Evaluate the following expression

Explanation

We will use the commutative and/or associative properties of addition so that we can add the positives and add the negatives separately. Then we will add those results to obtain the final answer.

It is easier to add integers that have the same sign than integers that have different signs. This approach lessens the possibility of an error, because we only have to add integers that have different signs once.

• Use the commutative property of addition to reorder the integers
  • -3 + 5 + (-12) + 2 = -3 + (-12) + 5 + 2
• Use the associative property of addition to group the negatives and group the positives.
  • = [-3 + (-12)] + (5 + 2)
• Use the rule for adding two integers that have the same sign twice.  Add the negatives within the brackets.  Add the positives within the parentheses.
  •  = -15 + 7
• Use the rule for adding two integers that have different signs.
  • = -8