Most students asked why is that ${a\over b}\div{c\over d}={ad\over bc}$ Most students asked why is that

$${a\over b}\div{c\over d}={ad\over bc}$$

I just told them: inverse the second fraction and multiply. Why? They ask me. I have no idea.

Any logical answers to them kids?

These day teachers just told students at secondary to memorise and no why is allowed in lessons. I think that is wrong. Putting people of studying maths.
By definition, $x \div y$ should be a number $z$ such that $x = y  z$.
So you just verify: $$ \dfrac{ad}{bc} \times \dfrac{c}{d} = \dfrac{a}{b}$$
Ultimately this works because of the associative and commutative laws of multiplication, but you don't have to tell the students that.

"Why" should always be allowed.
$\frac{a}{b}=\frac{\frac{ad}{b}}{d}$.  So $\frac{ad}{bc}$ is how many times $\frac{c}{d}$ goes into $\frac{\frac{ad}{b}}{d}$.