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I will assume you already agree that positive times negative is negative. Now consider this sequence:

-3 x 2 = -6

-3 x 1 = -3

-3 x 0 = 0

-3 x -1 = ???

What number would logically continue the sequence? The number to the right of the multiplication sign decreases by one at a time; the number to the right of the equal sign increase by 3 at a time, so the logical number is 3.

You might also reply, "To maintain the validity of certain mathematical rules, even for negative numbers - for example, the distributive property."

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Q: Why do two negatives multiplied together turn positive?
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