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additive inverses
Then you are adding two rational numbers with different signs! No big deal!
If the two numbers have different signs, then the result will be negative. If the two numbers have the same signs, the result will be positive. This assumes all the numbers are non-zero.
To add two integers with opposite signs . . . -- Ignore the signs, and write the difference between the two numbers. -- Give it the same sign as the larger original number has.
If two numbers have the same sign, their product is positive. If two numbers have opposite signs, their product is negative. So the answer is 'yes'.