How to work out this easy fraction?

I need help working out this fraction, I know it seems quite easy but I'm a bit stuck.

The question is:

$$\frac{\frac {5}{2}}{\frac{5}{9}}$$

My attempt was changing the denominators by multiplying by $2$ to make $18$ and then changing the same way the nominators:

$$\frac{\frac {45}{18}}{\frac{10}{18}}$$

The thing is that I'm not sure how to simplify it as no numbers go into all of them. Thank you, I know this is quite easy.

Question: Why is it considered a division if the easiest solution is by multiplication?

Answer

Remember that dividing by a fraction is the same as multiplying by its inverse.

In this case

$$\frac52 \Big/ \frac59 = \frac52 \times \frac95 = \frac92$$
because the $5$ cancels.