Fraction Calculator

Each operation on fractions follows its own rule, and this tool applies the correct one automatically based on what you select:

• Addition and subtraction require a common denominator first. The tool cross-multiplies to get a shared denominator: a/b ± c/d = (a×d ± c×b) / (b×d).
• Multiplication is the simplest — multiply the numerators together and the denominators together: a/b × c/d = (a×c) / (b×d).
• Division multiplies by the reciprocal of the second fraction (flip its numerator and denominator, then multiply): a/b ÷ c/d = a/b × d/c = (a×d) / (b×c).

After computing the raw result, the tool reduces it to simplest formby dividing both the numerator and denominator by their greatest common divisor (GCD) — the largest number that evenly divides both. A fraction is in simplest form when the GCD of its numerator and denominator is 1, meaning it can't be reduced any further.

If the simplified result has a numerator larger than its denominator (an improper fraction), the tool also shows it as a mixed number — a whole number plus a proper fraction, like 1 1/2 instead of 3/2. Both forms represent the same value; the mixed number is often easier to read at a glance.

Worked example:adding 1/2 + 1/3: common denominator is 2×3 = 6, so 1/2 = 3/6 and 1/3 = 2/6. Adding gives 3/6 + 2/6 = 5/6, which is already in simplest form (GCD of 5 and 6 is 1). As a decimal, 5/6 ≈ 0.83. Since 5 is less than 6, there's no mixed-number form for this particular result.