The properties of addition that were introduced in Section 1.2,Adding Whole
Numbers,are also true for integers.
2.2 Adding Integers 1493 Perform several additions to evaluate expressions.
To evaluate expressions that contain several additions, we make repeated use of the
rules for adding two integers.
EXAMPLE (^4) Evaluate:
StrategySince there are no calculations within parentheses, no exponential
expressions, and no multiplication or division, we will perform the additions,
working from the left to the right.
WHYThis is step 4 of the order of operations rule that was introduced in
Section 1.9.
Solution
Use the rule for adding two integers
that have different signs: 3 5 2.
Use the rule for adding two integers that have
different signs: 2 (12) 10.
Use the rule for adding two integers that have
different signs.
8
10 2
3 5 (12) 2 2 (12) 2
3 5 (12) 2
Self Check 4
Evaluate:Now TryProblem 4312 8 (6) 1
Commutative Property of AdditionThe order in which integers are added does not change their sum.Associative Property of AdditionThe way in which integers are grouped does not change their sum.Another way to evaluate an expression like that in Example 4 is to use these
properties to reorder and regroup the integers in a helpful way.
Self Check 5
Use the commutative and/or
associative properties of addition
to help evaluate the expression:Now TryProblem 4512 8 (6) 1
EXAMPLE (^5) Use the commutative and/or associative properties of
addition to help evaluate the expression:
StrategyWe 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.
WHYIt 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.
Solution
Use the commutative property of addition
to reorder the integers.
Negatives Positives
Use the associative property of addition to group
the negatives and group the positives.