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Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
Order of Operations
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Order of Operations

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  • 1. The Order of Operations
  • 2. What You'll Learn Vocabulary 1) order of operations Order of Operations
    • Evaluate numerical expressions by using the order of operations.
    • Evaluate algebraic expressions by using the order of operations.
  • 3. Internet service costs $4.95 per month which includes 100 hours. Additional time costs $0.99 per hour. Order of Operations
  • 4. Internet service costs $4.95 per month which includes 100 hours. Additional time costs $0.99 per hour. Nicole used her internet connection for 117 hours this past month. Write an expression describing her cost for the month? Order of Operations
  • 5. Internet service costs $4.95 per month which includes 100 hours. Additional time costs $0.99 per hour. Nicole used her internet connection for 117 hours this past month. Write an expression describing her cost for the month? Cost = $4.95 + $0.99(117 – 100) Order of Operations
  • 6. Internet service costs $4.95 per month which includes 100 hours. Additional time costs $0.99 per hour. Nicole used her internet connection for 117 hours this past month. Write an expression describing her cost for the month? Cost = $4.95 + $0.99(117 – 100) Numerical expressions often contain more than one operation. Order of Operations
  • 7. Internet service costs $4.95 per month which includes 100 hours. Additional time costs $0.99 per hour. Nicole used her internet connection for 117 hours this past month. Write an expression describing her cost for the month? Cost = $4.95 + $0.99(117 – 100) Numerical expressions often contain more than one operation. A rule is needed to let you know which operation to perform first. Order of Operations
  • 8. Cost = $4.95 + $0.99(117 – 100) Order of Operations
  • 9. Cost = $4.95 + $0.99(117 – 100) This rule is called the _________________ order of operations Order of Operations
  • 10. Step 1: Evaluate expressions inside grouping symbols. Cost = $4.95 + $0.99(117 – 100) This rule is called the _________________ order of operations Order of Operations
  • 11. Step 1: Evaluate expressions inside grouping symbols. Cost = $4.95 + $0.99(117 – 100) This rule is called the _________________ order of operations Cost = $4.95 + $0.99(17) Order of Operations
  • 12. Step 1: Evaluate expressions inside grouping symbols. Cost = $4.95 + $0.99(117 – 100) This rule is called the _________________ order of operations Cost = $4.95 + $0.99(17) Order of Operations Step 2: Evaluate all powers.
  • 13. Step 1: Evaluate expressions inside grouping symbols. Cost = $4.95 + $0.99(117 – 100) This rule is called the _________________ order of operations Cost = $4.95 + $0.99(17) Step 2: Evaluate all powers. Cost = $4.95 + $0.99(17) there are no powers to evaluate Order of Operations
  • 14. Step 1: Evaluate expressions inside grouping symbols. Cost = $4.95 + $0.99(117 – 100) This rule is called the _________________ order of operations Cost = $4.95 + $0.99(17) Step 2: Evaluate all powers. Cost = $4.95 + $0.99(17) there are no powers to evaluate Step 3: Do all multiplication and / or division from left to right. Order of Operations
  • 15. Step 1: Evaluate expressions inside grouping symbols. Cost = $4.95 + $0.99(117 – 100) This rule is called the _________________ order of operations Cost = $4.95 + $0.99(17) Step 2: Evaluate all powers. Cost = $4.95 + $0.99(17) there are no powers to evaluate Step 3: Do all multiplication and / or division from left to right. Cost = $4.95 + $16.83 Order of Operations
