Fraction arithmetic: basics and rules
Understanding the four basic operations with fractions
The arithmetic of fractions is a fundamental chapter of mathematics. A fraction consists of a numerator (top) and a denominator (bottom), separated by a fraction bar. The denominator indicates into how many equally sized parts a whole is divided; the numerator states how many of these parts are meant. So 3/4 represents three quarters of a whole.
When adding and subtracting fractions, you first need a common denominator: both fractions are expanded to the same denominator, after which the numerators can be added or subtracted. When multiplying, numerator is multiplied by numerator and denominator by denominator – no common denominator is needed. Division of fractions follows the rule: form the reciprocal of the second fraction and then multiply.
A result should always be fully reduced: the numerator and denominator are divided by their greatest common divisor (GCD). The result 6/8, for example, reduces to 3/4, because the GCD of 6 and 8 is 2. Our fraction calculator uses the Euclidean algorithm to efficiently determine the GCD and automatically reduce the result.