denominatore

Denominatore is the bottom part of a fraction, indicating into how many equal parts the whole is divided. In the fraction a/b, the number b is the denominatore, while a is the numerator. The denominatore is typically an integer and is required to be nonzero; in many contexts it is a positive integer, but fractions with algebraic denominatori are also considered in higher mathematics.

The term is used across various languages with the same mathematical meaning as denominator. It derives from a word family associated with naming or designating parts of a whole. In Italian, denoting the denominator of a fraction is a standard mathematical concept taught from early grades onward.

Key properties and usage: the size of the parts represented by a fraction is determined by the denominatore. When adding or subtracting fractions with different denominatori, one must first obtain a common denominatore, often by using the least common multiple. For multiplication, the fractions are multiplied by multiplying their numerators together and their denominatori together. Division by a fraction is equivalent to multiplying by its reciprocal, which swaps the numerator and denominatore of the divisor. Fractions can be simplified by dividing both numerator and denominatore by their greatest common divisor; a fraction with denominator 1 represents an integer. If the denominatore is negative, the usual convention is to move the sign to the numerator or front of the fraction.

See also: numerator, fraction, common denominator, least common multiple, greatest common divisor.