Zero Pairs

A number plus its opposite is always 0. $4 + \left(-4\right)$ is 0: you walk 4 steps right and 4 steps left, and end where you started. A number and its opposite are called a zero pair.

In a longer sum, look for zero pairs before doing anything else. In $-6+9+6$, the -6 and the 6 cancel, so the whole sum is just 9. They do not have to sit next to each other: a sum can be added in any order, for negative numbers just as for positive ones.

Why bother? Every number you cancel is a number you never have to add, and fewer steps means fewer chances to slip. Spotting a zero pair turns a three-number sum into one number.