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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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