Fraction Calculator is a powerful math tool designed to simplify arithmetic with rational numbers. Whether you need to add fractions with different denominators or divide complex ratios, this calculator handles the cross-multiplication and reduction automatically. This tool 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. This fraction solver simplifies the result by dividing by the GCD. Multiplication: multiply numerators together and denominators together, then reduce. Division: multiply the first fraction by the reciprocal of the second, then reduce. The calculator uses BigInt to handle large denominators exactly, ensuring your multiply fractions results are always precise.
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.
For other mathematical needs, check out our Average Calculator, Percentage Calculator, and GCD/LCM Calculator. Bookmark this page for the next time you need a reliable Fraction Calculator.