a negative integer is -1,-2,-3 and so on, but not -2.5 or 0
a positive integer is 1, 2, 3 and so on but not 7.2 or 0
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221.3
That is part of the basic rules of Math: A: Multiply a Negative and a Negative will result in a Postive. B. Multiply a Negative and a Postive will result in a Negative. BTW, unlike English grammar, rules of Math are true at all times.
a negative integer
a positive a negative times a negative also equals a positive
The smallest positive integer is 1. 1 is the multiplicative identity; ie anything times 1 is itself. The greatest negative integer is the most positive negative integer which is -1. Therefore the product of the greatest negative integer and the smallest positive integer is the greatest negative integer which is -1.