theoretically speaking, why is a negative number times a negative number a positive?

Question

logically, where does the rule come from?

Answer 1

Here is a simple analogy I used to explain this to my students: say east is positive and west is negative, you are facing west and you are walking backwards, you are going in the positive direction.

Answer 2

i will try explaining it simply...
when a negative number is multiplied a negative amount of times...it is like backtracking through numbers(in a positive direction) so -6 and negative amount of times will progressively grow, because you are slowly increasing... if it were just +6, then that a negative number of times would progressively decrease... it is just the inverse of that situation.


ex)
-6/-6=0 (grows in a positive direction)
*same goes for multiplication...
hmm...
i'm not sure if that made sense.
but i hope it did:]]]

Answer 3

If I owe $5 to 3 people it would be -5 x 3=-15 (I'm out 15 bucks)

Now say I owe $5 to 3 people, who quite tragically, died in a freak lightning storm. Well I get to keep my $15 because they're dead (-3 people), but I'll probably just put it towards flowers for the funerals anyway.

Or you could just say its 3 people who forgave the debt, depending on your morbidity threshold.

-$5 x -3 people= $15 in my pocket

Answer 4

-a/-b = -1*a/-(1*b) =a/b because anything divided by itself = 1.
Since multiplication is the inverse of division, it follows that
(-a)*(-b) = +ab. If not, our mathematics system would be inconsistent.