Evaluate -(-6) + (-18) - 4 - (-51)

Explanation

This expression involves one addition and two subtractions.  We will write each subtraction as addition of the opposite and then evaluate the expression.  It is easy to make an error when subtracting signed numbers.  We will probably be more accurate if we write each subtraction as addition of the opposite.

Solution

We apply the rule for subtraction twice.  Then we will add the positives and the negatives separately, and add those results (By the commutative and associative properties of addition, we can add the integers in any order.)

• Simplify: -(-6) = 6.  Add the opposite of 4, which is -4, and add the opposite of -51, which is 51.
  • -(-6) + (-18) - 4 - (-51) = 6 + (-18) + (-4) + 51
• Reorder the integers.  Then group the positives together and group the negatives together.
  • = (6 + 51) + [(-18) + (-4)]
• Add the positives within the parentheses.  Add the negatives within the brackets.
  • = 57 + (-22)
• Use the rule for adding integers that have different signs
  • = 35