Transcript Order of Operations

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Objective
Evaluate expressions using
the order of operations
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Vocabulary
Numerical expression
An expression that contains numbers and at
least one operation
3+4
7–6
6+4-3
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Vocabulary
Order of Operations
A set of rules to evaluate expressions
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Order of Operations Rules
P 1. Do all operations within grouping symbols first.
( )
[ ]
{ }
E 2. Evaluate all powers before other operations.
exponents
32
square roots  16
MD3. Multiply and divide in order from left to right.


x
3(4)
AS 4. Add and subtract in order from left to right.
+
-
Please Excuse My Dear Aunt Sally
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Example 1 Evaluate Expressions
Example 2 Evaluate Expressions
Example 3 Evaluate Expressions with Powers
Example 4 Evaluate Expressions with Powers
Example 5 Evaluate an Expression
Evaluate
27 - (18 + 2)
27 - 20
7
Write problem
Follow Order of Operations rules
P
E
MD
AS
Work inside parenthesis first
Bring down
Add
27 -
18 + 2
Subtract
20 from 27
Answer: 7
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Evaluate
Answer:
16
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Evaluate
15 + 5  3 - 2
15 + 15 - 2
Write expression
Follow Order of Operations Rules
P
E
MD
AS
Multiply before adding and
subtracting
Bring down 15 +
Multiply 5  3
Bring down - 2
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Evaluate
Follow rules of Order of Operations
15 + 15 - 2
30 - 2
P
E
MD
AS
Add and subtract from left to right
Add 15 + 15
28
Bring down - 2
Subtract 2 from 30
Answer: 28
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Evaluate
Answer: 15
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Evaluate
12  104
12  10,000
120,000
Write expression
Follow rules of Order of Operations
P
E
MD
AS
Do exponents first
Bring down 12 
Find 104
Multiply 12  10,000
Answer: 120,000
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Evaluate
Answer: 9,000
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Evaluate
28  (3 -
28  ( 2
)2
1)2
Write expression
Follow rules of Order of Operations
P
E
MD
AS
Work inside parenthesis first
Bring down 28  (
Subtract 3 - 1
Bring down )2
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Evaluate
28  ( 2 )2
28  4
Follow Order of Operations Rules
P
E
MD
AS
Do exponents
7
Bring down 28  (
Since 2 is in parenthesis, find the
square of 2
Answer: 7
Divide 28  4
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Evaluate
Answer: 4
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Evaluate
.
32 - 5 ( 4 + 2 ) + 8  2
Write expression
Follow Order of Operations Rules
P
E
MD
AS
32 - 5 ( 6 ) + 8  2
Work inside the parenthesis first
Bring down 32 - 5 (
Add 4 + 2
Bring down ) + 8  2
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Evaluate
32 - 5 ( 6 ) + 8  2
32 - 30 + 16
.
Follow Order of Operations Rules
P
E
MD
AS
Multiply from left to right
Bring down 32 Multiply 5(6)
Bring down +
Multiply 8  2
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Evaluate
.
32 - 30 + 16
Follow Order of Operations Rules
P
E
MD
AS
2 + 16
Add and subtract from left to right
18
Subtract 32 - 30
Bring down + 16
Add 2 + 16
Answer: 18
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Evaluate
Answer: 9
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Assignment
Lesson 1:3 Order of Operations
15 - 38 All
Use the table shown below. Taylor is buying two
video game stations, five extra controllers, and ten
games. What is the total cost?
Item
game station
controller
game
Quantity
2
Unit Cost
$180.00
5
$24.95
10
$35.99
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number
of game
stations
cost of
game
station
number of
controllers
2
$180
5
cost of
controller
number
of
games
cost
of game
$24.95
10
$35.99
Multiply from left to right.
Add.
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Check Check the reasonableness of the answer by
estimating. The cost is about (2 × 200) + (5 × 25)
+ (10 × 40) = 400 + 125 + 400, or about
$925. The solution is reasonable.
Answer: So, the total cost is $844.65.
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Use the table shown below. Suzanne is buying
a video game station, four extra controllers,
and six games. What is the total cost?
Item
Quantity
Unit Cost
game station
1
$180.00
controller
4
$24.95
game
6
$35.99
Answer: $495.74
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