Fractions Operations Calculator
Add, subtract, multiply, and divide fractions — with automatically simplified results, mixed numbers, decimal equivalents, and step-by-step working.
Frequently Asked Questions
How do you add or subtract fractions?
Bring both fractions to a common denominator, then add or subtract the numerators: a/b ± c/d = (a×d ± c×b) / (b×d), then simplify. Example: 1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6. Using the least common denominator keeps numbers smaller, but any common denominator works — the final simplification gives the same answer.
How do you multiply and divide fractions?
Multiplying is direct: a/b × c/d = (a×c)/(b×d) — multiply numerators together and denominators together. Dividing means multiplying by the reciprocal (invert and multiply): a/b ÷ c/d = a/b × d/c = (a×d)/(b×c). Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
How do you simplify a fraction?
Divide numerator and denominator by their greatest common divisor (GCD). For 10/12, the GCD of 10 and 12 is 2, so 10/12 = 5/6. A fraction is fully simplified (in lowest terms) when the GCD is 1. This calculator simplifies every result automatically and shows the pre-simplified value.
What is a mixed number versus an improper fraction?
An improper fraction has a numerator larger than its denominator (7/4); a mixed number combines a whole number and a proper fraction (1 3/4). Both express the same value. To convert, divide: 7 ÷ 4 = 1 remainder 3 → 1 3/4. This calculator shows both forms plus the decimal.