You can't just divide by any number!

The line "If $a\times b = c\times d$ is fulfilled, then $a\div c=d\div b$ must be fulfilled too" is made by dividing both sides of the equation by $bc$ : $a\times b = c\times d \Longrightarrow \frac{a\times b}{bc} = \frac{c\times d}{bc}\Longrightarrow a\div c=d\div b$ From the given, $a=2,b=0,c=3,d=0$ , and from above, $2\times 0 = 3\times 0 \Longrightarrow \frac{2\times 0}{0(3)} = \frac{3\times 0}{0(3)}\Longrightarrow 2\div 3=0\div 0$ Since $0\times 3 = 0$ , division by zero is implicitly made in the statement, which is not allowed.

It should be $\dfrac 2 3 \ne \dfrac 00$ . Since division by 0 is not allowed.