Assoziativ Gesetz bei Produkten



(a ⋅ b) ⋅ c = a ⋅ (b ⋅ c)



Durch das Kom­mu­ta­tiv­ge­setz kann du be­lie­big die Fak­to­ren der Mul­ti­pli­ka­ti­on ver­tau­schen:



 (a ⋅ b) ⋅ c = a ⋅(b ⋅ c) = b ⋅ (a ⋅ c) = (b ⋅ a) ⋅ c = ... = a ⋅ b ⋅ c



Dies gilt auch mit meh­re­ren Fak­to­ren ma­chen:



 a ⋅ (b ⋅ c ⋅ d) = (a ⋅ b) ⋅ (c ⋅d) = (a ⋅ b ⋅ c) ⋅ d = ... = a ⋅ b ⋅ c ⋅d



Nur in einem Pro­dukt darf man die Fak­to­ren um­stel­len und be­lie­big zu Teil­pro­duk­ten zu­sam­men­fas­sen.



Bei­spiel:



3a ⋅ 5b = (3 ⋅ 5) ⋅(a ⋅b) = 15ab

2,5x ⋅ 4y ⋅ 3 = (2,5 ⋅ 4 ⋅3) ⋅ (x ⋅y) = 30xy