1.1 Evaluate Expressions

Objective: To be able to evaluate algebraic expressions and use

exponents

8-18-15

equivalentANSWER

2, 3ANSWER

Prerequisite Skills VOCABULARY CHECK

Copy and complete the statement.231. In the fraction , is the numerator and

is the denominator.

? ?

2. Two fractions that represent the same number are called fractions.?

100ANSWER

3. The word percent (%) means “divided by .”

?

Prerequisite Skills SKILLS CHECK

Perform the indicated operation.

4. +23

35

5. –56

34

6. 35

25

7. 12

58

ANSWER 1

154

ANSWER 112

ANSWER 45

ANSWER 625

9. 23%

8. 4%

Prerequisite Skills SKILL CHECK

Write the percent as a decimal.

ANSWER 0.23

ANSWER 0.015

0.04ANSWER

10. 1.5%

11. 2.5% ANSWER 0.025

Prerequisite Skills SKILL CHECK

12. Find the perimeter and area of the rectangle.

11 in.

4 12

ANSWER

31 in., 49 in.212

• A variable is a letter used to represent one or more numbers.

• Expressions consist of numbers, variables and operations.

• An algebraic expression, or variable expression, is an expression that includes at least one variable.

• To evaluate an algebraic expression, substitute a number for each variable, perform the operation(s), and simplify the result, if necessary.

Algebraic Expressions

Algebraic expression

Meaning Operations

5(n) 5n 5●n

5 times n multiplication

14 divided by y

division

6 + c 6 plus c Additiony

14y14

Substitute 3 for n.Multiply.= 39

Subtract.= 2Substitute 3 for n.

Substitute 3 for n.

= 3 Divide.

EXAMPLE 1 Evaluate algebraic expressions

Evaluate the expression when n = 3.

a. 13 n = 13 3

93

b. 9n

=

c. n – 1 =

Substitute 3 for n.Add.= 11

d. n + 8 =

3 – 1

3 + 8

GUIDED PRACTICE for Example 1

= 12

= 6

= 4

Evaluate the expression when y = 2.

1. 6y

2. 8y

3. y + 4

= 9 4. 11 – y

EXAMPLE 2 Evaluate an expression

Movies

The total cost of seeing a movie at a theater can be represented by the expression a + r where a is the cost (in dollars) of admission and r is the cost (in dollars) of refreshments. Suppose you pay $7.50 for admission and $7.25 for refreshments. Find the total cost.

Add.

The total cost is $14.75

ANSWER

Substitute 7.50 for a and 7.25 for r.

= 14.75

= 7.50 + 7.25

Write expression.Total cost =

EXAMPLE 2 Evaluate an expression

SOLUTION

a + r

Expression Using Exponents

• A power is an expression that represents repeated multiplications of the same factor. For example, 81 is a power of 3 because 81 = (3)(3)(3)(3).

• A power can be written in a form using two numbers base and an exponent.

• The exponent represents the number of times the base is used as a factor.

If a number is in exponential form, the exponent represents how many times the base is to be used as a factor. A number produced by raising a base to an exponent is called a power. 27 and 33 are equivalent.

7ExponentBase

2

ProductWordsPower

EXAMPLE 3 Read and write powers

Write the power in words and as a product.

seven to the first powera. 71 7

five to the second power,or five squared

b. 52 5 5

c. 1 3 2

one half to the third power,or one half cubed

12

12

12

z to the fifth powerd. z5 z z z z z

GUIDED PRACTICE for Examples 2 and 3

5. WHAT IF? In Example 2, suppose you go back to the theater with a friend to see an afternoon movie. You pay for both admissions.Your total cost (in dollars) can be represented by the expression 2a. If each admission costs $4.75, what is your total cost?

The total cost is $9.50.

ANSWER

GUIDED PRACTICE for Examples 2 and 3

ProductWordsPower

Write the power in words and as a product.

Nine to the fifth power6. 95

Two to the eighth power7. 28

n to the fourth power

9 9 9 9 9

2 2 2 2 2 2 2 2

8. n4 n n n n

EXAMPLE 4 Evaluate powers

Evaluate the expression.

a. x4 = 24

= 16= (1.5)(1.5)(1.5)= 3.375

= 2 2 2 2b. n3 = 1.53

b. n3 when n = 1.5

SOLUTION

a. x4 when x = 2

GUIDED PRACTICE for Example 4

Evaluate the expression.

9. x3 when x = 8

9. 512 10. 6.25

10. k3 when k = 2.5

ANSWER

GUIDED PRACTICE for Example 4

Evaluate the expression.

11. d4 when d = 13

11. 181

ANSWER

SOLUTION

EXAMPLE 5 Evaluate a power

Storage cubes

Write formula for volume.= 143 Substitute 14 for s.= 2744 Evaluate power.

Each edge of the medium-sized pop-up storage cube shown is 14 inches long. The storage cube is made so that it can be folded flat when not in use. Find the volume of the storage cube.

V = s3

The volume of the storage cube is 2744 cubic inches.

GUIDED PRACTICE for Example 5

WHAT IF? In Example 5, suppose the storage cube is folded flat to form a square. Find the area of the square.

The area of the square is 196 in2.

ANSWER

Homework

1.1 Exercises 1-49 all pages 5 and 6