Warm Up Simplify. 1. 4 + 7 3 1 2. 87 15 5 3. 6(9 + 2) + 7 4. 35 7 5

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Warm Up Simplify. 1. 4 + 7 3 1 2. 87 15 5 3. 6(9 + 2) + 7 4. 35 7 5

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Warm Up Simplify. 1. 4 + 7 3 1 2. 87 15 5 3. 6(9 + 2) + 7 4. 35 7 5

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Warm Up

Simplify.

1. 4 + 7 3 1

2. 87 15 5

3. 6(9 + 2) + 7

4. 35 7 5

24

84

73

25

Vocabulary

variable

constant

algebraic expression

evaluate

A variable is a letter or symbol that represents a quantity that can change.

A constant is a quantity that does not change.

Algebraic Expressions

NOT Algebraic Expressions

An algebraic expression contains one or more variables and may contain operation symbols. So p 7 is an algebraic expression.

150 + y

85 ÷ 5

35 w + z

10 + 3 5

To evaluate an algebraic expression, substitute a number for the variable and then find the value by simplifying.

y

5 y

16

80

y = 27; 5 =

27

35

y = 35; 5 =

Additional Example 1A: Evaluating Algebraic Expressions

Evaluate the expression to find the missing values in the table.

Substitute for y in 5 y.

y = 16; 5 16 = 80

27

135

135

175

35

175

The missing values are 135 and 175.

z

z 5 + 4

Substitute for z in z 5 + 4.

20

20

45

60

Additional Example 1B: Evaluating Algebraic Expressions

Evaluate the expression to find the missing values in the table.

z = 20; 20 5 + 4 = 20

13

z = 45; __ 5 + 4 = __

45

13

60

16

z = 60; __ 5 + 4 = __

16

The missing values are 13 and 16.

t

8t

10

80

20

30

Check It Out: Example 1A

Evaluate each expression to find the missing values in the table.

160

240

m

52 -2m

4

17

7

10

Check It Out: Example 1B

Evaluate each expression to find the missing values in the table.

11

5

n

n ÷ 6 - 4

60

6

48

36

Check It Out: Example 1C

Evaluate each expression to find the missing values in the table.

4

2

b

3 (2 + b)

3

15

6

9

Check It Out: Example 1D

Evaluate each expression to find the missing values in the table.

24

33

Instead of . . .

You can write . . .

y

35

Writing Math

When you are multiplying a number times a variable, the number is written first. Write “3x” not “x3.” Read 3x as “three x.”

You can write multiplication and division expressions without using the symbols and .

x 3

x 3

x(3)

3x

35 ÷ y

Additional Example 2: Evaluating Expressions with Two Variables

A rectangle is 4 units wide. How many square units does the rectangle cover if it is 3, 4, 5, or 6 units long?

Make a table to help you find the number of square units for each length.

3 x 4 = square units

12

16

4 x 4 = square units

16

20

5 x 4 = square units

20

24

6 x 4 = square units

24

The rectangle will cover 12, 16, 20, or 24 square units.

z

8z + 2

7

58

9

11

Check It Out: Example 2A

Complete the table.

74

90

Check It Out: Example 2B

A rectangle is 7 units wide. What is the area of the rectangle if it is 8, 9, 10, or 11 units long?

7 · 8 = 56 square units;

7 · 9 = 63 square units;

7 · 10 = 70 square units;

7 · 11 = 77 square units

Check It Out: Example 2C

A rectangle has a length of 13 units. The perimeter of a rectangle is twice its width plus twice its length. Complete the table to find the perimeter of the rectangle if its width is 5, 6, 7, or 8 units wide.

l = 13

w

Check It Out: Example 2C Continued

38 units

40 units

42 units

Lesson Quizzes

Standard Lesson Quiz

Lesson Quiz for Student Response Systems

Lesson Quiz

1. Evaluate the expression to find the missing values in the table.

95

44

20

2. A rectangle is 6 units wide. What is the area of the rectangle cover if it is 2, 3, 4, or 5 units long?

12

18

24

30

Lesson Quiz for Student Response Systems

1. Evaluate the expression to find the missing values in the table.

A. 67, 97, 112

B. 67, 77, 92

C. 47, 77, 92

D. 47, 77, 112

Lesson Quiz for Student Response Systems

2. A rectangle is 8 units wide. How many square units does the rectangle cover if it is 5, 6, 7, or 8 units long?

A. 40, 46, 56, 66

B. 40, 48, 56, 64

C. 13, 14, 15, 16

D. 13, 15, 17, 19