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The rules for multiplying signed numbers may be formulated from the fact that multiplication serves as a shorthand notation for addition. For example, 4 x (−3), which means "4 times negative −3" is the same as the following: (-3) + (-3) + (-3) + (-3) = -12 Therefore, it follows that multiplication of a negative and positive number represents addition of negative numbers. This explanation with further content regarding mulitiplication of signed numbers may be referenced at: http://www.math.info/Arithmetic/Signed_Numbers_Mult

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Q: Why is The product of a negative integer and a positive integer is always negative integer?
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