Huh?

So, if you have 6/(-2), you can do the following:
6/(-2) = 6/(-1 * 2)
because -2 = -1 * 2
6/(-1 * 2) = (-1 * 6)/(-1 * -1 * 2)
because you can multiply the top and bottom by the same thing.
(-1 * 6)/(-1 * -1 * 2) = (-1 * 6)/(1 * 2)
because -1 * -1 = 1
(-1 * 6)/(1 * 2) = (-1 * 6)/2
because 1 * 2 = 2
(-1 * 6)/2 = -1 * (6/2)
because division and multiplication are commutative
-1 * (6/2) = -1 * 3
because 6/2 = 3
-1 * 3 = -3
because -3 = -1 * 3

Just some of my light reading tonight as I prepare for my math test on Monday to determine how much I've forgotten in the last.....ummm *few* years. Actually I'm feeling really old because I was just thinking how it's been almost 10 years since I was actually in a Math class. What the hell am I doing?????