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Today we will be learning about the

"Order of Operations"

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8 * 36 =

126 ÷ 6 =

29 * 5 =

42 ÷ 3 =

Let's do a few practice problems before we get started.

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Let's review what we learned in the last lesson.....

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A Numerical Expression is a combination of numbers and operations.

Examples: 4 + 3 * 5

22 + 6 ÷ 2

(10 * 8) - 7

1 2 34 56

Let's begin!

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Do you know what we mean by "Operations"?

We "operate " on the numbers by

Dividing

MultiplyingAdding

Subtracting+

-

÷x

1

2

3

4

5

67

8

9

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How might you solve this problem? 6 + 2 * 5 =

Could another student solve this problem differently?

6 + 2 * 5 =

How do we know which one is correct?????

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To find the correct answer, we need to follow an

Order of Operations

This tells us which operation to perform first so that everyone gets the same final answer!

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Order of Operations1.

Parentheses2. Exponents

3. Multiplication Division4. Addition Subtraction

Simplifying the expressionsinside grouping symbolsexamples: (3+5) or (4*6)Find the value of all powersexamples: 23 or 42

Perform multiplication or division in the order in which it occurs when reading the expression from left to right.

Perform addition or subtraction in theorder in which it occurs when reading the expression from left to right.

PEMDAS

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We can remember the Order of Operations as

PPEEMMDDAASSP E M D A Sarentheses

xponents

ultiplicationivisiondditionubtraction

"Please Excuse My Dear Aunt Sally"

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P E M D A Sarenthesesxponents

ultiplicationivisiondditionubtraction

Or

"Purple Eggplants Make Delicious Afternoon Snacks!"

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P E M D A Sarenthesesxponent

s ultiplicationivision

ddition ubtractio

n

Let's try some.....whichever comes first

whichever comes first

Numerical expression

4 + 3 * 5 =Read from left to right...just like a book.There are no Parentheses.There are no Exponents.There is some Multiplication so do this first.4 + 15

= We perform the Addition last.

19

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P E M D A Sarenthese

s

xponents

ultiplicatio

n ivision

dditionubtraction

whichever comes first whichever comes first

"Purple Eggplants Make Delicious Afternoon Snacks!"

10 - 2 + 8 =Read the expressionfrom left to right.

8 + 8 =We perform Addition and Subtraction in the order in which they occur.So do the Subtraction first!

Then do the Addition.16

Numerical Expression

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P E M D A Sarenthesesxponents

ultiplication

ivisiondditionubtraction

whichever comes first

whichever comes first

"Please Excuse My Dear Aunt Sally"

20 ÷ 4 + 17 * (9 - 6) =

Do the operations in Parentheses first.

20 ÷ 4 + 17 * 3 =

5 + 17 * 3 =

5 + 51 =56

There are no Exponents.

Perform Multiplication or Division in the order in which they occur.The Division should be done first.Then perform the Multiplication.Finally perform the Addition.

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Your turn!

10 + 2 x 15 =

25 x (5 - 2) ÷ 5

=

10 + (6 - 5) =

24 ÷ 23 + 6 =

PE

M

D

A

S

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Sometimes we have operations "nested" within the parentheses which must be completed first.

Example:60 ÷ (12 + 23) x 9 =60 ÷ (12 + 8) x 9 =

60 ÷ 20 x 9 =

3 x 9 =

27

We want to do the Parentheses but first we must take care of the Exponents WITHIN the Parentheses.

Then we can solve the Parentheses.Division comes before Multiplication when reading the expression from left to right.

Finally we can perform the Multiplication.

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Practice Problems

1) 9 + 3 - 5 =

2) (26 + 5) x 2 - 15 =

3) 18 ÷ (2 + 7) x 2 + 1 =

4) 52 + 8 ÷ 2 =

5) 10 - 3 + 9 =

6) 5 + (21 - 3) =

7) 21 ÷ (3 + 4) x 3 - 8 =

8) 19 - (32 + 4) + 6 =

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What is the value of 100 divided by 5 times 4 minus 79?

(Can you write this out as a "Numerical Expression"?)

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Can you develop an expression that usesmultiplication, division, addition, and subtraction,

as well as grouping symbols, whose solution is 2?????

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Adult admission to a football game is $5, and student

admission is $2. Which expression could be used tofind the total cost of 2 adult and 4 student

admissionsto the football game?

a.) 2 + $5 x 4 + $2b.) $5 + $2 + 6

c.) $2 + 4 x $5 + 2

d.) 2 x $5 + 4 x $2

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1.) Can you give me an example of a “ Numerical Expression“ ?

2.) What do I mean by "Operations“ ?

3.) In what order do I perform the "Operations“ ?

45 + 79 – (5 x3)

To operate on the numbers by using the rules of PEMDAS

ParenthesesP

E

M

D

A

S

Exponents

Multiplication

DivisionAddition

Subtraction

Your Your turnturn

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a.) 5 x 6 - (9 - 4) =

b.) 16 ÷ 2 + 8 x 3 =

c.) 43 - 24 + 8 =

d.) 45 ÷ 9 + 8 - 7 + 2 x 3 =

e.) (8 + 1) x 11 - 13 =

4.) Find the value of each expression?

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You did a GREAT job today!!!

*We learned to identify a "Numerical Expression".

4 + (8 x 2) - 3

* We learned about "Operations". + - ÷ x

* We learned that we need to perform "Operations" in a certain order.

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* We learned some funny ways to remember the "Order of Operations".

Please Excuse My Dear Aunt Sally!

Purple Eggplants Make Delicious Afternoon Snacks!

P

E

M

D

A

S

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

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You did a splendid Job

Be sure to practice what you have learned