Evaluate Algebraic Expressions

An expression is NOT an equation
because it DOES NOT have an equal sign.
There are 2 types of expressions.

5 + 84 Numerical
3x + 10 Algebraic
Notice there are no equal signs in these
expressions so they are not equations!
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A numerical expression contains only
numbers and symbols and NO LETTERS.

5 times 3 plus 8
(5•3) + 8


An algebraic expression contains
only numbers, symbols, and
variables. It is sometimes referred
to as a variable expression.
The product of 3 and x 3x
The sum of m and 8 m+8
The difference of r and 2 r-2


What is a variable?
A variable represents an unknown value.

1) 4 + x 2) 10 – ?
3) 5y 4) 20

A variable can be any letter of the
alphabet since it represents an unknown.

Word Phrases for multiplication are:
The product of 5 and a number c
5 • c or 5c
Seven times a number t
7 • t or 7t
6 multiplied by a number d
6 • d or 6d

The Placement rule for multiplication is:
The product of 5 and a number c
5 • c or 5c Always
Seven times a number t write the
7 • t or 7t variable
AFTER the
6 multiplied by a number d number.
6 • d or 6d

Evaluate means to find the value of an
algebraic expression by substituting
numbers in for variables.

m=2
6+m?
6+2
8

Evaluate means to find the value of an
algebraic expression by substituting
numbers in for variables.
r=3
7+r?
7+3
10

Evaluate the variable expression when n = 6.

1) n 8 2) n 2
6 8 6 2
14 4

Evaluate just means solve by substitution.


Evaluate the variable expression when n = 6.
3) 3n 4) n
6
3 6
6
18 6
1
Evaluate just means solve by substitution.


Evaluate the algebraic expression when n = 8.

1) 56 2) 20 n
n
20 8
56
8 12
7


Evaluate the expression if a = 3 and b = 4.
1) 3a b 2) 2b a
3 3 4 2 4 3
9 4 8 3
13 5


Evaluate the expression if a = 3 and b = 4.
3) 2ab 4) 5 ab
2 3 4 5 3 4
6 4 5 12
24 17


Evaluate the expression if x = 5 and y = 3.
3x 2) x 2
y 2
1)
y 2 2
5 3
3 5 25 9
3
15 34
3
5

Take Out Your Study Guide!!!


#1 TYPES OF EXPRESSIONS
An expression is NOT an equation because it
does not have an equal sign. There are 2 types
of expressions.
NUMERICAL EXPRESSION: Contains only numbers and
symbols. Example: 5 • 3 + 4
ALGEBRAIC EXPRESSION: Contains numbers,
symbols, and variables. Also known as a
variable expression. Example: m + 8
A VARIABLE is a letter or symbol that represents a
number. Example: x


#2
Evaluate if x = 3 and y = 4
2
2 x y Evaluate means solve.
2
2(3 4) Show the substitution.
2
2(7) Show your work down.
2(49) Circle your answer.
98
Show your work one step at a
time down. No equal signs!

Evaluate Algebraic Expressions

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