Answering a question about fractions

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}

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