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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
1. Do all operations within grouping symbols first.
( ) [ ] { }
2. Evaluate all powers before other operations.
exponents 32 square roots 16
3. Multiply and divide in order from left to right.
x 3(4)
4. Add and subtract in order from left to right.
+ -
Please Excuse My Dear Aunt Sally
P
E
MD
AS
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
Answer: 7
Write problem
Evaluate
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27 - (18 + 2)
P E MD AS
Work inside parenthesis first
Add 18 + 2
Bring down 27 -
27 - 20
Subtract 20 from 27
7
Follow Order of Operations rules
Answer: 16
Evaluate
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Evaluate
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Write expression15 + 5 3 - 2
P E MD AS15 + 15 - 2Follow Order of Operations Rules
Multiply before adding and subtracting
Multiply 5 3
Bring down - 2
Bring down 15 +
Answer: 28
Evaluate
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P E MD AS15 + 15 - 2
30 - 2
28
Follow rules of Order of Operations
Add and subtract from left to right
Add 15 + 15
Bring down - 2
Subtract 2 from 30
Answer: 15
Evaluate
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Answer: 120,000
Evaluate
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Write expression12 104
P E MD AS12 10,000
120,000
Follow rules of Order of Operations
Do exponents first
Bring down 12
Find 104
Multiply 12 10,000
Answer: 9,000
Evaluate
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Evaluate
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Write expression28 (3 - 1)2
P E MD AS28 ( 2 )2 Follow rules of Order of Operations
Work inside parenthesis first
Bring down 28 (
Subtract 3 - 1
Bring down )2
Answer: 7
Evaluate
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P E MD AS28 ( 2 )2
28 4
7
Follow Order of Operations Rules
Do exponents
Bring down 28 (
Since 2 is in parenthesis, find the square of 2
Divide 28 4
Answer: 4
Evaluate
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Evaluate .
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Write expression32 - 5 ( 4 + 2 ) + 8 2
P E MD AS32 - 5 ( 6 ) + 8 2
Follow Order of Operations Rules
Work inside the parenthesis first
Bring down 32 - 5 (
Add 4 + 2
Bring down ) + 8 2
Evaluate .
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P E MD AS32 - 5 ( 6 ) + 8 2
32 - 30 + 16
Follow Order of Operations Rules
Multiply from left to right
Bring down 32 -
Multiply 5(6)
Bring down +
Multiply 8 2
Answer: 18
Evaluate .
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P E MD AS32 - 30 + 16
2 + 16
18
Follow Order of Operations Rules
Add and subtract from left to right
Subtract 32 - 30
Bring down + 16
Add 2 + 16
Answer: 9
Evaluate
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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 Quantity Unit Cost
game station 2 $180.00
controller 5 $24.95
game 10 $35.99
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number of gamestations
cost of gamestation
number ofcontrollers
number of
gamescost
of gamecost of
controller
2 $180 5 10 $35.99$24.95
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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