Fractions Explained: The Four Operations

Fractions represent parts of a whole. Working with them involves a handful of rules that feel mechanical at first but follow a clear logic. Once the rules click, fraction arithmetic becomes straightforward — and the fraction calculator confirms your work instantly.

Adding and subtracting fractions

To add or subtract fractions, you need a common denominator. Find the LCM of the two denominators, convert each fraction to an equivalent fraction with that denominator, then add or subtract the numerators. For 1/3 + 1/4: LCM of 3 and 4 is 12. Rewrite as 4/12 + 3/12 = 7/12.

Multiplying and dividing fractions

Multiplication is the simplest fraction operation: multiply numerators together and denominators together. For 2/3 × 3/5 = 6/15 = 2/5. Division flips the second fraction (takes its reciprocal) and then multiplies: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

Simplifying the result

After calculating, always simplify by dividing numerator and denominator by their GCD (greatest common divisor). For 6/15, the GCD is 3, so 6/15 = 2/5. The fraction calculator simplifies automatically and also converts results to mixed numbers when the numerator is larger than the denominator.