Download - Training Objective: students will be able to evaluate expressions using the order of operations
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Order of OPerations E MD AS
Training Objective: students will be able to evaluate expressions using the order of operations.
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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.
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Pink Elephants Make Delicious Apple Sauce
Order of Operations
Parentheses () []
Exponents x2, √
Multiplication and Division (left to right)
Addition and Subtraction (left to right)
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Evaluate 37 - 2 5
= 37 - 10 (2 x 5 = 10, multiplication)
= 27 (37 – 10 = 27, subtraction)
PEMDAS
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Evaluate 30 ÷ 6 + 4 7
= 5 + 4 7 (30 ÷ 6 = 5, division)
= 5 + 28 (4 7 = 28, multiplication)
= 33 (5 + 28 = 33, addition)
PEMDAS
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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
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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
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Simplify16 - 2(10 - 3)
1. 22. -73. 124. 98
Answer
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Simplify24 – 6 · 4 ÷ 2
1. 722. 363. 124. 0
Answer
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Simplify102 + 25 - 32 · (2 + 3)
1. -102. 553. 804. 232
Answer
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True or False?
The parentheses in this equation serve a vital function:
(8 - 3) + 7 = 12
True False
Answer
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True or False?
The parentheses in this equation serve a vital function:
(2 + 4) 2 = 12
True False
Answer
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True or False?
The parentheses in this equation serve a vital function:
10 8 – (5 + 3) = 72
True False
Answer
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True or False?
The parentheses in this equation serve a vital function:
[(23) 3] ÷ 6 = 4
True False
Answer
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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.
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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
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Evaluate 8y – (2x2 + 6z) for x = 5, y = 7, z =1
= 8 5 – (2 72 + 6 1) (plug in)
PEMDAS with plug-ins
WRONG!
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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
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What is the value of (2m + n) ÷ tif n = -8, m = 6, and t = 22 ?
1. -22. 23. 44. 16
Answer
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What is the value of 10 – 4x if x = -13?
1. -622. -423. 424. 62
Answer
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What is the value of 5k3 if k = 3?
1. 452. 903. 1354. 3,375
Answer
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Basic Training Complete
You are now ready to evaluate
expressions using the order of operations.
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Special Forces Training Parentheses PyramidsTraining Objective: Graduates will be able to evaluate expressions involving multiple grouping brackets.
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Equations with Multiple{}{}{}{}{}{}{}{}Parentheses{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}
[16÷(9 - 1) + 4]2
9 - 1
16 ÷ 8 + 42
Thirty sixAnswer
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Equations with Multiple{}{}{}{}{}{}{}{}Parentheses{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}
[8 x (77 - 67) – 18 + 10] ÷ 3
77 - 67
8 x 10 – 18 + 10 ÷ 3
Twenty Four
Answer
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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
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The Generalissimo’s Bonus
Evaluate the following expression
[70 – (43 + 2 (1 + 72) ÷ 5) ÷ 9] 3 + 2 34
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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