The document discusses different types of expressions and how to evaluate algebraic expressions. It defines an expression as not containing an equal sign, and describes two types of expressions - numerical expressions containing only numbers and symbols, and algebraic expressions containing numbers, symbols, and variables. The document provides examples of expressions and explains that a variable represents an unknown value. It also discusses how to evaluate expressions by substituting values for variables.

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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

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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

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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.

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

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

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Evaluate means to find the value of an
algebraic expression by substituting
numbers in for variables.
m = 2
6 + m ?
6 + 2
8

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

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Evaluate the variable expression when n = 6.
1) n 8+ 2) n 2−
6 8+
14
6 2−
4
Evaluate just means solve by substitution.

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

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Evaluate the algebraic expression when n = 8.
1) 56
n
2) 20 n−
56
8
7
20 8−
12

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Evaluate the expression if a = 3 and b = 4.
1) 3a b+ 2) 2b a−
3 43• +
9 4+
13
2 34• −
8 3−
5

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Evaluate the expression if a = 3 and b = 4.
3) 2ab 4) 5 ab+
2 43• •
6 4•
5 43+ •
5 12+
1724

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

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Take Out Your Study Guide!!!

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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
TYPES OF EXPRESSIONS#1

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