Order of OPerations E MD AS

Training Objective: students will be able to evaluate expressions using the order of operations.

What is 7 + 4 3 ?

33?

The Order of Operations ensures that we all arrive at the same destination by ordering us what to do next.

Pink Elephants Make Delicious Apple Sauce

Order of Operations

Parentheses () []

Exponents x2, √

Multiplication and Division (left to right)

Addition and Subtraction (left to right)

Evaluate 37 - 2 5

= 37 - 10 (2 x 5 = 10, multiplication)

= 27 (37 – 10 = 27, subtraction)

PEMDAS

Evaluate 30 ÷ 6 + 4 7

= 5 + 4 7 (30 ÷ 6 = 5, division)

= 5 + 28 (4 7 = 28, multiplication)

= 33 (5 + 28 = 33, addition)

PEMDAS

Evaluate (28 – 12) ÷ 4 + 2 52

= 16 ÷ 4 + 2 52 (parentheses)

= 16 ÷ 4 + 2 25 (exponents)

= 4 + 2 25 (division)

= 4 + 50 (multiplication)

= 54 (addition)

PEMDAS

Evaluate 20 - 3 • 6 + 102 + (6 + 1) • 4

= 20 - 3 • 6 + 102 + 7 • 4 (parentheses)

= 20 - 3 • 6 + 100 + 7 • 4 (exponents)

= 20 - 18 + 100 + 7 • 4 (multiplication)

= 20 - 18 + 100 + 28 (multiplication)

= 2 + 100 + 28 (subtraction)

= 102 + 28(addition)

= 130 (addition)

PEMDAS

Simplify16 - 2(10 - 3)

1. 22. -73. 124. 98

Answer

Simplify24 – 6 · 4 ÷ 2

1. 722. 363. 124. 0

Answer

Simplify102 + 25 - 32 · (2 + 3)

1. -102. 553. 804. 232

Answer

True or False?

The parentheses in this equation serve a vital function:

(8 - 3) + 7 = 12

True False

Answer

True or False?

The parentheses in this equation serve a vital function:

(2 + 4) 2 = 12

True False

Answer

True or False?

The parentheses in this equation serve a vital function:

10 8 – (5 + 3) = 72

True False

Answer

True or False?

The parentheses in this equation serve a vital function:

[(23) 3] ÷ 6 = 4

True False

Answer

Evaluating a Variable expression

To evaluate an expression with variables, first plug in the value of each variable.

Next, evaluate the expression using the order of operations.

Evaluate n + (13 - n) 5 for n = 8

= 8 + (13 – 8) 5 (plug in)

= 8 + 5 5 (parentheses)

= 8 + 1 (division)

= 9 (addition)

PEMDAS with plug-ins

Evaluate 8y – (2x2 + 6z) for x = 5, y = 7, z =1

= 8 5 – (2 72 + 6 1) (plug in)

PEMDAS with plug-ins

WRONG!

Evaluate 8y – (2x2 + 6z) for x = 5, y = 7, z =1

= 8 7 – (2 52 + 6 1) (plug in)

= 8 7 – (2 25 + 6 1) (parentheses/exponents)

= 8 7 – (50 + 6 1) (parentheses/multiplication)

= 8 7 – (50 + 6) (parentheses/multiplication)

= 8 7 – 56 (parentheses/addition)

= 56 – 56 (multiplication)

= 0 (subtraction)

PEMDAS with plug-ins

What is the value of (2m + n) ÷ tif n = -8, m = 6, and t = 22 ?

1. -22. 23. 44. 16

Answer

What is the value of 10 – 4x if x = -13?

1. -622. -423. 424. 62

Answer

What is the value of 5k3 if k = 3?

1. 452. 903. 1354. 3,375

Answer

Basic Training Complete

You are now ready to evaluate

expressions using the order of operations.

Special Forces Training Parentheses PyramidsTraining Objective: Graduates will be able to evaluate expressions involving multiple grouping brackets.

Equations with Multiple{}{}{}{}{}{}{}{}Parentheses{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}

[16÷(9 - 1) + 4]2

9 - 1

16 ÷ 8 + 42

Thirty sixAnswer

Equations with Multiple{}{}{}{}{}{}{}{}Parentheses{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}

[8 x (77 - 67) – 18 + 10] ÷ 3

77 - 67

8 x 10 – 18 + 10 ÷ 3

Twenty Four

Answer

Equations with Multiple{}{}{}{}{}{}{}{}Parentheses{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}

[(92 – (31 + 29) ÷ 6 – 1) ÷ (20 + 32 – 2)] 5

31 + 29

92 - 60 ÷ 6 – 1 20 + 32 – 2 81 ÷ 27

5

Two Hundred Forty Three

Answer

The Generalissimo’s Bonus

Evaluate the following expression

[70 – (43 + 2 (1 + 72) ÷ 5) ÷ 9] 3 + 2 34

The Generalissimo’s Bonus {{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{solution}}}}}}}}}}}}}}}

[70 – (43 + 2 (1 + 49) ÷ 5) ÷ 9] 3 + 2 34 [70 – (43 + 2 50 ÷ 5) ÷ 9] ÷ 3 + 2 34 [70 – (43 + 100 ÷ 5) ÷ 9] ÷ 3 + 2 34 [70 – (43 + 20) ÷ 9] ÷ 3 + 2 34 [70 – 63 ÷ 9] ÷ 3 + 2 34 [70 – 7] ÷ 3 + 2 34 63 ÷ 3 + 2 34 21 + 2 34 21 + 68 89

Evaluate the following expression:

[70 – (43 + 2 (1 + 72) ÷ 5) ÷ 9] 3 + 2 34