Order of Operations and Evaluating Expressions

Order of Operations and Evaluating Expressions

Order of Operations

Lesson Objective: Students will solve math

problems using the order of operations

Critical Thinking~ Following Directions

(In your math notebook)

Describe why it is important to follow steps in

order in life. When could it cause serious

problems if you didn’t follow particular steps?

How can this relate to mathematics?

Order of Operations

Order of Operations

*Always multiply and
divide from left to right

*Always add and
subtract from left to right

*Inside (parentheses),
always follow the order
of operations

P
E

M D
A S

Parentheses () {} []

Exponents & Roots

Multiply

Divide

Add

Subtract

Order of Operations

Base
Exponent

Power

Example of Order of Operations

17 - 5 x 5 ÷ (2 + 3)

17- 25 ÷ 5

17 - 5 = 12

​Now Solve the problems in the remaining slides you can work with a partner but show all your work!

Multiple Choice

Solve the following:
-2 x (3 + 8 ÷ 4)²

• -16

• 1.375

• 4

• -50

Multiple Choice

2 + (9² - 4)

• 16

• 77

• 79

Multiple Choice

Simplify:
[25-(13+4)+4] ÷ 3

• 6

• 2

• 3

• 4

Fill in the Blank

[ (6 ÷ 2) x 6 + 4 x 7]

Multiple Choice

Solve the following:  
-8 + (15-3) ÷ 4

• -5

• 1

• -11

• 11

Fill in the Blank

[ ( 10 x 3) ] ÷ 5

Multiple Choice

Solve the following:
(2 + 7 - 1) ÷ 2²

• 16
• 2
• 72.25
• 8.75

Reorder

What is the order of the steps for the following expression? 50- 16 ÷ 2 x (12-4)²

• parentheses

• exponent

• division

• multiplication

• subtraction

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Multiple Choice

90 - 3(5² )

• 15

• 240

• 195

Fill in the Blank

24 ÷ 6 + 4²

Multiple Choice

(7 + 41) ÷ 2 – 15

• 19
• 9
• 25
• 3

Fill in the Blank

Solve the following:
5 - 6² ÷ 4 - 3

Multiple Choice

8+5∙4+(7-3)

• 32
• 23
• 25
• 12

Fill in the Blank

4 + 3² + 8 ÷ 4

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

Fill in the Blank

5 x (7-2) + (3-6)²

Multiple Choice

(82 ÷ 2) × 3 – 17

• 206
• 100
• 106
• 5

Reorder

Put in the order the operations would be done:

(18 - 14)² - 6 x 10

• 18 - 14
• 4²
• 6 x 10
• 16 - 60

1

2

3

4

• 1
• 2
• 3
• 4

Multiple Choice

75 ÷ 5 × 9 – 9

• 126
• 226
• 711
• 300

Fill in the Blank

Evaluate: 100 - 25 x 2² + 17

Multiple Choice

15 + 7 × 2 – 11 + 35=

• 38

• 251

• 53

• 50

Fill in the Blank

Evaluate:
10³ - 500 + 250

Multiple Choice

(15 ÷ 3)² + 9 ÷ 3

• 11.3

• 28

• 13

Multiple Choice

15 x 19 + 18 ÷ 6 = 

• 250

• 199

• 400

• 288

Fill in the Blank

Evaluate:
(7² + 51) ÷ (4 x 25)

Multiple Choice

4 + 9 + 8 ÷ 4

• 5.25

• 5

• 25

• 15

Fill in the Blank

18 + (6 – 2) × 2

Multiple Choice

40 - 2⁴ + 8

• 40

• 32

• 24

• 42

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

3(2² ) + 24 ÷ 8

• 15

• 10.5

• 4.5

Fill in the Blank

Simply:

Multiple Choice

2 + (9² - 4)

• 16
• 77
• 79
• 88

Multiple Choice

91 + 27 ÷ (72 ÷ 24)

• 100

• 96

• 90

• 127

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

• They added wrong numbers

• Multiplied worng

Fill in the Blank

Evaluate the expression 2p - (p + 3) ÷ 3. For p = 6

Multiple Choice

Simplify

• 232

• 278

• 332

• 488

Multiple Choice

4 + 9 + 8 ÷ 4

• 5.25
• 5
• 25
• 15

Multiple Choice

Simplify:
[25-(13+4)+4] ÷ 3

• 6

• 2

• 3

• 4

Multiple Choice

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

• 20
• 31
• 36
• -4

Multiple Choice

• -7

• 23

• -9

• 43

Multiple Choice

In PEMDAS, what does the M stand for?

