Fraction Addition & Subtraction Calculator
Add or subtract two fractions using a common denominator, then see the answer reduced to lowest terms and as a mixed number.
How it works
a/b ± c/d = (a·d ± c·b) ÷ (b·d), then divide top and bottom by their GCD
To add or subtract fractions they need the same denominator. The reliable way is to use the product of the two denominators as a common denominator, rescale each numerator to match, then add or subtract the numerators. Finally divide the numerator and denominator by their greatest common divisor to reduce the fraction to lowest terms.
Worked example
For 1/2 + 1/3, the common denominator is 2·3 = 6. Rescale to 3/6 + 2/6 = 5/6. Since GCD(5, 6) = 1, the answer is already in lowest terms: 5/6 ≈ 0.8333.
Frequently asked questions
Do I have to find the least common denominator?
No. Multiplying the two denominators always gives a valid common denominator. It may not be the smallest one, but reducing the final fraction by its GCD gives exactly the same answer as using the least common denominator.
How do I subtract when the second fraction is larger?
The calculator handles it automatically — the result is simply negative. For example 1/3 − 1/2 = −1/6.
Can I enter negative fractions?
Yes. Put the minus sign on the numerator (for example −3 over 4). The sign is carried through the arithmetic and shown on the numerator of the reduced answer.
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This calculator is for educational purposes. Double-check important results before acting on them.