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

2. 33? The Order of Operations ensures that we all arrive at the same destination by ordering us what to do next.

3. 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)

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

5. Evaluate 30 ÷ 6 + 4 7 = 5 + 4 7 (30 ÷ 6 = 5, division) = 5 + 28 (4 7 = 28, multiplication) = 33 (5 + 28 = 33, addition)

6. 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)

7. 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)

8. 1. 2 2. -7 3. 12 4. 98

9. 1. 72 2. 36 3. 12 4. 0

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

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

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

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

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

15. To evaluate an expression with variables, first plug in the value of each variable. Next, evaluate the expression using the order of operations.

16. Evaluate n + (13 - n) 5 for n = 8 = 8 + (13 – 8) 5 (plug in) = 8 + 5 5 (parentheses) = 8 + 1 (division) = 9 (addition)

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

18. 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)

19. 1. -2 2. 2 3. 4 4. 16

20. 1. -62 2. -42 3. 42 4. 62

21. 1. 45 2. 90 3. 135 4. 3,375

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

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

24. [16÷(9 - 1) + 4] 2 9 - 1 16 ÷ 8 + 4 2 Thirty six

25. [8 x (77 - 67) – 18 + 10] ÷ 3 77 - 67 8 x 10 – 18 + 10÷ 3 Twenty Four

26. [(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

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

28. [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