  • 16. Step 1: Evaluate expressions inside grouping symbols. Cost = $4.95 + $0.99(117 – 100) This rule is called the _________________ order of operations Cost = $4.95 + $0.99(17) Step 2: Evaluate all powers. Cost = $4.95 + $0.99(17) there are no powers to evaluate Step 3: Do all multiplication and / or division from left to right. Cost = $4.95 + $16.83 Step 4: Do all addition and / or subtraction from left to right. Order of Operations
  • 17. Step 1: Evaluate expressions inside grouping symbols. Cost = $4.95 + $0.99(117 – 100) This rule is called the _________________ order of operations Cost = $4.95 + $0.99(17) Step 2: Evaluate all powers. Cost = $4.95 + $0.99(17) there are no powers to evaluate Step 3: Do all multiplication and / or division from left to right. Cost = $4.95 + $16.83 Step 4: Do all addition and / or subtraction from left to right. Cost = $21.78 Order of Operations
  • 18. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Order of Operations
  • 19. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: Order of Operations
  • 20. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 Order of Operations
  • 21. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 3 + 2 • 3 + 5 = 3 + 2 • 3 + 5 Order of Operations
  • 22. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 3 + 2 • 3 + 5 = 3 + 2 • 3 + 5 = 3 + 6 + 5 Order of Operations
  • 23. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 3 + 2 • 3 + 5 = 3 + 2 • 3 + 5 = 3 + 6 + 5 = 9 + 5 Order of Operations
  • 24. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 3 + 2 • 3 + 5 = 3 + 2 • 3 + 5 = 3 + 6 + 5 = 9 + 5 = 14 Order of Operations
  • 25. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 3 + 2 • 3 + 5 = 3 + 2 • 3 + 5 = 3 + 6 + 5 = 9 + 5 = 14 15 ÷ 3 • 5 – 4 2 Order of Operations
  • 26. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 3 + 2 • 3 + 5 = 3 + 2 • 3 + 5 = 3 + 6 + 5 = 9 + 5 = 14 15 ÷ 3 • 5 – 4 2 15 ÷ 3 • 5 – 4 2 = 15 ÷ 3 • 5 – 16 Order of Operations
  • 27. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 3 + 2 • 3 + 5 = 3 + 2 • 3 + 5 = 3 + 6 + 5 = 9 + 5 = 14 15 ÷ 3 • 5 – 4 2 15 ÷ 3 • 5 – 4 2 = 15 ÷ 3 • 5 – 16 = 5 • 5 – 16 Order of Operations
  • 28. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 3 + 2 • 3 + 5 = 3 + 2 • 3 + 5 = 3 + 6 + 5 = 9 + 5 = 14 15 ÷ 3 • 5 – 4 2 15 ÷ 3 • 5 – 4 2 = 15 ÷ 3 • 5 – 16 = 5 • 5 – 16 = 25 – 16 Order of Operations
  • 29. Some students remember the order by using the following mnemonic: P E M D A S lease xcuse y ear unt ally (parentheses / grouping symbols) (exponents) (multiplication) (division) (addition) (subtraction) Evaluate each expression: 3 + 2 • 3 + 5 3 + 2 • 3 + 5 = 3 + 2 • 3 + 5 = 3 + 6 + 5 = 9 + 5 = 14 15 ÷ 3 • 5 – 4 2 15 ÷ 3 • 5 – 4 2 = 15 ÷ 3 • 5 – 16 = 5 • 5 – 16 = 25 – 16 = 9 Order of Operations
  • 30. Evaluate each expression: Order of Operations P E M D A S lease xcuse y ear unt ally
  • 31. Evaluate each expression: 2(5) + 3(4 + 3) Order of Operations P E M D A S lease xcuse y ear unt ally
  • 32. Evaluate each expression: 2(5) + 3(4 + 3) 2(5) + 3(4 + 3) = 2(5) + 3(7) Order of Operations P E M D A S lease xcuse y ear unt ally
  • 33. Evaluate each expression: 2(5) + 3(4 + 3) 2(5) + 3(4 + 3) = 2(5) + 3(7) = 10 + 21 Order of Operations P E M D A S lease xcuse y ear unt ally
  • 34. Evaluate each expression: 2(5) + 3(4 + 3) 2(5) + 3(4 + 3) = 2(5) + 3(7) = 10 + 21 = 31 When more than one grouping symbol is used, start evaluating within the innermost grouping symbol. Order of Operations P E M D A S lease xcuse y ear unt ally
  • 35. Evaluate each expression: 2(5) + 3(4 + 3) 2(5) + 3(4 + 3) = 2(5) + 3(7) = 10 + 21 = 31 When more than one grouping symbol is used, start evaluating within the innermost grouping symbol. 2[5 + (30 ÷ 6) 2 ] Order of Operations P E M D A S lease xcuse y ear unt ally
  • 36. Evaluate each expression: 2(5) + 3(4 + 3) 2(5) + 3(4 + 3) = 2(5) + 3(7) = 10 + 21 = 31 When more than one grouping symbol is used, start evaluating within the innermost grouping symbol. 2[5 + (30 ÷ 6) 2 ] 2[5 + (30 ÷ 6) 2 ] = 2[5 + (5) 2 ] Order of Operations P E M D A S lease xcuse y ear unt ally
