additive inverses
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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'.
negative
If two numbers have opposite signs then they are at the same distance from zero but on opposite sides of it. Conventionally, positive numbers are to the right of the zero or above it whereas negative numbers are to the left or below.
If two numbers have opposite signs, then their product and quotient are both negative.