The easiest way to do this is to temporarily ignore the signs and then subtract the smallest from the largest. Since they are opposite signs, they cancel each other out (meaning you'd subtract rather than add). Then add whichever sign of the largest starting number to the answer.
For instance, take -52 and 12. Since the signs are opposite, adding turns into subtraction. Put another way, adding the 12 to the -52 makes the -52 less negative (more positive). So subtract 12 from 52 and you get 40. Since -52 has a greater absolute value than 12, the answer gets the negative sign, thus you have -40. So adding the 12 makes the -52 smaller (less negative) by 12.
Or to demonstrate the other way, take 30 and -10. That is easy, since when you add a negative, you are subtracting. So 30 minus 10 is 20. Since the largest starting number is positive, you don't have to worry about the sign when you are done.
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-- write the difference between the integers without regard to their signs -- give the difference the same sign as the larger of the two integers
The examples show that, to find the of two integers with unlike signs first find the absolute value of each integers.
When you add two negative integers, the answer is still negative.
If you mean integers, well if you have two integers of the same sign that you are adding, add and the sign stays the same. If you have different signs, subtract and keep the sign of the one that has more. Regular numbers you just add them.
-4 + -4 = -8