Fraction arithmetic requires finding common denominators, cross-multiplying, and reducing results to lowest terms — error-prone by hand, especially with large numbers. This calculator performs exact fraction arithmetic and always returns results in fully reduced form, showing the steps and both the improper and mixed number representations.
Addition/Subtraction: find the LCM of the denominators, convert both fractions, then add/subtract numerators. Reduce by dividing by GCD. Multiplication: multiply numerators together and denominators together, then reduce. Division: multiply the first fraction by the reciprocal of the second (flip the second fraction), then reduce. The calculator uses BigInt to handle large denominators (like LCMs of large numbers) exactly.
Find the lowest common denominator (LCM of the two denominators). Convert each fraction to that denominator, then add the numerators. Example: 1/3 + 1/4 → LCM=12 → 4/12 + 3/12 = 7/12.
Dividing both numerator and denominator by their Greatest Common Divisor (GCD) until no common factor remains. 12/18 reduces to 2/3 because GCD(12,18)=6; 12÷6=2, 18÷6=3.
An improper fraction has a numerator ≥ denominator (e.g. 7/3). A mixed number combines a whole number and a proper fraction (e.g. 2⅓). They are equivalent — 7/3 = 2⅓.
Yes — enter a negative numerator (e.g. -3/4). The calculator handles negative values correctly in all four operations.
See also the Average Calculator, Percentage Calculator, and the GCD/LCM Calculator.