This is for a friend who has a question about why one fraction equals another.

The question is why does $\frac{45}{-30}=\frac{-3}{2}$

Let us take this through the steps one at a time:

The obvious start is that the answer should equal itself to begin with:

$\frac{45}{-30}=\frac{45}{-30}$

By convention the negative sign should be on the top so we multiply both sides by $\frac{-1}{-1}$

$\frac{-1}{-1}*\frac{45}{-30}=\frac{-45}{30}$

Now we factorise -45 and 30, but we can think of -45 as $-1 * 45$ so we only need to factorise 45:

30 = {1, 2, 3, 5, 6, 10, 15}

45 = {1, 3, 5, 15}

The largest factor is 15 for each so we will use that for our reduction:

$\frac{-1*45/15}{30/15}=\frac{-1*3}{2}=\frac{-3}{2}$