  • 37. Evaluate each expression: 2(5) + 3(4 + 3) 2(5) + 3(4 + 3) = 2(5) + 3(7) = 10 + 21 = 31 When more than one grouping symbol is used, start evaluating within the innermost grouping symbol. 2[5 + (30 ÷ 6) 2 ] 2[5 + (30 ÷ 6) 2 ] = 2[5 + (5) 2 ] = 2[5 + 25] Order of Operations P E M D A S lease xcuse y ear unt ally
  • 38. Evaluate each expression: 2(5) + 3(4 + 3) 2(5) + 3(4 + 3) = 2(5) + 3(7) = 10 + 21 = 31 When more than one grouping symbol is used, start evaluating within the innermost grouping symbol. 2[5 + (30 ÷ 6) 2 ] 2[5 + (30 ÷ 6) 2 ] = 2[5 + (5) 2 ] = 2[5 + 25] = 2[30] Order of Operations P E M D A S lease xcuse y ear unt ally
  • 39. Evaluate each expression: 2(5) + 3(4 + 3) 2(5) + 3(4 + 3) = 2(5) + 3(7) = 10 + 21 = 31 When more than one grouping symbol is used, start evaluating within the innermost grouping symbol. 2[5 + (30 ÷ 6) 2 ] 2[5 + (30 ÷ 6) 2 ] = 2[5 + (5) 2 ] = 2[5 + 25] = 2[30] = 60 Order of Operations P E M D A S lease xcuse y ear unt ally
  • 40. Evaluate the expression: A fraction bar is another type of grouping symbol. It indicates that the numerator and denominator should each be treated as a single value. Order of Operations P E M D A S
  • 41. Evaluate the expression: A fraction bar is another type of grouping symbol. It indicates that the numerator and denominator should each be treated as a single value. Order of Operations P E M D A S
  • 42. Evaluate the expression: A fraction bar is another type of grouping symbol. It indicates that the numerator and denominator should each be treated as a single value. Order of Operations P E M D A S
  • 43. Evaluate the expression: A fraction bar is another type of grouping symbol. It indicates that the numerator and denominator should each be treated as a single value. Order of Operations P E M D A S
  • 44. Evaluate the expression: A fraction bar is another type of grouping symbol. It indicates that the numerator and denominator should each be treated as a single value. Order of Operations P E M D A S
  • 45. Like numerical expressions, algebraic expressions often contain more than one operation. Order of Operations
  • 46. Like numerical expressions, algebraic expressions often contain more than one operation. Algebraic expressions can be evaluated when _______________________________. Evaluate: a 2 – (b 2 – 4c) Order of Operations
  • 47. Like numerical expressions, algebraic expressions often contain more than one operation. Algebraic expressions can be evaluated when _______________________________. the value of the variables are known Evaluate: a 2 – (b 2 – 4c) Order of Operations
  • 48. Like numerical expressions, algebraic expressions often contain more than one operation. Algebraic expressions can be evaluated when _______________________________. the value of the variables are known Evaluate: a 2 – (b 2 – 4c) if a = 7, b = 3, and c = 5 Order of Operations
  • 49. Like numerical expressions, algebraic expressions often contain more than one operation. Algebraic expressions can be evaluated when _______________________________. the value of the variables are known First, replace the variables with their values. Evaluate: a 2 – (b 2 – 4c) Order of Operations if a = 7, b = 3, and c = 5
  • 50. Like numerical expressions, algebraic expressions often contain more than one operation. Algebraic expressions can be evaluated when _______________________________. the value of the variables are known First, replace the variables with their values. Evaluate: a 2 – (b 2 – 4c) if a = 7, b = 3, and c = 5 a 2 – (b 2 – 4c) = 7 2 – (3 3 – 4 •5) Order of Operations
  • 51. Like numerical expressions, algebraic expressions often contain more than one operation. Algebraic expressions can be evaluated when _______________________________. the value of the variables are known First, replace the variables with their values. Evaluate: a 2 – (b 2 – 4c) if a = 7, b = 3, and c = 5 a 2 – (b 2 – 4c) = 7 2 – (2 2 – 4 •5) Order of Operations
