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Algebra I
1.1 Evaluate Expressions
Question:
How do you evaluate algebraic
expressions and powers?
Answer:
By substituting numbers in for the
variable and performing the indicated
operation(s)
Vocabulary
• Variable — a letter used to
represent one or more numbers
• Expression--numbers, variable,
and operations (ex: mn)
• Algebraic Expression — an
expression that includes at least
one variable
Section 1.1
EVALUATING AN EXPRESSION WITH
ONE OR MORE VARIABLES
Please look at the handy chart below & let’s talk it out:
Algebraic
Real Meaning
Expression
5(n) 5·n 5n
5 times n
14/y
14÷y
Operation
Used
Multiplication
14 divided by y
Division
6+c
6 plus c
Addition
8–x
8 minus x
Subtraction
Evaluate algebraic expressions
Evaluate the expression when n = 3.
a. 13 •n =13 •3
=39
Substitute 3 for n.
Multiply.
b. 9/n =9/3
=3
Substitute 3 for n.
Divide.
c. n -1 = 3 - 1
=2
Substitute 3 for n.
Subtract.
d. n + 8 = 3 + 8
= 11
Substitute 3 for n.
Add.
Let’s Practice
Let y = 2
1. 6y
2. 8 divided by y
3. y + 4
4. 11 take away y
Here’s the
situation:
You’re saving
money to buy
an iPhone…
If you know how much it costs ($360) and how
much you earn each week, you can determine how
many weeks it will take you to save enough $$$.
You earn about $64/week, how many weeks will it
take you to buy your iPhone?
You can do this by EVALUATING AN EXPRESSION THAT
INVOLVES A VARIABLE:
64w = ?
$399
Section 1.1
EVALUATING AN EXPRESSION WITH
ONE OR MORE VARIABLES
Evaluate the expression BELOW when:
w = 2, w = 3, w = 4… until you get an answer.
64w = ?
64(2) = 128
64(3) = 192
64(4) = 256
64(5) = 320
64(6) = 384
Section 1.1
EVALUATING AN EXPRESSION WITH
ONE OR MORE VARIABLES
The total cost of seeing a movie at a theater can be
represented by the expression a + r where a equals
the cost of admission (in dollars) and r is the cost (in
dollars) of refreshments. Let’s say you pay $7.25 for
admission and $7.50 for refreshments. Find the total
cost.
total cost = a + r
= 7.25 + 7.50
= 14.75
Vocab
• Power — an expression that
represents repeated multiplication
of the same factor
• Exponent — the number of times
the base gets repeated
• Base — the number that is
multiplied as many times as the
exponent
Power
(1/2)3
Words
Product
Seven to the first
power
7
Five to the second
power
5•5
One half to the third
power -ORone half cubed
½•½•½
Z5
Z to the fifth power z•z•z•z•z
71
52
More Practice…
Write in words and expand using numbers
1. 95
2.
28
3.
N4
4.
x3 when x = 8
5.
k2 when k = 2.5
Section 1.1
EVALUATING AN EXPRESSION WITH
ONE OR MORE VARIABLES
Each edge or side of a medium sized pop-up storage cube
is 14 inches long. The storage cube is made so that it can
be folded flat when not in use. Find the volume of the
storage cube.
V = s3
= 143
= 2,744
The volume of the storage
cube is 2,744 cubic inches.
14 in.
Closer
How do you evaluate an expression that
contains variables?
• You substitute the values of the
variable in the expression and simplify
the resulting numerical expression.