Integer operations
Subtracting a negative adds; a product or quotient is negative only when exactly one of the signs is negative.
A worked example
For 5 − (−16), the two minus signs make a plus, so 5 + 16 = 21. And −52 ÷ 4 = −13, since exactly one sign is negative.
The mistake people actually make
In a mixed expression, multiply and divide before adding or subtracting, so a negative product gets combined last, not first.