How do you determine whether a sum will be positive, negative, or 0 when adding a positive and a negative integer?

If the integers have the same absolute value ... they're the same number
but with different signs ... then their sum is zero.

Example:    (plus) 927 added to (negative) 927  =  zero

If the integers have different absolute values ... they're different numbers with different
signs ... then their sum has the same sign as the one with the bigger absolute value.

Examples:

==>   (plus) 92 added to (negative) 91
         92 and 91 are 1 number apart on the number line.
         The positive number is bigger than the negative number.
         So the sum is  +1 . 

==>    (plus) 35 added to (negative) 37
          35 and 37 are 2 numbers apart on the number line.
          The negative number is bigger than the positive one.
          So the sum is  -2 .