2-2 Variables and Expressions

Warm UpSimplify.

1. 4 + 7 3 1

2. 87 15 5

3. 6(9 + 2) + 7

4. 35 7 5

24

84

73

25

2-2 Variables and Expressions

Vocabularyvariableconstantalgebraic expressionevaluate

2-2 Variables and Expressions

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

A constant is a quantity that does not change.

2-2 Variables and Expressions

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

Algebraic Expressions NOT Algebraic Expressions

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.

2-2 Variables and Expressions

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

Additional Example 1A: Evaluating Algebraic Expressions

Substitute for y in 5 y.y 5 y

16

27

35

80 y = 16; 5 16 = 80

135

175

27 135

35 175

y = 27; 5 =

y = 35; 5 =

The missing values are 135 and 175.

2-2 Variables and Expressions

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

Additional Example 1B: Evaluating Algebraic Expressions

z z 5 + 4

20

45

60

20 z = 20; 20 5 + 4 = 20

z = 45; __ 5 + 4 = __

z = 60; __ 5 + 4 = __

13

16

45 13

60 16

The missing values are 13 and 16.

Substitute for z in z 5 + 4.

2-2 Variables and Expressions

Check It Out: Example 1A

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

t 8t

10

20

30

80

160

240

2-2 Variables and Expressions

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

Check It Out: Example 1B

m 52 - 2 m

4

7

10

17

11

5

2-2 Variables and Expressions

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

Check It Out: Example 1C

n n ÷ 6 - 4

60

48

36

6

4

2

2-2 Variables and Expressions

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

Check It Out: Example 1D

b 3 (2 + b)

3

6

9

15

24

33

2-2 Variables and Expressions

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

Instead of . . . You can write . . .

x 3 x 3

35 ÷ y

x(3) 3x

35y

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

Writing Math

2-2 Variables and Expressions

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

Additional Example 2: Evaluating Expressions with Two Variables

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

3 x 4 = square units

20

16

l w l x w

3 4 12

4 4

5 4

6 4

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

4 x 4 = square units

5 x 4 = square units

6 x 4 = square units

12

16

20

2424

2-2 Variables and Expressions

Complete the table.

Check It Out: Example 2A

z 8 z + 2

7

9

11

58

74

90

2-2 Variables and Expressions

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

Check It Out: Example 2B

7 · 8 = 56 square units;

7 · 9 = 63 square units;

7 · 10 = 70 square units;

7 · 11 = 77 square units

2-2 Variables and Expressions

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.

Check It Out: Example 2C

w

l = 13

2-2 Variables and Expressions

Check It Out: Example 2C Continued

w2 13 + 2 w

5 36 units6

7

8

38 units

42 units

40 units

2-2 Variables and Expressions

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

2-2 Variables and Expressions

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

Lesson Quiz

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?

95

44

20

12

l w l x w

2 6

3 6

4 6

5 6

18

24

30

x x2 – 5

10

7

5

2-2 Variables and Expressions

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

x 5x + 22

9

15

18

2-2 Variables and Expressions

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

Lesson Quiz for Student Response Systems

l w l x w

5 8

6 8

7 8

8 8