Fraction Calculator – Add, Subtract, Multiply, Divide
Perform addition, subtraction, multiplication, and division on fractions. Results are automatically simplified to lowest terms with step-by-step explanations.
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Fraction Arithmetic Rules
Addition and subtraction require a common denominator: find the LCM (Least Common Multiple) of both denominators, convert fractions, then add or subtract numerators. Multiplication is simpler: multiply numerators together and denominators together. Division: multiply by the reciprocal (flip the second fraction and multiply).
Simplifying Fractions (Reducing to Lowest Terms)
Divide both numerator and denominator by their GCD (Greatest Common Divisor). For 12/18: GCD(12, 18) = 6. 12÷6 = 2, 18÷6 = 3. Simplified: 2/3. The Euclidean algorithm efficiently finds GCD: GCD(a, b) = GCD(b, a mod b), repeating until remainder is 0.
Mixed Numbers and Improper Fractions
An improper fraction has a numerator larger than the denominator (7/3). A mixed number combines a whole number and fraction (2⅓). To convert: divide numerator by denominator. 7 ÷ 3 = 2 remainder 1, so 7/3 = 2⅓. To reverse: multiply whole number by denominator and add numerator: 2×3+1 = 7, over 3 = 7/3.