Why does a positive plus a negative equal a positive integers?

Positives and negatives have different rules when it comes to adding/subtracting , then when it comes to multiplying/dividing.

adding/subtracting
if u add/subtract and the numbers have the same sign, u add the numbers and keep the same sign
-2 + (-2) = -4             -5 + (-3) = -8
4 + 5 = 9                    3 + 1 = 4
but if the signs are different, u subtract and take the sign of the larger number
5 - 4 = 1             -2 + 7 = 5
-5 + 4 = -1            8 - 2 = 6

do not get these mixed up with multiplying/dividing with signs...they are not the same

multiplying/dividing
with these rules, if the signs are the same...either both positive or both negative, the result will be positive

if the signs are different...negative and positive, then the result will be negative

so for ur questiona positive + a negative will ONLY equal a positive if the largest number is positivebut if the largest number is negative, then it will equal a negative.