  • 52. Like numerical expressions, algebraic expressions often contain more than one operation. Algebraic expressions can be evaluated when _______________________________. the value of the variables are known First, replace the variables with their values. Evaluate: a 2 – (b 2 – 4c) if a = 7, b = 3, and c = 5 a 2 – (b 2 – 4c) = 7 2 – (3 3 – 4 •5) Order of Operations
  • 53. Like numerical expressions, algebraic expressions often contain more than one operation. Algebraic expressions can be evaluated when _______________________________. the value of the variables are known First, replace the variables with their values. Evaluate: a 2 – (b 2 – 4c) if a = 7, b = 3, and c = 5 a 2 – (b 2 – 4c) = 7 2 – (3 3 – 4 •5) Then, find the value of the numerical expression using the order of operations. Order of Operations
  • 54. Like numerical expressions, algebraic expressions often contain more than one operation. Algebraic expressions can be evaluated when _______________________________. the value of the variables are known First, replace the variables with their values. Evaluate: a 2 – (b 2 – 4c) if a = 7, b = 3, and c = 5 a 2 – (b 2 – 4c) = 7 2 – (3 3 – 4 •5) Then, find the value of the numerical expression using the order of operations. = 49 – (27 – 20) Order of Operations
  • 55. Like numerical expressions, algebraic expressions often contain more than one operation. Algebraic expressions can be evaluated when _______________________________. the value of the variables are known First, replace the variables with their values. Evaluate: a 2 – (b 2 – 4c) if a = 7, b = 3, and c = 5 a 2 – (b 2 – 4c) = 7 2 – (3 3 – 4 •5) Then, find the value of the numerical expression using the order of operations. = 49 – (27 – 20) = 49 – ( 7) Order of Operations
  • 56. Like numerical expressions, algebraic expressions often contain more than one operation. Algebraic expressions can be evaluated when _______________________________. the value of the variables are known First, replace the variables with their values. Evaluate: a 2 – (b 2 – 4c) if a = 7, b = 3, and c = 5 a 2 – (b 2 – 4c) = 7 2 – (3 3 – 4 •5) Then, find the value of the numerical expression using the order of operations. = 49 – (27 – 20) = 49 – ( 7) = 42 Order of Operations
  • 57. Write an expression involving division in which the first step in evaluating the expression is addition . Order of Operations
  • 58. Write an expression involving division in which the first step in evaluating the expression is addition . Sample answer: 2 + 4 ÷ 3 Order of Operations
  • 59. Write an expression involving division in which the first step in evaluating the expression is addition . Sample answer: 2 + 4 ÷ 3 Order of Operations How can you “force” the addition to be done before the division?
  • 60. Write an expression involving division in which the first step in evaluating the expression is addition . Sample answer: 2 + 4 ÷ 3 ( ) Order of Operations How can you “force” the addition to be done before the division?
  • 61. Finding error(s) in your calculations is a skill that you must develop. Determine which calculation is incorrect and identify the error . Order of Operations 3[4 + (27 ÷ 3)] 2 = 3(4 + 9 2 ) = 3(4 + 81) = 3(85) = 255 3[4 + (27 ÷ 3)] 2 = 3(4 + 9) 2 = 3(13) 2 = 3(169) = 507
  • 62. Finding error(s) in your calculations is a skill that you must develop. Determine which calculation is incorrect and identify the error . Order of Operations 3[4 + (27 ÷ 3)] 2 = 3(4 + 9 2 ) = 3(4 + 81) = 3(85) = 255 3[4 + (27 ÷ 3)] 2 = 3(4 + 9) 2 = 3(13) 2 = 3(169) = 507 Incorrect quantity raised to the second power. The exponent is outside the grouping symbol.
  • 63. Credits End of Lesson! PowerPoint created by http://robertfant.com Robert Fant

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