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...but then someone asked me after class, "why DO two negatives equal a positive?" and i was like "err... cause multiplication is the addition of groups and when you have a negative and you put it into negative groups... Hmmph! i don't actually know dammit!"

So, i've been chewing it over, and i think i've made some sense thinking about it in terms of negative meaning direction, and multiplying meaning you increase the magnitude... but i dunno.... i want a better explanation. Please.