• Masterful

• McDonald

• Math

• Multiplication

Multiple Choice

(82 ÷ 2) × 3 – 17

• 206
• 100
• 106
• 5

Multiple Choice

2 + (9² - 4)

• 16
• 77
• 79

Multiple Choice

• 45

• 7

• 3

• 12

Multiple Choice

Simplify.
3[(4 + 6) ÷ 2]

• 15

• 21

• 9

• 12

Multiple Choice

4 + 9 + 8 ÷ 4

• 5.25

• 5

• 25

• 15

Multiple Choice

True or false:
Addition ALWAYS comes before subtraction.

• True

• False

Multiple Choice

Simplify!

• 8

• 5

• -8

• 0

Multiple Choice

11² - 8 ⋅ 7 + 2

• 100

• 793

• 67

• 49

Multiple Choice

In PEMDAS, what does the M stand for?

• Masterful
• Mad
• Math
• Multiplication

Multiple Choice

7[12 − (6 − 2) ÷ 4]

• 7
• 77
• 14
• 0

Multiple Choice

Simplify!

• 14

• -2

• 5

• 22

Multiple Choice

2 + (9² - 4)

• 16
• 77
• 79

Multiple Choice

Simplify!

• 1

• -2

• 15

• 10

Multiple Choice

True or false:
Addition ALWAYS comes before subtraction.

• True

• False

Multiple Choice

Simplify!

• 2

• 3

• 4

• 5

Multiple Choice

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

• addition

• multiplication

• subtraction

• exponents

Multiple Choice

Simplify!

• -1

• 1

• 0

• 2

Multiple Choice

True or False?
2 + (4 x 5 - 2) + 8 = 28

• True

• False

Multiple Choice

2 + (9² - 4)

• 16

• 77

• 79

Multiple Choice

Simplify!

• 7

• 5

• -7

• -5

Multiple Choice

Solve the following:
5 - 6² ÷ 4 - 3

• 1

• -10.75

• -31

• -7

Multiple Choice

Simplify!

• 5

• 9

• -18

• -9

Multiple Choice

7(3²)=

• 63

• 62

• 50

• 27

Multiple Choice

Simplify!

• 1

• -4

• -1

• 2

Multiple Choice

What does the E in PEMDAS stand for?

• Exceptional

• Egg

• Exponent

Multiple Choice

What does 3² mean?

• 3 x 2

• 3 x 3

• 2 x 2 x 2

Multiple Choice

Simplify!

• -12

• 9

• -13

• 4

Multiple Choice

Solve the following:
(2 + 7 - 1) ÷ 2²

• 16

• 2

• 72.25

• 8.75

Multiple Choice

Simplify!

• -6

• 4

• 6

• -8

Multiple Choice

Simplify! TALK TO MR. MICHELOT ABOUT THIS PROBLEM CAN BE TRICKY!!!!!!!!

• 70

• -8

• 87

• 77

Multiple Choice

Simplify! TALK TO MR. MICHELOT ABOUT THIS PROBLEM CAN BE TRICKY!!!!!!!!

• 4

• -15

• 23

• 15

Reorder

Order the operations you would use to Simplify:

-2 ⋅ (3 + 8 ÷ 4)²

• Division

• Addition

• Exponents

• Multiplication

1

2

3

4

• 1
• 2
• 3
• 4

​This ends the Order of Operations Portion! Please take a break and wait for Mr. Michelot to direct you to the next activity which is EVALUATING EXPRESSIONS.

​Evaluating Expressions

Lesson Objective: Students will evaluate algebraic expressions with positive and negative integers.

