About this tool
This calculator performs the four basic fraction operations and always reduces the result to its simplest form using the greatest common divisor. Everything runs locally in your browser.
How to use the Fraction Calculator
- Enter the first fraction as numerator over denominator.
- Choose an operation — add, subtract, multiply, or divide.
- Enter the second fraction — the result updates instantly, already simplified.
How each operation works
Adding and subtracting fractions requires a common denominator first — this tool finds it automatically by converting both fractions to the least common multiple of their denominators, then adds or subtracts the numerators. Multiplying fractions is the simplest operation: multiply the numerators together and the denominators together. Dividing by a fraction is the same as multiplying by its reciprocal (flipping the numerator and denominator) — this tool handles that flip automatically.
Worked example
Adding 1/2 and 3/4: the least common denominator is 4, so 1/2 becomes 2/4. Adding the numerators gives 2/4 + 3/4 = 5/4, which is already in lowest terms (5 and 4 share no common factors), so the final answer is 5/4 — or 1¼ as a mixed number, shown here as its decimal equivalent, 1.25.
Things to watch out for
A denominator of zero isn't a valid fraction, since division by zero is undefined — the calculator won't produce a result if either denominator is set to zero. Negative fractions work correctly when entered with a negative numerator (like -1/2) rather than a negative denominator, which is the standard mathematical convention.
Frequently asked questions
The result is automatically simplified to its lowest terms — for example, 4/8 is simplified to 1/2, since both represent the same value. This matches standard math convention for a final answer.
Enter a whole number as itself over 1 (like 5 as "5/1"), or as just the numerator with the denominator left at 1. Mixed numbers (like 2½) should be converted to an improper fraction first (2½ becomes 5/2) before entering them.
A fraction represents division, and dividing by zero is undefined in standard arithmetic — there's no number that answers "how many zeros fit into this amount." A denominator of zero isn't a valid fraction.