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

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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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Order of Operations P arentheses () [] E xponents x 2, M ultiplication and D ivision (left to right) A ddition and S ubtraction (left to right)

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Evaluate 37 - 2 5 = 37 - 10 (2 x 5 = 10, multiplication) = 27 (37 – 10 = 27, subtraction)

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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)

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Evaluate (28 – 12) ÷ 4 + 2 5 2 = 16 ÷ 4 + 2 5 2 (parentheses) = 16 ÷ 4 + 2 25 (exponents) = 4 + 2 25 (division) = 4 + 50 (multiplication) = 54 (addition)

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Evaluate 20 - 3 6 + 10 2 + (6 + 1) 4 = 20 - 3 6 + 10 2 + 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)

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1. 2 2. -7 3. 12 4. 98

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1. 72 2. 36 3. 12 4. 0

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1. -10 2. 55 3. 80 4. 232

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The parentheses in this equation serve a vital function: (8 - 3) + 7 = 12 TrueFalse

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The parentheses in this equation serve a vital function: (2 + 4) 2 = 12 TrueFalse

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The parentheses in this equation serve a vital function: 10 8 – (5 + 3) = 72 TrueFalse

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The parentheses in this equation serve a vital function: [(2 3 ) 3] ÷ 6 = 4 TrueFalse

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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)

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

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

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1. -2 2. 2 3. 4 4. 16

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1. -62 2. -42 3. 42 4. 62

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1. 45 2. 90 3. 135 4. 3,375

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You are now ready to evaluate expressions using the order of operations.

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Training Objective: Graduates will be able to evaluate expressions involving multiple grouping brackets.

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[16÷(9 - 1) + 4] 2 9 - 1 16 ÷ 8 + 4 2 Thirty six

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[8 x (77 - 67) – 18 + 10] ÷ 3 77 - 67 8 x 10 – 18 + 10÷ 3 Twenty Four

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[(92 – (31 + 29) ÷ 6 – 1) ÷ (20 + 3 2 – 2)] 5 31 + 29 92 - 60 ÷ 6 – 120 + 3 2 – 2 81 ÷ 27 5 Two Hundred Forty Three

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Evaluate the following expression [70 – (43 + 2 (1 + 7 2 ) ÷ 5) ÷ 9] 3 + 2 34

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[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 + 7 2 ) ÷ 5) ÷ 9] 3 + 2 34

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