Page 150 - Basic College Mathematics with Early Integers

S E C T I O N 2.3 I ADDING INTEGERS 127

Recall that numbers such as 7 and -7 are called opposites. In general, the sum
of a number and its opposite is always 0.
7 + 1-72 = 0 -26 + 26 = 0 1008 + 1-10082 = 0

opposites opposites opposites
If a is a number, then
-a is its opposite. Also,

a + 1-a2 = 0
r The sum of a number and its opposite is 0.
-a + a = 0

Examples Add. PRACTICE 12–13
Add.
12. -21 + 21 = 0
12. 15 + 1-152
13. 36 + 1-362 = 0
13. -80 + 80
Work Practice 12–13

Concept Check What is wrong with the following calculation?
6 + 1-222 = 16

In the following examples, we add three or more integers. Remember that by the
associative and commutative properties for addition, we may add numbers in any
order that we wish. In Examples 14 and 15, let’s add the numbers from left to right.
Example 14 Add: 1-32 + 4 + 1-112 PRACTICE 14
Add: 8 + 1-32 + 1-132
Solution: 1-32 + 4 + 1-112 = 1 + 1-112
=-10
Work Practice 14

Example 15 Add: 1 + 1-102 + 1-82 + 9 PRACTICE 15
Add: 5 + 1-32 + 12 + 1-142
Solution: 1 + 1-102 + 1-82 + 9 = -9 + 1-82 + 9
=-17 + 9
= -8
The sum will be the same if we add the numbers in any order.To see this, let’s first
add the positive numbers together and then the negative numbers together.
1 + 9 = 10 Add the positive numbers.
1-102 + 1-82 =-18 Add the negative numbers.
10 + 1-182 =-8 Add these results.
The sum is -8.
Work Practice 15

Don’t forget that addition is commutative and associative. In other words,
numbers may be added in any order.
Answers
Objective Evaluating Algebraic Expressions 12. 0 13. 0 14. -8 15. 0

We can continue our work with algebraic expressions by evaluating expressions Concept Check Answer
given integer replacement values. 6 + 1-222 =-16