Best answer:
Keep in mind that the negative sign indicates the number is the additive inverse of what it's applied to. There are only two real number operations: addition and multiplication. Subtraction is the addition of the additive inverse, and division is multiplication by the multiplicative inverse. That may seem like...
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Best answer: Keep in mind that the negative sign indicates the number is the additive inverse of what it's applied to. There are only two real number operations: addition and multiplication. Subtraction is the addition of the additive inverse, and division is multiplication by the multiplicative inverse. That may seem like it's over-complicating things, but it's really just getting back to the basic definition of the operations.
Looking at it this way also allows us to prove that the product of two negatives is a positive. It's not good enough to just say it's the way it is, or it's a rule or law of math. We need to demonstrate why this "rule" is consistent with the other definitions governing the number system.
First let's think about a negative times a positive.
Suppose you have (-2)(3). Why is this -6?
Well, if you take (2)(3) + (-2)(3) = 6 + (-2)(3), by the distributive property that's equal to
(2 + (-2))(3) = 0(3) = 0
So (-2)(3) is additive inverse of 6, or -6
Similarly, (2)(-3) works out to be the same thing, -6.
Now suppose you have (-2)(-3)
Consider (-2)(-3) + (2)(-3), which is equal to (-2 + 2)(-3) = 0
So (-2)(-3) must be the additive inverse of (2)(-3), which is -6.
So (-2)(-3) = +6
I hope this was helpful.
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