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Order of Operations

4 3. Order of Operations. . ( ). +. -. X. The Order of Operations tells us how to do a math problem with more than one operation, in the correct order. P lease E xcuse M y D ear A unt S ally. This will help to you to remember the order of operations.

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Order of Operations

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  1. 43 Order of Operations  ( ) + - X

  2. The Order of Operations tells us how to do a math problem with more than one operation, in the correct order.

  3. Please Excuse My Dear Aunt Sally This will help to you to remember the order of operations.

  4. Please Excuse My Dear Aunt Sally P Parentheses ( ) E Exponents 43 M D Multiply x Divide  A S Add + Subtract -

  5. Please Excuse My Dear Aunt Sally Parentheses ( ) Always do parentheses 1st.

  6. Please Excuse My Dear Aunt Sally Exponents 43 Always do Exponents 2nd.

  7. Please Excuse My Dear Aunt Sally Multiply  Divide  Do multiplication and division 3rd, from left to right.

  8. Please Excuse My Dear Aunt Sally Add + Subtract - Do addition and subtraction 4th, from left to right.

  9. Let’s Try Some  Problems!

  10. 3+23 - (9+1) PEMDAS 3+23 - 10 3+8-10 11-10 1

  11. 3 (9+1) + 62 PEMDAS 3(10)+62 3(10)+36 30+36 66

  12. 4+5 (6-2) PEMDAS 4+5 4 4+20 24

  13. 4+ 10 23 -16 PEMDAS 4+10 8 -16 4+ 80 -16 84-16 68

  14. 21 + 102 10 PEMDAS 21+10010 21 + 10 31

  15. 10+72-2  5 PEMDAS 10+49–2  5 10+49- 10 59 - 10 49

  16. 64  (9  3-19) PEMDAS 64(27 –19) 64 8 8

  17. Example #114 ÷ 7 • 2 - 3 = 2 • 2 - 3 (Divide) = 4 - 3 (Multiply.) = 1(Subtract.)

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

  19. 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.)

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

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

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

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

  24. 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.)

  25. 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.)

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

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

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

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