Fraction calculator
Add, subtract, multiply, and divide fractions with exact reduced answers and an equal-parts preview.
How it works & useful details
How it works & limits
Enter integer numerators and nonzero denominators of up to 30 digits. Negative denominators are normalized and results are reduced using exact integer arithmetic. Division by a zero fraction is undefined.
The reduced fraction is exact. The optional decimal preview uses floating-point arithmetic rounded to 12 significant digits; it is not an exact decimal expansion.
Your working space
Change the values to explore the preview. Use the action below to create a copyable, downloadable result. All calculations stay on this device; refreshing clears your work.
About this tool
Fraction calculator adds, subtracts, multiplies, and divides fractions and returns an exact reduced answer, with an equal-parts preview that makes the operation visible. It handles the awkward cases, including negative fractions and zero denominators.
Results stay as fractions rather than decimals, so nothing is lost to rounding. Everything is computed locally in the page.
How to use it
- Enter the two fractions.
- Choose the operation.
- Read the exact reduced result, including any whole part.
- Check the equal-parts preview to see why the result is correct.
Worked example
To add 3/4 and 5/6, first find a common denominator. The least common multiple of 4 and 6 is 12, so 3/4 = 9/12 and 5/6 = 10/12. Their sum is 19/12, which is already in lowest terms because 19 is prime. As a mixed number that is 1 7/12, or about 1.583333.
The calculator returns 19/12 exactly, plus a decimal approximation rounded to 12 significant digits. Many fractions, such as 1/3 or 19/12, have decimal expansions that never end, which is why the fraction is the exact answer and the decimal is only a preview.
The four operations in one place
- Add or subtract: convert to a common denominator, then add or subtract the numerators.
- Multiply: multiply numerators together and denominators together: 2/3 × 9/10 = 18/30 = 3/5.
- Divide: multiply by the reciprocal of the second fraction: 2/3 ÷ 4/9 = 2/3 × 9/4 = 18/12 = 3/2.
- Reduce: divide numerator and denominator by their greatest common divisor.
Because the tool uses exact integer arithmetic, numerators and denominators with up to 30 digits stay exact. Ordinary floating-point arithmetic would start losing digits after about 15 to 17 significant figures.
Frequently asked questions
Can the result be a decimal too?
The exact fraction is the primary result; the preview shows the value in context, and you can convert to a decimal yourself if needed.
What happens with a zero denominator?
It is rejected with an explanation, since division by zero has no defined value.
Are mixed numbers supported?
Enter improper fractions or whole parts explicitly; the calculator reduces the result and shows any whole part.
Can I enter negative fractions?
Yes. Put the minus sign on the numerator or the denominator. A negative denominator is normalized so the sign appears on the numerator in the result.