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Order of O P erations E MD AS

Order of O P erations 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.

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Order of O P erations E MD AS

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

  2. 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.

  3. PinkElephantsMake Delicious Apple Sauce Order of Operations • Parentheses () [] • Exponents x2, √ • Multiplication and Division (left to right) • Addition and Subtraction (left to right)

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

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

  6. 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)

  7. 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)

  8. Simplify16 - 2(10 - 3) • 2 • -7 • 12 • 98 Answer

  9. Simplify24 – 6 · 4 ÷ 2 • 72 • 36 • 12 • 0 Answer

  10. Simplify102 + 25 - 32 · (2 + 3) • -10 • 55 • 80 • 232 Answer

  11. True or False? The parentheses in this equation serve a vital function: (8 - 3) + 7 = 12 True False Answer

  12. True or False? The parentheses in this equation serve a vital function: (2 + 4)  2 = 12 True False Answer

  13. True or False? The parentheses in this equation serve a vital function: 10  8 – (5 + 3) = 72 True False Answer

  14. True or False? The parentheses in this equation serve a vital function: [(23)  3] ÷ 6 = 4 True False Answer

  15. 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.

  16. PEMDAS with plug-ins • Evaluaten + (13 - n)  5 for n = 8 • = 8 + (13 – 8) 5(plug in) • = 8 + 5 5 (parentheses) • = 8 + 1 (division) • = 9 (addition)

  17. PEMDAS with plug-ins • Evaluate 8y – (2x2+ 6z) for x = 5, y = 7, z =1 • = 8 5 – (2 72+ 6 1) (plug in) WRONG!

  18. PEMDAS with plug-ins • 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)

  19. What is the value of (2m + n) ÷ tif n = -8, m = 6, and t = 22 ? • -2 • 2 • 4 • 16 Answer

  20. What is the value of 10 – 4x if x = -13? • -62 • -42 • 42 • 62 Answer

  21. What is the value of 5k3 if k = 3? • 45 • 90 • 135 • 3,375 Answer

  22. Basic Training Complete • You are now ready to evaluate expressions using the order of operations.

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

  24. Equations with Multiple{}{}{}{}{}{}{}{}Parentheses{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{} • [16÷(9 - 1) + 4]2 9 - 1 2 16 ÷ 8 + 4 Thirty six Answer

  25. Equations with Multiple{}{}{}{}{}{}{}{}Parentheses{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{} • [8 x (77 - 67) – 18 + 10] ÷ 3 Answer 77 - 67 8 x10 – 18 + 10 ÷ 3 Twenty Four

  26. Equations with Multiple{}{}{}{}{}{}{}{}Parentheses{}{}{}{}{}{}{}{}{}{}{}{}{}{}{}{} • [(92 – (31 + 29) ÷ 6 – 1) ÷ (20 + 32 – 2)] 5 31 + 29 Answer 92 - 60 ÷ 6 – 1 20 + 32 – 2 81÷27 5 Two Hundred Forty Three

  27. TheGeneralissimo’sBonus • Evaluate the following expression [70 – (43 + 2  (1 + 72) ÷ 5) ÷ 9]  3 + 2 34

  28. TheGeneralissimo’sBonus {{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{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

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