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.
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