How to use the Fraction Calculator
Enter the numerator and denominator for each fraction, choose your operation from the dropdown, and the result updates live. The answer appears as a simplified fraction and as a decimal.
- Add (+): finds a common denominator and adds the numerators.
- Subtract (-): same process, subtracts the second numerator from the first.
- Multiply (x): multiplies the numerators together and the denominators together.
- Divide (/): flips the second fraction (takes the reciprocal) and multiplies.
The tool reduces the result using the greatest common divisor (GCD), so 4/8 becomes 1/2 automatically.
How fraction arithmetic works
A quick reference for the four operations:
| Operation | Method | Example | Result |
|---|
| Add | (a/b) + (c/d) = (ad + bc) / bd | 1/2 + 1/3 | 5/6 |
| Subtract | (a/b) - (c/d) = (ad - bc) / bd | 3/4 - 1/4 | 1/2 |
| Multiply | (a/b) x (c/d) = ac / bd | 2/3 x 3/4 | 1/2 |
| Divide | (a/b) / (c/d) = ad / bc | 1/2 / 1/4 | 2 |
After the operation, divide both the numerator and denominator by their GCD to simplify.
What is the greatest common divisor?
The GCD of two numbers is the largest integer that divides both of them evenly. For 8 and 12, the divisors of 8 are 1, 2, 4, 8 and the divisors of 12 are 1, 2, 3, 4, 6, 12, so the GCD is 4. Dividing numerator and denominator by their GCD reduces the fraction to its simplest form: 8/12 becomes 2/3. The calculator uses Euclid's algorithm, which is fast even for large numbers and has been solving this problem since roughly 300 BC.
Frequently asked questions
How do I add fractions with different denominators?
Multiply the first numerator by the second denominator and the second numerator by the first denominator, add the results, and use the product of the two denominators as the new denominator. Then simplify. For example, 1/2 + 1/3 = (1x3 + 1x2) / (2x3) = 5/6.
How do I divide fractions?
Flip the second fraction to get its reciprocal, then multiply. Dividing 3/4 by 1/2 becomes 3/4 x 2/1 = 6/4 = 3/2.
What does simplify a fraction mean?
A simplified (or reduced) fraction has no common factor in the numerator and denominator other than 1. To simplify, divide both by their greatest common divisor. 6/9 divided by 3 gives 2/3, which cannot be reduced further.
Is this fraction calculator free?
Yes, completely free. No account needed, nothing is sent to a server. All arithmetic happens instantly in your browser.