Algebra 1
Ch 1.3 – Order of
Operations
Objective

Students will use the order of operations
to evaluate algebraic expressions
Comment



It is expected that you already know the
rules for the order of operations…
You have been working with this concept
since elementary school…
This lesson should be a quick review…
Order of Operations

The order of operations are:
• Parenthesis
• Exponents
• Multiplication & Division, in order, from left to
right
• Addition & Subtraction, in order, from left to
right
PEMDAS is used to remember the order of operations.
Working with the order of
operations


Mathematicians have established an
order of operations to evaluate an
expression involving more than one
operation.
Start with operations within grouping
symbols. Then evaluate powers. Then
do multiplication and division in order
from left to right. Finally, do addition and
subtraction from left to right.
Evaluating Algebraic Expressions

When evaluating any algebraic
expression you are to use the following
process:
1. Write the expression
2. Substitute
3. Simplify
Note: At this level you are required to demonstrate
your understanding of the material. Anything less than
the above process will not be acceptable for credit!
Comment…

Ok…now that you know the rules and
the process…let’s put it together and
look at some examples…
Example #1

Evaluate the expression 3x2 + 1 when x = 4
3x2 + 1
1. Write the expression
3(42) + 1
2. Substitute 4 for x
3(16) + 1
3. Evaluate the power
48 + 1
4. Evaluate the product
49
5. Evaluate the sum
Answer: The value of the expression is 49
Example #2

Evaluate the expression 32  x2 – 1 when x = 4
32  x2 – 1
1. Write the expression
32  (42) – 1
2. Substitute 4 for x
32  16 – 1
3. Evaluate the power
2–1
4. Evaluate the quotient
1
5. Evaluate the difference
Answer: The value of the expression is 1
Using a Fraction Bar



A fraction bar can act as a grouping symbol.
The expression (1 + 2)  (4 – 1) is the same
as 1 + 2
4–1
It doesn’t matter if you do the top or the
bottom first. However, you must follow the
order of operations to simplify the numerator
and the denominator.
Example #3 – Using a fraction
bar
74
8 7 1
1. Write the expression
2
74
2. Evaluate the power
8  49  1
28
3. Simplify the numerator
8  49  1
28
56
1
2
4. Simplify the denominator
working from left to right
5. Simplify the fraction
Comments



On the next couple of slides are some
practice problems…The answers are on the
last slide…
Do the practice and then check your
answers…If you do not get the same answer
you must question what you did…go back
and problem solve to find the error…
If you cannot find the error bring your work to
me and I will help…
Your Turn
Evaluate the expression for the given value of the variable
3
1. 3 + 2x when x = 2
2 . 6  2p when p = 5
2
3.
x
 16 w hen x = 14
7
4 . 27 -
24
w hen b = 8
b
5.
4
5
 n + 13 w hen n =
1
5
Your Turn

Evaluate the expression
6. 6  3 + 2  7
9.
13  4
18  4  1
2
7 . 7[(18 - 6) - 6]
5 2
3
10.
8. [10 + (5  2 )]  6
2
1 6  8
2
Your Turn Solutions
1.
2.
3.
4.
5.
19
300
18
24
17
6.
7.
8.
9.
10.
16
49
10
3
250
29
Summary



A key tool in making learning effective is
being able to summarize what you learned in
a lesson in your own words…
In this lesson we talked about the order of
operations…Therefore, in your own words
summarize this lesson…be sure to include
key concepts that the lesson covered as well
as any points that are still not clear to you…
I will give you credit for doing this
lesson…please see the next slide…
Credit



I will add 25 points as an assignment grade for you working on
this lesson…
To receive the full 25 points you must do the following:
• Have your name, date and period as well a lesson number as
a heading.
• Do each of the your turn problems showing all work
• Have a 1 paragraph summary of the lesson in your own
words
Please be advised – I will not give any credit for work submitted:
• Without a complete heading
• Without showing work for the your turn problems
• Without a summary in your own words…