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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