If we had two number variables A and B with their product to be a constant C; A x B = C. Doesn't that mean that if I increased A by an amount "n" and decreased B with the same amount "n" , then their product should not change and stays equal to C.
But its not true, since for example : 5x3=15 ; (5-1)x(3+1)=16 and not equal to 15
I know that I have proved it wrong, but intuitively I'm still not convinced..
That's what I meant. If $ab=c$ then for $n \ne 0$ $$ \left(na\right)\left(\frac{b}{n}\right)=ab\frac{n}{n}=c $$ With an example $8\times10=80$ and $$ \left(2\times 8\right)\left(\frac{10}{2}\right)=16\times 5=80 $$