Basic Mathematics for College Students

186 Chapter 2 The Integers

EXAMPLE 7

Evaluate:

StrategyWe will work within the parentheses first and then within the brackets.

Within each pair of grouping symbols, we will follow the order of operations rule.

WHYWe must work from the innermostpair of grouping symbols to the outermost.

Solution

Do the division within the

parentheses: 66 (6) 11.

Do the addition within the

parentheses: 16 (11) 5.

Do the subtraction within the

brackets: 1  5 4.

 4 The opposite of 4 is 4.

[4]

[15]

C 1  116 (11) (^2) D
Evaluate the exponential
expression within the
parentheses: 2^4 16.
c 1 a 24 

66

 6

bdc 1 a 16 

66

 6

bd

c 1 a 24 

66

 6

bd

Self Check 7

Evaluate:

Now TryProblem 37

c 8 a 33 

90

 9

bd

EXAMPLE 8

Evaluate:

StrategyWe will evaluate the expression above and the expression below the

fraction bar separately. Then we will do the indicated division, if possible.

WHYFraction bars are grouping symbols that group the numerator and the de-

nominator. The expression could be written.

Solution

 7 Do the division indicated by the fraction bar.

In the numerator, add:  20 (15) 35.

In the denominator, subtract: 21  16 5.



 35

5

In the numerator, do the multiplication:

3(5) 15. In the denominator, evaluate

the exponential expression: (4)^2 16.

 20 3(5)

21 (4)^2



 20 ( 15 )

21  16

[ 20 3(5)][21 (4)^2 ]

 20 3(5)

21 (4)^2

Self Check 8

Evaluate:

Now TryProblem 41

 9 6(4)

28 (5)^2

3 Evaluate expressions containing absolute values.

Earlier in this chapter, we found the absolute values of integers. For example, recall

that and. We use the order of operations rule to evaluate more

complicated expressions that contain absolute values.

0  30  3 0100  10

EXAMPLE (^9) Evaluate each expression: a. b.
StrategyWe will perform the calculation within the absolute value symbols first.
Then we will find the absolute value of the result.
WHYAbsolute value symbols are grouping symbols, and by the order of
operations rule, all calculations within grouping symbols must be performed first.
Solution
a. Do the multiplication within the absolute value symbol: 4(3) 12.
Find the absolute value of 12.
b. Do the addition within the absolute value symbol:  6  1 5.
 5 Find the absolute value of 5.

0  6  10  0  50

 12

0 4(3) 0  0  120

0 4(3) 0 0  6  10

Self Check 9

Evaluate each expression:

a.

b.

Now TryProblem 45

0  3  960

0 (6)(5) 0