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# Order of Operations (Algebra1 1_2)

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Students learn of the Order of Operations.

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• In the small window it looks like 15 (plus) 3.
View it in full-screen and you will see that it is actually 15 (divided by) 3.

It is difficult to tell the difference between the two symbols in the smaller window.
Great question though, very observant.

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### Order of Operations (Algebra1 1_2)

1. 1. The Order of Operations
2. 2. What You'll Learn Vocabulary 1) order of operations Order of Operations <ul><li>Evaluate numerical expressions by using the order of operations. </li></ul><ul><li>Evaluate algebraic expressions by using the order of operations. </li></ul>
3. 3. Internet service costs \$4.95 per month which includes 100 hours. Additional time costs \$0.99 per hour. Order of Operations
4. 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. 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. 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. 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. 8. Cost = \$4.95 + \$0.99(117 – 100) Order of Operations
9. 9. Cost = \$4.95 + \$0.99(117 – 100) This rule is called the _________________ order of operations Order of Operations
10. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 30. Evaluate each expression: Order of Operations P E M D A S lease xcuse y ear unt ally
31. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 45. Like numerical expressions, algebraic expressions often contain more than one operation. Order of Operations
46. 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. 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. 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. 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. 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. 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 – (3 3 – 4 •5) Order of Operations
52. 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. 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. 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. 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. 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. 57. Write an expression involving division in which the first step in evaluating the expression is addition . Order of Operations
58. 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. 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. 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. 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. 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. 63. Credits End of Lesson! PowerPoint created by http://robertfant.com Robert Fant