Fraction Calculator

A fraction whose numerator and denominator share no common factor other than 1, so it cannot be simplified further. Dividing both by their greatest common divisor (GCD) reduces a fraction: 6/20 divided by the GCD 2 becomes 3/10. This calculator uses the Euclidean algorithm to find the GCD and always shows results in lowest terms.

To add or subtract fractions with different denominators, use the least common multiple (LCM) of the denominators as the common denominator. Multiply each fraction's numerator and denominator by the same factor so the denominators match, then combine the numerators. For example, 1/2 + 1/3 uses the common denominator 6: 3/6 + 2/6 = 5/6.

An improper fraction has a numerator greater than or equal to its denominator (e.g. 5/3), while a mixed number combines a whole number with a proper fraction (e.g. 1 2/3). To convert, divide the numerator by the denominator: the quotient becomes the whole part and the remainder becomes the new numerator. Since 5 ÷ 3 = 1 remainder 2, 5/3 = 1 2/3.

The arithmetic is the same — only sign rules are added. In multiplication and division, an odd number of negative values gives a negative result, and an even number gives a positive one. By convention the sign is written on the numerator (-3/4) and the denominator is kept positive; this calculator moves any negative sign from the denominator to the numerator automatically.

Divide the numerator by the denominator: 3/4 = 3 ÷ 4 = 0.75. If the denominator's only prime factors are 2 and 5, the decimal terminates; otherwise it repeats, like 1/3 = 0.333…. This calculator shows the decimal rounded to six decimal places.