/6. The least common denominator is 12, so 9/12 + 10/12 = 19/12. These are the results the calculator gives:
| Question | Result |
|---|---|
| Input: First fraction – numerator | 3 |
| Input: First fraction – denominator | 4 |
| Input: Operation | Add (+) |
| Input: Second fraction – numerator | 5 |
| Input: Second fraction – denominator | 6 |
| Result | 19/12 |
| Mixed number | 1 7/12 |
| Decimal | ≈ 1.583333 |
| Percentage | ≈ 158.333333% |
| Working | 3/4 + 5/6 = 9/12 + 10/12 = 19/12 |
Assumptions and limits
- Numerators, denominators and whole numbers must be whole numbers, up to 30 digits. Denominators must be 1 or more.
- For a negative mixed number, put the minus sign on the whole number and keep the numerator positive: −1 1/2 means −(1 + 1/2) = −3/2.
- Dividing by a fraction equal to 0 is impossible and is reported as an error.
- Decimals are not accepted as numerators or denominators. Convert them first: 0.25 is 25/100.
- The decimal and percentage shown for fractions that do not end (1/3, 5/6) are rounded to 6 decimals and marked with ≈; the fraction itself is exact.
Frequently asked questions
How do I add fractions with different denominators?
Rewrite both over a common denominator, add the numerators and keep the denominator, then simplify. For 3/4 + 5/6, the common denominator is 12: 9/12 + 10/12 = 19/12, which is 1 7/12.
How do I multiply and divide fractions?
To multiply, multiply the numerators and the denominators: 2/3 × 3/4 = 6/12 = 1/2. To divide, multiply by the reciprocal of the second fraction: 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.
How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator and keep the denominator: 2 1/4 = (2 × 4 + 1)/4 = 9/4. The calculator does this when you fill in the whole-number field.
How do I simplify a fraction?
Divide the numerator and the denominator by their greatest common divisor. 18/24 has a GCD of 6, giving 3/4. The calculator always returns the simplified form.
How do I turn a fraction into a decimal or a percentage?
Divide the numerator by the denominator for the decimal (3/8 = 0.375), then multiply by 100 for the percentage (37.5%). Both are shown under the result.
Why is a decimal sometimes shown with ≈?
Fractions such as 1/3 or 5/6 have decimals that never end, so any decimal is rounded. The fraction shown as the result is exact, which is why it is the main answer.