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Order of Operations

Please Excuse My Dear Aunt Sally​

Now, what does the phrase above mean? Well, the phrase above helps us understand a math concept: the order of operations. In this lesson, you will learn about the order of operations.​

Let's start off with a simple question!​

Here is a simple question: What is an operation? An operation is a mathematical action. Addition, subtraction, multiplication, division, and calculating the root are all examples of operations. But, what are the order of operations? The order of operations is when you solve a mathematical problem with this word, P E M D A S, or PEMDAS. And, this brings us back to Aunt Sally.​

​PEMDAS: Introduction

​PEMDAS, or rather P E M D A S, is when you solve a math problem in order. To remember this abbreviation, you will know this phrase: Please Excuse My Dear Aunt Sally. Now, let's take a closer look of what PEMDAS stands for.

PEMDAS: What it means​

P: Parentheses. We solve what is in the parentheses.

E: Exponents. We figure out the exponent.

M: Multiplication. We multiply to figure out the problem.

D: Division. We divide to figure out the problem.

A: Addition. We add to figure out the problem.

S: Subtraction​. We subtract to figure out the problem.

Let's go over a problem together using PEMDAS!

Problem 1: 7x4-6=?​

How do we solve this problem?​

​Should you subtract 6 from 4 and then multiply by 7? No. According to PEMDAS, we multiply before we subtract. So, multiply 7 and 4, you get 28. Then, subtract 6 from 28. We get 22. So, 7x4-6=22. Let's go over another problem!

Problem 2: 7+7x3=?​

How do we solve this problem?​

We add 7 and 7, we get 14. Then, we multiply 14 and 3, we get 42. But, this way is wrong! Remember, you do not add first. We multiply first. So, we multiply 7 and 3, we get 21. Then, we add 7 and 21, we get 28. ​So, 7+7x3=28. Let's look at some more complex problems.

Problem 3: 6x3²=?​

How do we solve this problem?​

This problem will seem tricky.​ Here is the wrong way to solve the problem: (6x3)². Multiply 6 and 3, we get 18. Then, you now get 18², which is 324. Why is that wrong? Because you violated the order of operations. You do not multiply first. You figure out the exponent first. Here is how is should be done: 3² is equal to 9, so, multiply 6 and 9, we get 54. So, 6x3²=54. Let's look out one more problem. The next problem may seem challenging.

Problem 4: 5x10-(8x6-15)+4x20/4=?​

How do we solve this problem?​

Remember the order of operations. First, we solve what's in the parentheses. 8x​6 is 48, then subtract 15, you get 33. Next, you multiply. Multiply 5 and 10, you get 50. Then, multiply 4 and 20, you get 80. Then divide 4, you get 20. Here is the equation now: 50-33+20=? Then, there could be an impossible way to solve, but now, it should look like this: 50-13. We now get 37. So, 5x10-(8x6-15)+4x20/4=37. Now, let's take a quiz!

Multiple Choice

16 + 5 x 8

• 168

• 29

• 65

• 56

• 861

Multiple Choice

3 +(35 – 21) x 2

• 34

• 13

• 31

• 43

• 20

Multiple Choice

7 + 2 x (6 + 3) ÷ 3 – 7 

• 6

• 5

• 7

• 4

• 8

Multiple Choice

11 + 19 x 2

• 60

• 50

• 49

• 54

• 72

Multiple Choice

(14 + 2) x 2 + 3

• 21

• 35

• 80

• 43

• 68

Multiple Choice

120 ÷ (6 + 12 x 2)

• 150

• 40

• 6

• 4

• 20

Multiple Choice

12 + 2 x 44

• 100

• 616

• 110

• 600

• 660

Multiple Choice

 10 x 2 – (7 + 9)

• 21

• 16

• 4

• 13

• 24

Order of Operations

GEMDAS

GEMDAS are the rules we use to simplify or evaluate complicated numerical expressions.

GEMDAS

• G - grouping

• E - exponents

• M - multiplication

• D - Division

• A - Addition

• S -

Multiple Choice

The grouping in GEMDAS stands for?

• Commas, Periods, Question Marks

• Exponents, Multiplication, Division

• Brackets, Braces, Parentheses

• Subtraction, Addition, Multiplication

Multiple Choice

What operation would you do first in this expression?

• 15-8

• 
  

  $8\div4$

• 4 x 7

Multiple Choice

What operation would you do first in this expression?

• $15\div5$

• 5 - 2

• 2 x 12

Multiple Choice

Which operation would you perform first between addition and subtraction?

• You do subtraction first.

