Understand that Subtraction is the SAME as Adding the Opposite of a number.
Converting a subtraction expression into adding with a negative allows you to regroup the integers using the commutative property to a group with positive integers and a group with negative integers (and if there is an integer and its additive inverse, grouping this together makes zero). If you have groups of integers with the same sign, you just add their absolute values together and keep the original sign.
