Perform addition, subtraction, multiplication or division on two fractions, with the result automatically simplified.
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Adding and subtracting fractions requires a common denominator, achieved by cross-multiplying: a/b + c/d = (a×d + c×b) / (b×d). Multiplying fractions is simpler: multiply numerators together and denominators together. Dividing by a fraction is the same as multiplying by its reciprocal.
After calculating the result, this tool automatically simplifies the fraction by dividing both numerator and denominator by their greatest common divisor, so results like 4/8 are shown as the simplified 1/2.
Adding 1/2 + 1/3: cross-multiplying gives (1×3 + 1×2) / (2×3) = (3 + 2) / 6 = 5/6. Since 5 and 6 share no common factor besides 1, the result is already in simplest form: 5/6, or 0.8333 as a decimal.
Adding or subtracting numerators and denominators straight across (1/2 + 1/3 ≠ 2/5), fractions need a common denominator first, this calculator handles that automatically via cross-multiplication.
Forgetting that dividing by a fraction means multiplying by its reciprocal, so 1/2 ÷ 1/3 is 1/2 × 3/1 = 3/2, not 1/2 × 1/3.
Expecting an unsimplified result like 4/8 instead of 1/2, this tool always reduces to lowest terms, which is standard practice but can look different from an intermediate step shown in a textbook.
Yes, this calculator supports negative numerators and denominators for all four operations.
Simplifying to lowest terms is standard mathematical practice and makes the result easier to read and use in further calculations.
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