Is it true for any real $a$ and $b$ that if $a*b > 0$ => $a/b>0$?

Question

Is it true for any real $a$ and $b$ that if $a*b > 0$ => $a/b>0$ ?

Answer 1

$b\neq0$ because otherwise, from the given we obtain $0>0$, which is wrong.

Thus, $b^2>0$ and from the given again we obtain: $$\frac{a}{b}=\frac{ab}{b^2}>0.$$

Answer 2

$a,b \not =0$, real.

Assume $ab>0 \Rightarrow a/b<0.$

Then

$(ab)(a/b)<0$

(sign change since $(a/b) <0$).

$a^2 <0.$

Since $a$ real a contradiction.