• With subtraction and addition, you go left to right.

• You do addition first.

Multiple Choice

Which operation would you perform first?  $\left(-3\right)\times\left(-2\right)\times\left(1\right)\div2$  

•  $-3\times-2$ 

•  $-2\times1$ 

•  $1\div2$ 

Multiple Choice

 $Solve:$   $\ 2+3\times6\div3$  

• 10

• 6.6

• 8

Multiple Choice

Solve: $5-2\left(2^3-5\right)$  

• -1

• 3

• -9

• 9

Multiple Choice

Solve: $\left(10-5\right)^2+\left(12\div4\right)$  

• 13

• 28

• -22

• 7

Multiple Choice

 $Solve:4\left(2\times3^2\right)$  

• 32

• 72

• 48

• 44

Multiple Choice

 $\left(-12\right)-\left(-6\right)\div3$  

Solve:

• -2

• 2

• -10

• 10

Order of Operations

by Mrs. Schiel

​Vocabulary

• ​Expression - representation of a quanitiy. Has no equal sign

• ​Operations - Add, subtract, multiply, divide

• Grouping symbols - parenthesis and brackets

• Simplify - means to solve

• Evaluate - means to solve

​What is the order of operations?

• ​The order of operations is the way to simplify expressions by performing operations in a specific order

​What is the order of operations?

1. ​Solve anything inside of grouping symbols ( ) { } these are parenthesis and brackets

2. Solve for exponents

3. ​Going from left to right solve any multiplication and division, which ever comes first

4. ​Going from left to right solve any addition or subtraction, which ever comes first.

​So what does it look like to solve using the order of operations?

​ Let's take a look at this following expression.

​

​

​

​Try to solve it yourself.

Poll

What did you get when you solved this? 

• 22

• 19

• I got a different answer

​So what happened?

​If you solve WITHOUT the order of operations, you would add and then multiply.

3 + 8 x 2

​11 x 2

​22

​

​If you solve WITH the order of operations you would multiply and then add.

​3 + 8 x 2

​3 + 16

​19

​Let's look at some examples

​Simplify 4 + 3 x (2 - 4)

​Step 1: Are there parenthesis? Solve what is inside. 4 + 3 x (2 - 4)

​Step 2: What's next? Is there multiplication or division? 4 + 3 x 2

​Step 3: What's next? Is there additon or subtraction? 4 + 6

​Step 4: What is your answer? 10

​Let's try another

Multiple Choice

Which is the correct order of operations?

• PEMDAS

• DASMPE

• PEMASD

• SAPMED

Multiple Choice

Which should you look for FIRST when using the order of operations. 

• Parenthesis 

• Multiplication 

• Division 

• Addition 

Multiple Choice

Which operation is performed FIRST? (13 - 1) + 4

• addition

• subtraction

• multiplication

Multiple Choice

Which operation is performed FIRST: 38 + (9 x 6) ÷ 3

• addition +

• division ÷

• multiplication X

Multiple Choice

What would be my first step? 3 + 4 x 6 - 4 =

• addition

• multiplication

• subtraction

• exponents

Multiple Choice

What are the steps to solve the following expression? 50 − 16 ÷ 2

• add, multiply

• subtract, divide

• divide, subtract

• subtract, multiply

Multiple Choice

Do you multiply or divide first? 

• Multiply

• Divide

• Go from left to right. Whichever comes first! 

Multiple Choice

Do you add or subtract first?

• ADD

• SUBTRACT

• it depends on which comes first moving left to right.

A number raised to a power.

​

​STEP TWO:

What is an exponent?

​

Simplify the problem inside the parenthesis

​

Do Parenthesis First

​

• Do the multiplication or division ​in your problem.

• Proceed from left to right​

​Multiply or Divide

​From Left to Right

• Complete your addition or subtraction

• Move from left to right​

​

ADD or SUBTRACT

​

Multiple Choice

What is the first step in this problem?

• 6 + 5 + 10 + 2 = 24
• 10 ÷ 2 = 5
• (6 + 5) = 11
• 5 x 10 = 50

Multiple Choice

Pick the correct order for Order of Operations

• Parentheses, Multiplication, Division, Addition, Exponents, Subtraction

• Exponents, Multiplication, Division, Addition, Parentheses, Subtraction

• Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

Multiple Choice

What is the first step in the problem shown? 

• Multiplication
• Addition

Multiple Choice

Which operation should you perform first in the expression

$$-4+3^3\div5$$  

• exponent

• division

• addition
  

• subtraction

Multiple Choice

Which operation would you do first in the following equation?

