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Mastering Order of Operations: A Step-by-Step Guide to Evaluating Expressions

This instructional resource empowers students to effectively use the order of operations, known as PEMDAS, to evaluate mathematical expressions confidently. Through various examples and clear explanations, students will learn to navigate expressions including parentheses, exponents, multiplication, division, addition, and subtraction. Key exercises challenge students to apply these concepts, ensuring they arrive at consistent and accurate results. Engage with practical examples that reinforce theoretical understanding, establishing a strong foundation in mathematics.

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Mastering Order of Operations: A Step-by-Step Guide to Evaluating Expressions

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  1. ObjectiveThe student will be able to: use the order of operations to evaluate expressions. Designed by Skip Tyler, Varina High School

  2. Evaluate 7 + 4 • 3. Is your answer 33 or 19? You can get 2 different answers depending on which operation you did first. We want everyone to get the same answer so we must follow the order of operations.

  3. Remember the phrase“Please Excuse My Dear Aunt Sally” or PEMDAS. ORDER OF OPERATIONS 1. Parentheses - ( ) or [ ] 2. Exponents or Powers 3. Multiply and Divide (from left to right) 4. Add and Subtract (from left to right)

  4. Once again, evaluate 7 + 4  3 and use the order of operations. = 7 + 12 (Multiply.) =19(Add.)

  5. Example #114 ÷ 7 • 2 - 3 = 2 • 2 - 3 (Divide l/r.) = 4 - 3 (Multiply.) = 1(Subtract.)

  6. Example #23(3 + 7) 2 ÷ 5 = 3(10) 2 ÷ 5 (parentheses) = 3(100) ÷ 5 (exponents) = 300 ÷ 5 (multiplication) =60 (division)

  7. Example #320 - 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 (Multiply l/r.) = 20 - 18 + 100 + 28 (Multiply l/r.) = 2 + 100 + 28 (Subtract l/r.) = 102 + 28 (Add l/r.) =130 (Add.)

  8. Answer Now Which of the following represents 112 + 18 - 33· 5in simplified form? • -3,236 • 4 • 107 • 16,996

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

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

  11. Evaluating a Variable ExpressionTo evaluate a variable expression: • substitute the given numbers for each variable. • use order of operations to solve.

  12. Example # 4 n + (13 - n)  5 for n = 8 = 8 + (13 - 8)  5 (Substitute.) = 8 + 5 5 (parentheses) = 8 + 1 (Divide l/r.) = 9(Add l/r.)

  13. Example # 5 8y - 3x2+ 2n for x = 5, y = 2, n =3 = 8  2- 3  52 + 2  3 (Substitute.) = 8  2 - 3  25 + 2  3 (exponents) = 16- 3  25 + 2  3 (Multiply l/r.) = 16 -75 + 2  3 (Multiply l/r.) = 16 - 75 + 6 (Multiply l/r.) = -59 + 6 (Subtract l/r.) = -53 (Add l/r.)

  14. Answer Now What is the value of -10 – 4x if x = -13? • -62 • -42 • 42 • 52

  15. Answer Now What is the value of 5k3 if k = -4? • -8000 • -320 • -60 • 320

  16. Answer Now What is the value ofif n = -8, m = 4, and t = 2 ? • 10 • -10 • -6 • 6

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