The Order of Operations

Section 3.4

Today’s Objective

• Recall PEMDAS

• Perform the proper order of Integer Operations

The Order of Operations

The Order of Operations• Number sentences and equations MUST be

solved in an exact order.– Parentheses– Exponents– Multiplication & Division –in order from left to

right– Sometimes you will divide before you multiply!

– Addition & Subtraction –in order from left to right-Sometimes you will subtract before you add!

The Order of Operations(PARENTHESES

)We always do parentheses first.

[Brackets are square parentheses.]

If there are no parentheses, skip this step.

The Order of Operations

EXPONENTS2

Exponents are also known as “powers” (e.g. two to the third power)

23= 2 x 2 x 2 = 4 x 2 = 8

We now interrupt this show for a mini-lesson on MANNERS!

If you were to walk down the street and see two people you know, you would greet the person you come to first… and not ignore them to talk to the second person first … I HOPE! You can talk to the second person in a minute.

Ready????

Good Manners

Mr. Division

Ms. Multiplication

Hello Ms. Multiplication! How are you

today?

Hello Mr. Division! How

are you today?

Doing great,

thanks! Gotta fly!

Kinda tired today, but thanks for

asking!

In this case, we talked with multiplication first, then

division because that was the order in which we met them. We did what was

polite! Hooray!

Good MannersMs.

Multiplication

Mr. Division

Hello Mr. Division! How

are you today?

Hello Ms. Multiplication! How are you

today?

Not bad at all! Walking in my

sleep is a great way to get exercise!

Fantastic! There is no

traffic up here!

In this case, we talked with division first, then

multiplication because that was the order in which we met them. We did what

was polite! Hooray!

Bad MannersMs.

Multiplication

Mr. Division

Ms. Multiplication! I need to see you!

Hold on a minute!

Why didn’t you talk to Division

first?

But I thought I was supposed to

see you first!

Nope! You blew it, Buddy! How rude! What

am I? Chopped liver? I was here

first!

But I thought…Oh, Boy! I guess

I was wrong!

Oops! You blew it! Never ignore the first person to get to

the second! It is rude and wrong!

Now back to our regularly scheduled program!

You need to practice the manners lesson for the next two steps…

With multiplication and division, you need to “talk to”whichever comes first.

– Sometimes you will multiply first then divide.– Sometimes you might divide first then multiply. – Sometimes you may have to multiply, divide, then

multiply again. – Sometimes you may only have one of these

operations.The same rule applies for addition and subtraction!

The Order of Operations

Multiplication = Division

Multiplication and Division are equals! Do them in order left to right. Sometimes you might have to do division first. Think of our mini-lesson on manners!

The Order of Operations

Addition = Subtraction

Addition and Subtraction are equals! Do them in order left to right. Sometimes you might have to do subtraction first. Think of our mini-lesson on manners!

Good Manners

Mr. Subtraction

Mr. Addition

Hello Mr. Addition!

How are you today?

Hello Mr. Subtraction! How are you

today?

In a hurry! Gotta run!

A bit under the weather…

It will pass!

Good MannersMr. Addition

Mr. Subtraction

Hello Mr. Subtraction! How are you

today?

Hello Mr. Addition!

How are you today?

Not too bad! I think this rain is

helping me grow!

Great! Getting my exercise!

Bad MannersMr. Addition

Mr. Subtraction

Mr. Addition! Can I talk to you

for a minute!

Why didn’t you talk to Subtraction

first?

But I thought I was supposed to

see you first!

What am I? Chopped liver? I was here first! Rude people!

But I thought…Oh, Boy! I guess

I was wrong!

Nope! Don’t be rude! Talk to the dude who comes

first!

Example #1Always show all of your steps!

(2 + 3) x 9x 945

(2 + 3) x 9 = 45

5

Example #2Always show all of your steps!

16 ÷ 4 x 24 x

2816 ÷ 4 x 2 = 8

Example #3Always show all of your steps!

9 x (3 – 1) ÷ 62 ÷ 69 x

÷ 6183

9 x (3 – 1) ÷ 6 = 3

Example #4Always show all of your steps!

6 - 3 x 2 + 46 - 6 + 4

+ 404

6 - 3 x 2 + 4 = 4

Example #5Always show all of your steps!

(14 - 10)2 ÷ 8 = 2

(14 - 10)2 ÷ 8÷ 8(4)24 x

4 16 ÷ 82

Let’s Practice…

Practice #1

(4 + 6) ÷ 5 – 2

(10) ÷ 5 – 22 – 2

0Answer:

(4 + 6) ÷ 5 – 2

Practice #2

7 x 9 ÷ 3 – (8 – 5)

7 x 9 ÷ 3 – (3)63 ÷ 3 – (3)

18Answer: 21 – (3)

7 x 9 ÷ 3 – (8 – 5)

Practice #3

36 ÷ 6 + 3 x 5 – 2 x 336 ÷ 6 + 3 x 5 – 2 x 3

6 + 3 x 5 – 2 x 3

15Answer:

6 + 15 – 2 x 36 + 15 – 6

21 – 6

Practice #4

Answer: -10

Practice #5

Answer: 0

EXIT TICKET

-3 x (3 x 5 - 3 x 8)