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 signs ... if the signs are the same, u add them and keep the sign.

-4 + (-2) = - 4 - 2 = - 6 ... 2 + 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 + 7 ... subtract 7 - 4 = 3 ... the larger number (7) is positive, so ur answer is positive ... so ur answer is 3

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

but dont get this confused with multiplying/dividing with signs ... they have different rules