Basic Mathematics for College Students

There is another important fact about the operation of addition and 0. To

illustrate it, we use the number line below to add 6 and its opposite,. Notice that

6 (6) 0.

 6

150 Chapter 2 The Integers

EXAMPLE (^6) Evaluate:
StrategyWe will perform the addition within the brackets and the addition
within the parentheses first. Then we will add those results.
WHYBy the order of operations rule, we must perform the calculations within the
grouping symbols first.
SolutionUse the rule for adding two integers that have the same sign to do the
addition within the brackets and the rule for adding two integers that have
different signs to do the addition within parentheses.
Add within each pair of grouping
symbols.
Use the rule for adding two integers that
have the same sign.

 37

[ 21 (5)]( 17  6 ) 26 ( 11 )

[ 21 (5)]( 17 6)

Self Check 6

Evaluate:

Now TryProblem 47

( 6 8)[10(17)]

4 Identify opposites (additive inverses) when adding integers.

Recall from Section 1.2 that when 0 is added to a whole number, the whole number

remains the same. This is also true for integers. For example, and

0 (43) 43. Because of this, we call 0 the additive identity.

 5  0  5

The Language of Mathematics Identityis a form of the word identical,

meaning the same. You have probably seen identicaltwins.

Addition Property of 0

The sum of any integer and 0 is that integer. For example,

 3  0  3 ,  19  0  19 , and 0 (76) 76

If the sum of two numbers is 0, the numbers are said to be additive inversesof

each other. Since , we say that 6 and are additive inverses. Likewise,

is the additive inverse of 7, and 51 is the additive inverse of.

We can now classify a pair of integers such as 6 and in three ways: as opposites,

negatives, or additive inverses.

 6

 7  51

6 (6) 0  6

6  (6)  0

− 8 − 7 − 6 − 5 − 4 − 3 − 2 − 1012345 6 7 8

End

Begin

6

− 6

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.

Use the rule for adding two integers that have different signs.

This is the same result as in Example 4.

 8

 15  7