Yes.
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When they are added together and the absolute value of the positive integer is bigger than the absolute value of the negative integer or when the negative integer is subtracted from the positive integer.
Only if the first positive integer is greater. 4 - 9 = -5
When the absolute value of the positive integer is smaller than the absolute value of the negative one.
Yes, and also a negative integer divided by a negative integer is equal to a positive number (but not necessarily an integer).
As long as the negative integer is greater than the positive integer, a negative integer will result from addition, subtraction, multiplication, and division.