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The easiest way to show you how to add integers is to work out some examples.

13 + (-5) is the same as 13 - 5 = 8

-5 + 13 is also the same as 13 - 5 = 8

and -13 + (-5) is the same as -13 - 5 = -(13 + 5) = -18

because of the distributive law.