Fraction Calculator
Perform arithmetic operations (add, subtract, multiply, divide) on fractions or simplify a single fraction.
Enter fractions and select an operation.
What This Calculator Does
Fraction arithmetic gets error-prone fast once denominators stop matching, and simplifying the result afterward is easy to forget. This tool takes two fractions, applies whichever operation you choose — addition, subtraction, multiplication, or division — and returns the result already reduced to lowest terms, or it can simplify a single fraction on its own without a second one involved at all.
How to Use It
Enter Numerator 1 and Denominator 1, pick an Operation, and — unless that operation is Simplify Fraction — fill in Numerator 2 and Denominator 2 as well. Mixed numbers aren't accepted directly: convert them to an improper fraction first, so 1½ becomes 3/2 before you type it in. Whatever operation you run, the answer that comes back is already fully simplified, so you never need a separate step to reduce it afterward.
The Formula
Addition and subtraction find a common denominator before combining the numerators; multiplication multiplies numerators together and denominators together; division multiplies the first fraction by the reciprocal of the second. Every result is then reduced by dividing both numerator and denominator by their greatest common divisor, which is what "simplify" actually does under the hood, whether you invoke it directly or it runs automatically at the end of another operation.
A Worked Example
½ + ½: both fractions already share a denominator, so the numerators add directly to give 2/2, which simplifies down to 1/1 — displayed as a whole number result. A case that actually needs a common denominator: 1/3 + 1/6. The least common denominator is 6, so 1/3 becomes 2/6, and 2/6 + 1/6 = 3/6, which simplifies to 1/2. And for a division example, 1/2 ÷ 1/4 multiplies by the reciprocal: 1/2 × 4/1 = 4/2, which simplifies to 2/1 — a whole number again, since dividing by a smaller fraction naturally produces a larger result.
FAQ
- Can I enter mixed numbers?
- Not directly — enter each fraction as a numerator and denominator. To use a mixed number, convert it to an improper fraction first (e.g. enter 1½ as 3/2).
- Does it simplify fractions automatically?
- Yes, all results are automatically simplified to their lowest terms.