Multiplikationszahl

Multiplikationszahl, literally “multiplication number,” is a term used in some German mathematical texts to denote the factor by which a quantity is multiplied to obtain another quantity. In standard terminology, this quantity is commonly called a Faktor or Multiplikator, while the result is the Produkt; in linear algebra the corresponding entity is a Skalar.

In an equation y = k · x, the number k is the Multiplikationszahl that maps x to y: x is multiplied by k to produce y. The Multiplikationszahl can be any real number or, in a broader context, a complex number or a matrix in generalized scaling. When k > 1, the quantity grows; 0 < k < 1 yields a shrinkage; k = 0 collapses to zero; negative k reverses direction.

In practical terms, the concept appears in arithmetic, algebra and scaling operations: Doubling a recipe uses k = 2 as the Multiplikationszahl; multiplying prices by 1/3 uses k = 1/3; in geometric transformations, multiplying coordinates by k enlarges or reduces distances.

Note that “Multiplikationszahl” is not uniformly used as a formal term across all German mathematics; many textbooks prefer “Faktor” or “Skalar.” Nevertheless, the idea of a Multiplikationszahl—the numeric factor that causes one quantity to become another—remains central to understanding multiplication, scaling, and linear relationships.