Fraction Calculator
Add, subtract, multiply or divide two fractions.
This tool runs entirely in your browser. Your files are never uploaded to a server.
What this calculator does
Adds, subtracts, multiplies, or divides two fractions and simplifies the result to its lowest terms using the greatest common divisor.
How to use it
Enter a numerator and denominator for each fraction, choose an operation (+, −, ×, ÷), and the simplified result appears immediately. A whole-number result (denominator of 1) displays as a single number instead of a fraction.
Worked example
With the defaults of 1/2 + 1/3, the calculator cross-multiplies to (1×3 + 1×2) / (2×3) = 5/6, which is already in lowest terms since 5 and 6 share no common factor besides 1.
Formulas
Addition/subtraction: a/b ± c/d = (ad ± bc) / bd. Multiplication: a/b × c/d = ac/bd. Division: a/b ÷ c/d = ad/bc (flip the second fraction and multiply). Every result is then reduced by dividing both the numerator and denominator by their greatest common divisor (GCD), found using the Euclidean algorithm.
Simplifying with the GCD
Reducing a fraction to lowest terms means dividing the numerator and denominator by the largest number that evenly divides both. For example, 6/8 and 3/4 represent the same value, but 3/4 is in lowest terms because 3 and 4 share no common factor — the calculator always returns this reduced form rather than the raw cross-multiplied result.
Limitations
A denominator of zero on either input, or a zero numerator on the second fraction in division, has no valid answer, so the calculator shows an error instead of a result in those cases. Negative numerators or denominators are accepted and handled with correct sign rules, but this tool works with simple numeric fractions only, not mixed numbers or fractions containing variables.
Scope, sources and privacy
Fraction arithmetic and simplification via the greatest common divisor are standard results taught in arithmetic worldwide. Calculations run locally in your browser; the values you enter are never uploaded.
Frequently Asked Questions
- Is the result automatically simplified?
- Yes, the result is reduced to its lowest terms using the greatest common divisor.
- What happens if I try to divide by zero?
- Division is undefined if the second fraction's numerator is zero; the calculator won't show a result in that case.
- Can I enter negative fractions?
- Yes, negative numerators and denominators are supported.