Integer addition is about combining directed quantities on the number line. Same-sign numbers reinforce each other; different signs cancel, and the leftover has the sign of whichever side had more magnitude.

Steps

1. Same signs: add the absolute values and keep that shared sign.
2. Different signs: subtract the smaller absolute value from the larger, then keep the sign of the number with the larger absolute value.
3. Sanity-check by picturing a move left (negative) or right (positive) on a number line.