Basic Mathematics for College Students

 

 

At certain times, the addition property of opposites can be used to make addition
of several integers easier.

2.2 Adding Integers 151

Addition Property of Opposites

The sum of an integer and its opposite (additive inverse) is 0. For example,

4 (4) 0 ,  53  53  0 , and 710 (710) 0

Self Check 7

Evaluate:

Now TryProblem 51

8 (1) 6 (8) 1

opposites

5 Solve application problems by adding integers.

Since application problems are almost always written in words, the ability to understand
what you read is very important. Recall from Chapter 1 that words and phrases such as
gained, increased by,and riseindicate addition.

EXAMPLE (^8) Record Temperature Change At the beginning of this
section, we learned that at 7:30 A.M. on January 22, 1943, in Spearfish, South
Dakota, the temperature was. The temperature then rose 49 degrees in just
2 minutes. What was the temperature at 7:32 A.M.?
StrategyWe will carefully read the problem looking for a key word or phrase.
WHYKey words and phrases indicate what arithmetic operations should be used
to solve the problem.
SolutionThe phrase rose 49 degreesindicates addition. With that in mind, we
translate the words of the problem to numbers and symbols.
was plus

 4  49

To find the sum, we will use the rule for adding two integers that have different
signs. First, we find the absolute values: and.

Subtract the smaller absolute value from the larger absolute value:

49  4 45. Since the positive number, 49, has the larger absolute

value, the final answer is positive.

At 7:32 A.M., the temperature was 45°F.

 4  49  45

0  40  4 0490  49

The temperature

at 7:32 A.M.

49 degrees.

the temperature

at 7:30 A.M.

The temperature

at 7:32 A.M.

4°F

Self Check 8

TEMPERATURE CHANGEOn the

morning of February 21, 1918, in

Granville, North Dakota, the

morning low temperature was

. By the afternoon, the
temperature had risen a record
83 degrees. What was the
afternoon high temperature in
Granville? (Source:Extreme
Weatherby Christopher C. Burt)
Now TryProblem 83

33°F

EXAMPLE (^7) Evaluate:
StrategyInstead of working from left to right, we will use the commutative and
associative properties of addition to add pairs of opposites.
WHYSince the sum of an integer and its opposite is 0, it is helpful to identify such
pairs in an addition.
Solution
opposites
Locate pairs of opposites and add
them to get 0.
The sum of any integer and 0 is that
integer.

 6

12 (5) 6  5 (12) 0  0  6

12 (5) 6  5 (12)