```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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