SOLUTION: why is a negative number times a negative number equal to a positive number?

Question 114622:
why is a negative number times a negative number equal to a positive number?
Found 2 solutions by stanbon, checkley71:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
why is a negative number times a negative number equal to a positive number?
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There are a number of ways to describe this.
Here is one:
If a + -a = 0 and a = n(-m) you can write:
n(-m)+-(n(-m)) = 0
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But n(-m) = -nm
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Substituting -mn for n(-m) you get:
-nm + -(n(-m))= 0
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Also -nm + nm = 0
Therefore nm = -(n(-m))
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You can also discribe the double negative geometrically.
If 2 is two to the right on the number line
and -2 is two to the left.
The 2*-2 is two to the left twice.
And -(2*-2) is the opposite of twice two to the left which is
the same as two twice to the right.
So, -2*-2 = 2*2
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You can also describe it financially as the loss of a loss,
which would be a gain.
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Cheers,
Stan H.

Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
THERE HAS TO BE BASIC RULES FOR ANY SYSTEM TO WORK THE SAME ALL THE TIME.
ONE OF THESE RULES ASSOCIATED WITH MATH IS:
(+*+)=+, (+*-)=-, (-*+)=- & (-*-)=+
OR SIMPLY PUT;
LIKE SIGNS WHEN MULTIPLIED OR DIVIDED RESULT IN A + ANSWER.
UNLIKE SIGNS WHEN MULTIPLIED OR DIVIDED RESULT IN A - ANSWER.
IT HAS BEEN A WHILE SINCE I HAVE HAD TO DEAL WITH THIS QUESTION (60 YEARS) & IF THERE IS A PROOF -- I HAVE FORGOTTEN IT.
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