bruchteil

Bruchteil is a German noun meaning a portion of something that is smaller than the whole. In everyday language it denotes a fraction of a quantity, for example: "nur ein Bruchteil der Bevölkerung" means only a small part of the population. The term emphasizes partiality or a subdivision rather than a complete or whole part.

In mathematics, Bruchteil has a precise meaning: the fractional part of a real number. For any real number x, the Bruchteil {x} is defined as x minus the greatest integer not larger than x, and it lies in the interval [0, 1). For example, the Bruchteil of 3.75 is 0.75. The complementary part is the Ganzteil, i.e., the integer part. The concept is distinct from a mathematical fraction (Bruch) that represents a ratio p/q.

The word derives from Bruch, “break”, and Teil, “part”, reflecting a subdivision of a quantity. It is commonly used in German mathematics education when distinguishing between the whole, its integer part and the remaining fractional component. See also Bruch, Ganzzahl, Dezimalbruch.