10 - 4 ÷ 1 x 5

• Subtraction

• Division

• Multiplication

• Addition

Multiple Choice

What does 3² mean?

• 3 x 2
• 3 x 3
• 2 x 2 x 2

Multiple Choice

Three squared is:

• 3 x 3 = 9

• 3 x 2 = 6

• 3 + 3 = 6

• 3 + 2 = 5

Multiple Choice

Solve This Expression - 
( 7 x 3 ) + 9

• 29
• 30
• 31
• 32

Multiple Choice

4 x 6 -2 =

• 20

• 24

• 22

• 18

Multiple Choice

Solve: (2×10)+4

• 20

• 26

• 7

• 24

Multiple Choice

Who is correct?

Sallie

$$16\div2\times8=64$$  

Brian

$$16\div2\times8=1$$  

• Sallie

• Brian

• I'm not sure

• Both

Order of Operations

Parenthesis (Grouping Symbols)

Exponents

Multiplication and Division - left to right (first come, first served!)

Addition and Subtraction - left to right (first come, first served!)

We think of PEMDAS when solving expressions!

Be careful! In the expression 14/2 * 5,

we would DIVIDE before we MULTIPLY, because we look for multiplication and division at the same time, and solve them in the order we see them, going left to right!

Remember:

Parenthesis (Grouping Symbols)

Exponents

Multiplication and Division - left to right (first come, first served!)

Addition and Subtraction - left to right (first come, first served!)

Multiple Choice

Which operation would you solve first in this expression? (3 * 4) - 2 + 8/8

• multiplication

• subtraction

• addition

• division

Which operation would you solve first in this expression? (3 * 4) - 2 + 8/8

You would solve multiplication because you solve parenthesis first! :)

Multiple Choice

Which operation would you solve first in this expression? 3 * (4 - 2) + 8/8

• multiplication

• subtraction

• addition

• division

Which operation would you solve first in this expression? 3 * (4 - 2) + 8/8

You would solve subtraction first because alway solve the parenthesis first!

Multiple Choice

Which operation would you solve first in this expression? 3 * 4 - 2 + 8/8

• multiplication

• subtraction

• addition

• division

Which operation would you solve first in this expression? 3 * 4 - 2 + 8/8

You would solve multiplication first because there are no parenthesis, and no exponents. Next you look for multiplication and division going left to right, and you see MULTIPLICATION first!

Multiple Choice

Solve this expression: 3 x (4 -1)

• 11

• 9

• 15

• 0

Solve this expression: 3 x (4 -1)

3 x (4 - 1)

3 x 3

9 :)

Multiple Choice

Solve this expression on a piece of paper, solving one operation at a time, using Order of Operations: 4 + 8 * 3 - 1

• 35

• 20

• 27

• 33

Solve this expression on a piece of paper, one operation at a time, using Order of Operations: 4 + 8 * 3 - 1

4 + 8 * 3 - 1

4 + 24 - 1

28 - 1

27 :)

Multiple Choice

2 + (9² - 4)

• 16
• 77
• 79

Multiple Choice

6 + (4)3

• 18
• 30
• 13
• 42

Multiple Choice

(10 + 2) ×10-3

• 145
• 27
• 117
• 53

Multiple Choice

90 - 5² × 3

• 15
• 240
• 195

Multiple Choice

What would be my first step to simplify?
3 + 4 x 6 - 4 

• addition
• multiplication
• subtraction
• exponents

Multiple Choice

18 + (6 – 2) × 2

• 26
• 29
• 44
• 40

Multiple Choice

Find and explain the error.    
 5 - 3 + 2
     5 - 5
        0

• There is no error.
• Addition was done first and you should have subtracted first
• There is a subtraction error

Multiple Choice

2x + 5(y - 1) when x=8 and y=5

• 20
• 31
• 36
• -4

Multiple Choice

Evaluate 2a + 4b 
if a = 10     and    b = 6

• 20
• 24
• 44
• 4

Multiple Choice

3x + 8   if x = 2

• 13
• 14
• 15
• 16

Multiple Choice

Evaluate 7y - 3y for y=2

• 40
• 73
• 8
• 4

Multiple Choice

b² + 4
when b = 3

• 10
• 12
• 13
• 11

Multiple Choice

Evaluate -2x + -3y if x = 10 and y = -6

• 18

• -38

• 12

• -2

Multiple Choice

If p = -6, what does -10(p + 4) equal?

• 2

• 20

• -2

• -20

Multiple Choice

Evaluate the following expression:
t² - t + 1 when t = 5

• 25
• 22
• 23
• 21