Intermediate Algebra (11th edition)

Using the Order of Operations

Simplify.

Evaluate the power and the root.

Multiply.

or Subtract; --ab=ab NOW TRY

11

18

=

- 11

- 18

,

=

5 - 16

18 - 36

=

5 + 1 - 82122

6 # 3 - 9 # 4

5 + 1 - 232122

6 # 9 - 9 # 4

EXAMPLE 6

28 CHAPTER 1 Review of the Real Number System

OBJECTIVE 4 Evaluate algebraic expressions for given values of variables.

Any sequence of numbers, variables, operation symbols, and/or grouping symbols

formed in accordance with the rules of algebra is called an algebraic expression.

and Algebraic expressions

Algebraic expressions have different numerical values for different values of the vari-

ables. We evaluate such expressions by substitutinggiven values for the variables.

For example, if movie tickets cost $9 each, the amount in dollars you pay for x

tickets can be represented by the algebraic expression 9x. We can substitute different

numbers of tickets to get the costs of purchasing those tickets.

6 ab, 5 m- 9 n, - 21 x^2 + 4 y 2

Work separately above and below

the fraction bar.

NOW TRY
EXERCISE 7
Evaluate the expression
for and

x^2 - 2 z

• 3 xy

z=36.

x=-4,y=7,

NOW TRY
EXERCISE 6
Simplify.

 36 - 4 # 32

• 22 - 8 # 3 + 13

(b)

Substitute and

Work separately above and below the fraction bar.

or Write in lowest terms; also,

(c)

Substitute and

Evaluate the powers and the root.

Multiply.

= 67 Subtract. NOW TRY

= 192 - 125

=- 31 - 642 - 25152

=- 31 - 423 - (^1522) A (^25) B m=-4,n=5, q=25.

• 
  

  3 m^3 - n^2 Aq (^) B
  a

  
  


• 
  

  b=-

  
  

a

- b.

1

4

=

6

- 24

,

=

- 4 + 10

- 24

= m=-4,n=5, p=-6.

- 4 + 2152

41 - 62

m+ 2 n

4 p

NOW TRY ANSWERS

6. 2 7. 425

Evaluating Algebraic Expressions

Evaluate each expression for and

(a)

Substitute and

Multiply.

=- 65 Subtract.

=- 20 - 45

= 51 - 42 - 9152 m=- 4 n=5.

5 m- 9 n

m=-4,n=5,p=-6, q=25.

EXAMPLE 7

Use parentheses

around substituted

values to avoid errors.