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Variables, Algebraic Expressions,
and Simple Equations
1
Can you form your own definition of
a variable based on the following?
These are variables
These are not
A = # , C = #,
X = #,r = #, n = #
=#
=#
3, 10, 75, 8,
12, 1, 0
2
Discuss and make a list of
similarities and differences
(compare and contrast)
These are variables
A = # , C = #,
X = #,r = #, n = #
=#
=#
How they’re the
same:
These are not
3, 10, 75, 8,
12, 1, 0
How they’re different:
See if your definition that you came
up with matches the definition of a
variable:
Variable is…. A letter or symbol that stands
for an unknown number.
Examples: a , C, x, N,
,
Copy this down in your notes
4
Algebraic Expressions
• An expression consists of a combination of numbers,
operation symbols, and grouping symbols such as
parentheses ( ). An algebraic expression is an
expression that contains one or more variables an
operation and one or more numbers.
• Expressions:
3+4
6–2
(6 + 3) -1
Algebraic Expressions
3 (c + 8)
Notice that you
don’t see any
2a
equal signs
9–x
5
Reading and Writing Algebraic Expressions
+
plus
sum
more than
increased
by
total
in all
added to
-
minus
difference
less than
subtract
decreased
by
Take away
Subtracted
from
x
times
product
multiplied
each
of

divided
quotient
divided by
Other ways to show Other ways to show
division:
multiplication :
5(6)
5·6
12/6
6
Glue this in your notes and go over examples of how to read/write algebraic expressions
Using your notes, try to figure out what operation
(+,-,x,/) to use for the following:
4 increased by a number
25 less than a number
The phrase “a number” or
“some number” means that a
variable is needed.
7
Now, that we know the components of this expression, let’s
try to write an algebraic expression for each word phrase
4 increased by a number
4+c
*it does not matter what
letter you use, just as
long as you include a
variable.
25 less than a number
n – 25
*just because we see
25 first in the word
phrase, doesn’t mean
that 25 is written first
in the expression.
8
Try to write these on your own:
Add 3 to a number
Some number multiplied by 16
9
Now, try to translate, or write the
following algebraic expressions into a
word phrase on your own.
1) n - 5
2) 9 + t
10
Now, try to translate, or write the
following algebraic expressions into a
word phrase on your own.
Answers will vary…
1) n - 5 1) Take 5 away from a
number
2) 9 + t 2) 9 added to a number
11
When we evaluate algebraic expressions, we are
substituting a number in place of variable, then
solving for an answer
Evaluate each expression
when a = 12
1) a + 3
2) 17 – a
12
When we evaluate algebraic expressions, we are
substituting a number in place of variable, then
solving for an answer
Evaluate each expression
when a = 12
1) a + 3
12 + 3
15
2) 17 – a
17 – 12
5
13
You try to evaluate the following
when n = 4
1) 9n
*(what operation does this mean when a
number is right beside a variable? Look at
your notes if you don’t know)
2) 40 / n
14
You try to evaluate the following
when n = 4
1) 9n
9x4
36
2) 40 / n
40 / 4
10
15
An Equation is a complete
sentence that is either true or false
= shows that each side has the same value
examples:
x + 7 = 14
7 + 7 = 14
14 = 14
47 = 50 – 3
y – 6 = 13
16
Determine if the following are
expressions or equations:
1) 7x
2) (6-3) – 1 = 2
3) 14 = 7(2)
4) X + 9 = 13
5) 12 – 5
17
Determine if the following are
expressions or equations:
1) 7x
2) (6-3) – 1 = 2
3) 14 = 7(2)
4) X + 9 = 13
5) 12 – 5
•
•
•
•
•
1) expression
2) equation
3) equation
4) equation
5) expression
How could you tell the difference between the two?
18
#1 - In your own words, tell me what a
variable is?
#2 - Write down at least 2 examples of
variables:
#1 - In your own words, tell me what a
variable is? A variable is a letter or symbol
that represents an unknown #
#2 - Write down at least 2 examples of
variables: C, x, n,
Answers may vary
Write an algebraic expression for
each word phrase:
#3) subtract 14 from a number
#4) 15 is decreased by a number
#5) add 8 to a number
Write an algebraic expression for
each word phrase:
#3) take 14 from a number
n – 14
#4) 15 is decreased by a number
15 – n
#5) add 8 to a number
n + 8 or 8 + n
• Evaluate means to substiture a value, then
solve the problem.
Evaluate each expression when
x=9
#6) 7 + x _________
#7) x – 3 _________
Evaluate each expression when
x=9
#6) 7 + x _________
7 + 9 = 16
#7) x – 3 _________
9–3=6