Rationale Zahlen

a / b = a * c / b * c

a / b = (a : c) / (b : c)

(a / c) + (b / c) = (a +- b) / c

(a / c) + (b / d) = ad/cd +- bc/cd = (ad +- bc) / cd

(a / b) * (c / d) = (a * c) / (b * d)

(a / b) : (c / d) = (a / b) * (d / c)

Kommutativgesetz a * b = b * a
Assoziativgesetz a * (b * c) = (a * b) *c
Distributivgesetz a * (b + c) = a * b + a * c

binomsche Formeln

(a + b)^2 = a^2 + 2*a*b + b^2
(a - b)^2 = a^2 - 2*a*b + b^2
(a + b) * (a - b) = a^2 - b^2

binomscher Lehrsatz

(a^n-b^n) : (a - b) = a^(n-1) + a^(n-2)*b + a^(n-3)*b^2+...+a*b^(n-2)+b^(n-1)