If you're talking about multiplication or division, then opposite signs will result in a negative number.
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No, the product of two negative numbers is always a positive.
If I understand the question correctly, the sum of two positive numbers will *always* yield a positive number. The product of two positive or two negative numbers will always yield a positive number. The division of two positive or two negative numbers will always yield a positive number. There are more examples along this line. I am not sure if this is what you wanted to know.
Adding two negative numbers always gives a negative number.
No. Adding two negative numbers will give a number which is more negative.
If ever you have an odd number of negative numbers, the product will always be a negative number. So the answer to this question is negative.