Why do I need a common denominator to add fractions?

Fractions must share the same denominator before adding or subtracting because you can only combine parts that are the same size; this calculator converts them automatically.

How is the simplified fraction calculated?

The calculator finds the greatest common divisor of the numerator and denominator and divides both by it to reduce the fraction to its lowest terms.

Fraction Calculator

Add, subtract, multiply and divide fractions with simplified results

What is the Fraction Calculator?

The Fraction Calculator performs the four basic operations on fractions — addition, subtraction, multiplication and division — and returns the raw result, the simplified (lowest-terms) fraction, and its decimal equivalent.

How to Use the Fraction Calculator

Enter the first fraction as numerator and denominator.
Choose an operation — add, subtract, multiply or divide.
Enter the second fraction and click Calculate.

How Fraction Operations Work

Addition/Subtraction: a/b ± c/d = (a×d ± c×b) / (b×d)
Multiplication: a/b × c/d = (a×c) / (b×d)
Division: a/b ÷ c/d = (a×d) / (b×c)

Example

1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6. Since 5 and 6 share no common factor, 5/6 is already in its simplest form (decimal: 0.8333).

Frequently Asked Questions

Fractions represent parts of a whole divided into equal pieces. You can only add or subtract pieces that are the same size, so the denominators must match — this calculator does that conversion for you automatically.

The calculator finds the greatest common divisor (GCD) of the numerator and denominator and divides both by it, reducing the fraction to its lowest terms.