Explain why you add to find the sum of two integers, but subtract to find the sum of a positive and negative integer

This has to do the adding/subtracting signs...

when u r adding/subtracting signsif the signs are the same, u add them and keep the sign.
-4 + (-2) = -4 - 2 = -62 + 5 = 7-3 + (-1) = -3 - 1 = -4

when ur adding/subtracting signs...if the signs are different, u subtract and take the sign of the larger number...
-4 + 7subtract 7 - 4 = 3the larger number (7) is positive, so ur answer is positiveso ur answer is 3

4 - 7subtract 7 - 4 = 3the larger number(-7) is negative, so ur answer is negativeur answer is -3

but dont get this confused with multiplying/dividing with signsthey have different rules