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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 (division)
= 20 - 18 + 100 + 28 (multiplication)
= 2 + 100 + 28 (addition)
= 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