+118608 this can be demonstrated in many ways.
Normally I wiould show you with number patterns.
Today I'll try something different - logic 
Say you borrow 'parcel' of $3 from your mum. You borrow 5 parcels of $3 altogether.
If you owe someone money than this is a negative amount that you have (really don't have)
So you now have 5*-$3 = -$15
Now you want to get rid of this debt you want to SUBTRACT this debt (get rid of it). Then you will have nothing (and owe nothing)
so -15-(-15)=-15+15=0
(5*-3)-5*-3=0
but 20-2 is the same as 20+(-2)
that is
(5*-3)+(-5*-3)=0
-15+ [ ]=0
well 15 has to go in the box so -5*-3=+15
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I expect that is about as clear as mud. LOL
I don't think i will try to explain it that way again.
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I have answered differently in the next post.
You can comment on my answer if you are there. Think about it a little first though. 
+118608 3*2=6
3*1=3
3*0=0
continuing the pattern
3*-1=-3
3*-2=-6
etc
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now
-2*3= -6 I just did that one
-2*2=-4
-2*1=-2
-2*0=0
continuing the pattern
-2*-1=-2
-2*-2=-4
hence a neg times by a negative is a positive
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Is that more help? 
+128408 I like to explain it in this manner:
Suppose we have a 30 gallon bucket half full of water that has a hole in the bottom.. And water leaks out of the bucket at one gallon per minute → (-1) gallon per minute.
And suppose that time going forward is positive, and time going backward is negative.
So, five minutes from now, the bucket will contain (-1)*(5) = -5 gallons less than it does now.
But, 10 minutes ago, the bucket contaned (-1)*(-10) = 10 gallons more than it does now.
So, in the first case, a negative times a positive is a negative. And in the second case, a negative times a negative is a positive !!!!
+118608 Where did the -(-1) come from Chris?
I like the rest of the explanation.
