2-1
2-1 Variables
Variablesand
andExpressions
Expressions
Warm Up
Problem of the Day
Lesson Presentation
Course
1
Course 11
Course
2-1 Variables and Expressions
Warm Up
Simplify.
1. 4 + 7  3  1 24
2. 87  15  5
84
3. 6(9 + 2) + 7 73
4. 35  7  5
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25
2-1 Variables and Expressions
Problem of the Day
How can the digits 1 through 5 be arranged
in the boxes to make the greatest product?
4

Course 1
3
5
1
2
2-1 Variables and Expressions
Learn to identify and evaluate expressions.
Course 1
2-1 Variables and Expressions
Vocabulary
variable
constant
algebraic expression
Course 1
2-1 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.
Course 1
2-1 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
150 + y
35  w + z
NOT Algebraic Expressions
85 ÷ 5
10 + 3  5
To evaluate an algebraic expression, substitute
a number for the variable and then find the
value.
Course 1
2-1 Variables and Expressions
Additional Example 1A: Evaluating Algebraic
Expressions
Evaluate the expression to find the missing
values in the table.
y
5y
16
80
y = 16; 5  16 = 80
27
135
y = 27; 5  27 = 135
35
175
y = 35; 5  35 = 175
Substitute for y in 5  y.
The missing values are 135 and 175.
Course 1
2-1 Variables and Expressions
Additional Example 1B: Evaluating Algebraic
Expressions
Evaluate the expression to find the missing
values in the table.
z
z  5 + 42
20
20
z = 20; 20  5 + 16 = 20
45
25
z = 45; 45
__  5 + 16 = 25
__
60
28
z = 60; 60
__  5 + 16 = 28
__
Substitute for z in z  5 + 42.
The missing values are 25 and 28.
Course 1
2-1 Variables and Expressions
Check It Out: Example 1A
Evaluate the expression to find the missing
values in the table.
x
x9
18
2
x = 18; 18  9 = 2
36
4
x = 36; 36  9 = 4
54
6
x = 54; 54  9 = 6
Substitute for x in x  9.
The missing values are 4 and 6.
Course 1
2-1 Variables and Expressions
Check It Out: Example 1B
Evaluate the expression to find the missing
values in the table.
z
8  z + 23
7
64
z = 7; 8  7 + 8 = 64
9
80
9 8 = __
80
z = 9; 8  __+
11
96
11 + 8 = __
96
z = 11; 8  __
Substitute for z in 8  z + 23.
The missing values are 80 and 96.
Course 1
2-1 Variables and Expressions
You can write multiplication and division expressions
without using the symbols  and .
Instead of . . .
x3
35 ÷ y
You can write . . .
x3
x(3)
3x
35
y
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.”
Course 1
2-1 Variables and Expressions
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
l
w
l x w number of square units for each length.
3
4
12
3 x 4 = 12 square units
4
4
16
4 x 4 = 16 square units
5
4
20
5 x 4 = 20 square units
6
4
24
6 x 4 = 24 square units
The rectangle will cover 12, 16, 20, or 24 square units.
Course 1
2-1 Variables and Expressions
Check It Out: Example 2
A rectangle is 3 units wide. How many square
units does the rectangle cover if it is 2, 3, 4, or
5 units long?
Make a table to help you find the
l
w
l x w number of square units for each length.
2
3
6
2 x 3 = 6 square units
3
3
9
3 x 3 = 9 square units
4
3
12
4 x 3 = 12 square units
5
3
15
5 x 3 = 15 square units
The rectangle will cover 6, 9, 12, or 15 square units.
Course 1
2-1 Variables and Expressions
Lesson Quiz
x
x2 – 5
95
10
44
7
20
5
1. Evaluate the expression to find
the missing values in the table.
2. A rectangle is 6 units wide.
How many square units does
the rectangle cover if it is 2, 3,
4, or 5 units long?
Course 1
l
w
l xw
2
6
12
3
6
18
4
6
24
5
6
30