Fill in the Blank

Evaluate: $$\frac{8^2-4}{5}$$   

Fill in the Blank

Evaluate the expression x² - x; x = -6

Fill in the Blank

Evaluate the expression.   Let g = 3    h = 9 
4h + 2g + 4

Fill in the Blank

Evaluate the following expression if a = –2, b = 6, c = 1:    b² – 4ac

Multiple Choice

Evaluate m² if m = 7

• 42

• 43

• 49

• 51

Multiple Choice

Evaluate x ÷ 4 if x = 80

• 4

• 20

• 40

• 80

Multiple Choice

Evaluate n³ if n = 4

• 12

• 16

• 32

• 64

Multiple Choice

Evaluate m - n if m = 29 and n = 11

• 29

• 28

• 19

• 18

Multiple Choice

Divide.

• 3
• 12
• 6
• 8

Multiple Choice

What is -3 + 4 -12 +17 - 23

• 14

• 37

• -17

• -15

Multiple Choice

3r + 2e; r = 3  e = 2

• 15
• 13
• 54
• 12

Multiple Choice

What is the value of x?
3x + 4 when x = -2

• 10
• 2
• -2
• 4

Multiple Choice

Simplify the following:  
-8 + (15 - 3) ÷ 4

• -5
• 1
• -11
• 11

Multiple Choice

5m + 9n if m = -7 and n = 4

• 71

• 1

• -1

• -71

Multiple Select

One number is 4 times as large as another. Their sum is 45. What are the numbers? Select the two that apply.

• 6

• 9

• 12

• 27

• 36

Multiple Choice

The larger of two numbers is 12 more than the smaller number. If the sum of the two numbers is 74, find the two numbers.

• 12 and 24

• 31 and 43

• 24 and 36

• 51 and 63

Multiple Choice

The length of a rectangle is 3 inches more than its width. If the perimeter is 42 inches, find the dimensions of the rectangle.

• 9 in by 12 in

• 3 in by 14 in

• 10 in by 11 in

• 8 in by 13 in

Multiple Choice

Find two consecutive numbers whose sum is 115.

• 57 and 58

• 44 and 45

• 56 and 57

• 225 and 226

Multiple Choice

p + 95 = 215

What is the best first step to solve this equation?

• Add 95 to both sides.

• Subtract 215 from both sides.

• Subtract 95 from both sides.

• Subtract "p" from both sides.

Multiple Choice

Marco and Polo are making the world's largest apple pie. They will need 215 apples. Marco has already picked 95 apples. How many apples will Polo need to pick so they have enough?

Select the equation that best describes this problem.

• p - 95 = 215

• 215 + p = 95

• p + 95 = 215

• 95p = 215

Multiple Choice

$$\frac{s}{5}=3$$  

Find s

• 15

• $$\frac{3}{5}$$  

• 1.667

• 8

Multiple Choice

Johnny borrowed $270 from you and he needs 3 months to pay it back. How much money does he need to give you each month?

This problem can be shown by the equation

3m = 270

What are the steps and solution to this problem?

• Divide both sides by 3, m = 90

• Multiply both sides by 3, m = 810

• Subtract 3 from both sides, m = 267

• none of these

Fill in the Blank

Find three consecutive numbers that add to give you 54.

Fill in the Blank

Find two consecutive numbers that add to give you 197.

Fill in the Blank

Find two consecutive odd numbers that add to give you 28.

Multiple Choice

Which of the following setups would be used to find four consecutive integers?

• n
  n+2
  n+4
  n+6
• n
  2n
  4n
  6n
• n+1
  n+2
  n+3
  n+4
• n
  n+1
  n+2
  n+3

Multiple Choice

Five less than twice a number is equivalent to 47. 

• 5 - 2x = 47 
• 2x - 5 = 47 
• 5x - 2 = 47 
• 2 - 5x = 47 

Multiple Choice

The sum of three consecutive integers is 147. Which equation can be used to find the first integer? 

• 3x = 147
• x + 3 = 147 
• x + x + 1 + x + 2 = 147 
• x ⋅ x ⋅ x = 147 

Multiple Choice

The sum of four consecutive odd integers is equivalent to 232.  Which equation can be used to find the first integer? 

• 4x = 232 
• x + x + 2 + x + 4 + x + 6 = 232 
• x + x + 1 + x + 3 + x + 5 = 232 
• x ⋅ x ⋅ x ⋅ x = 232