From: AZMAT Subject: A question for someone in math 223 I would like to know why (-3)x(-2)=+6, I need an explanation that would satisfy someone at the grade eight level Thanks AZ

AZ: I posed this question to Ed Giesbrecht from Algoma College and he suggested an example like the following. Suppose it is noon, I have a tank containing 10 liters of water, and water is being added at a rate of 3 liters per hour. At 2 pm there will be 10 + (3)x(2) = 10 + 6 = 16 liters in the tank. That is 10 + (the rate at which the volume is increasing)x(the time since noon). So at 10 am there were 10 + (3)x(-2) = 4 liters in the tank. Suppose now that the tank is leaking at a rate of 3 liters per hour. Again, if at noon there were 10 liters in the tank then, using the same expression, at 2 pm there will be 10 + (-3)x(2) = 10 - 6 = 4 liters in the drum. But we also know that in this leaky tank there were 16 liters at 10 am since the tank lost 6 liters in this 2 hour period. From the expression used above this is 10 + (-3)x(-2), so (-3)*(-2) must be 6 liters. I hope this helps. Harley and Ed Giesbrecht

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