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

2. Evaluate • 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.
= (Multiply.)
= (Add.)

5. Example #1 14 ÷ 7 • 2 - 3
= 2 • (Divide l/r.)
= (Multiply.)
= 1 (Subtract.)

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

7. Example # • (6 + 1) • 4
= • (7) • 4 (parentheses)
= • (7) • 4 (exponents)
= (7) • (Multiply l/r.)
= (Multiply l/r.)
= (Subtract l/r.)
= (Add l/r.)
= (Add.)

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

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

10. Simplify 24 – 6 · 4 ÷ 2 72 36 12
Answer Now

11. Evaluating a Variable Expression To 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)  (Substitute.)
=  (parentheses)
= (Divide l/r.)
= (Add l/r.)

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

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

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

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

17. Properties of Real Numbers
Commutative
Associative
Distributive
Identity + ×
Inverse + ×

18. Commutative Properties
Changing the order of the numbers in addition or multiplication will not change the result.
Commutative Property of Addition states: = or a + b = b + a.
Commutative Property of Multiplication states: 4 • 5 = 5 • 4 or ab = ba.

19. Associative Properties
Changing the grouping of the numbers in addition or multiplication will not change the result.
Associative Property of Addition states: 3 + (4 + 5)= (3 + 4)+ 5 or a + (b + c)= (a + b)+ c
Associative Property of Multiplication states: (2 • 3) • 4 = 2 • (3 • 4) or (ab)c = a(bc)

20. Distributive Property
Multiplication distributes over addition.

21. Additive Identity Property
There exists a unique number 0 such that zero preserves identities under addition.
a + 0 = a and 0 + a = a
In other words adding zero to a number does not change its value.

22. Multiplicative Identity Property
There exists a unique number 1 such that the number 1 preserves identities under multiplication.
a ∙ 1 = a and 1 ∙ a = a
In other words multiplying a number by 1 does not change the value of the number.

23. Additive Inverse Property
For each real number a there exists a unique real number –a such that their sum is zero.
a + (-a) = 0
In other words opposites add to zero.

24. Multiplicative Inverse Property
For each real number a there exists a unique real number such that their product is 1.

25. Let’s play “Name that property!”

26. State the property or properties that justify the following.
3 + 2 = 2 + 3

27. State the property or properties that justify the following.
3 + 2 = 2 + 3
Commutative Property

28. State the property or properties that justify the following.
10(1/10) = 1

29. State the property or properties that justify the following.
10(1/10) = 1
Multiplicative Inverse Property

30. State the property or properties that justify the following.
3(x – 10) = 3x – 30

31. State the property or properties that justify the following.
3(x – 10) = 3x – 30
Distributive Property

32. State the property or properties that justify the following.
3 + (4 + 5) = (3 + 4) + 5

33. State the property or properties that justify the following.
3 + (4 + 5) = (3 + 4) + 5
Associative Property

34. State the property or properties that justify the following.
(5 + 2) + 9 = (2 + 5) + 9

35. State the property or properties that justify the following.
(5 + 2) + 9 = (2 + 5) + 9
Commutative Property

36. Which Property?
3 + 7 = 7 + 3

37. Commutative Property of Addition
Which Property?
3 + 7 = 7 + 3
Commutative Property of Addition

38. Which Property?
8 + 0 = 8

39. Identity Property of Addition
Which Property?
8 + 0 = 8
Identity Property of Addition

40. Which Property?
6 • 4 = 4 • 6

41. Commutative Property of Multiplication
Which Property?
6 • 4 = 4 • 6
Commutative Property of Multiplication

42. Which Property?
17 + (-17) = 0

43. Inverse Property of Addition
Which Property?
17 + (-17) = 0
Inverse Property of Addition

44. Which Property?
2(5) = 5(2)

45. Commutative Property of Multiplication
Which Property?
2(5) = 5(2)
Commutative Property of Multiplication

46. Which Property?
(2 + 1) + 4 = 2 + (1 + 4)

47. Associative Property of Addition
Which Property?
(2 + 1) + 4 = 2 + (1 + 4)
Associative Property of Addition

48. Which Property?
even + even = even

49. Which Property?
3(2 + 5) = 3•2 + 3•5

50. Distributive Property
Which Property?
3(2 + 5) = 3•2 + 3•5
Distributive Property

51. Which Property?
6(7•8) = (6•7)8

52. Associative Property of Multiplication
Which Property?
6(7•8) = (6•7)8
Associative Property of Multiplication

53. Which Property?
5 • 1 = 5

54. Identity Property of Multiplication
Which Property?
5 • 1 = 5
Identity Property of Multiplication

55. Properties Using
Negatives

56. Which Property?
(6 – 3)4 = 6•4 – 3•4

57. Distributive Property
Which Property?
(6 – 3)4 = 6•4 – 3•4
Distributive Property

58. Which Property?
1(-9) = -9

59. Identity Property of Multiplication
Which Property?
1(-9) = -9
Identity Property of Multiplication

60. Which Property?
3 + (-3) = 0

61. Inverse Property of Addition
Which Property?
3 + (-3) = 0
Inverse Property of Addition

62. Which Property?
1 + [-9 + 3]
= [1 + (-9)] + 3

63. Associative Property of Addition
Which Property?
1 + [-9 + 3]
= [1 + (-9)] + 3
Associative Property of Addition

64. Which Property?
-3(6) = 6(-3)

65. Commutative Property of Multiplication
Which Property?
-3(6) = 6(-3)
Commutative Property of Multiplication

66. Which Property?
= -8

67. Identity Property of Addition
Which Property?
= -8
Identity Property of Addition

68. Which Property?
3•7 – 3•4 = 3(7 – 4)

69. Distributive Property
Which Property?
3•7 – 3•4 = 3(7 – 4)
Distributive Property

70. Which Property?
6 + [(3 + (-2)]
= (6 + 3) + (- 2)

71. Associative Property of Addition
Which Property?
6 + [(3 + (-2)]
= (6 + 3) + (- 2)
Associative Property of Addition

72. Which Property?
7 + (-5) =

73. Commutative Property of Addition
Which Property?
7 + (-5) =
Commutative Property of Addition

74. Which Property?
(5 + 4)9 =

75. Distributive Property
Which Property?
(5 + 4)9 =
Distributive Property

76. Which Property?
-3(5 • 4) = (-3 • 5)4

77. Associative Property of Multiplication
Which Property?
-3(5 • 4) = (-3 • 5)4
Associative Property of Multiplication

78. Which Property?
-8(4) = 4(-8)

79. Commutative Property of Multiplication
Which Property?
-8(4) = 4(-8)
Commutative Property of Multiplication

80. Properties Using
Fractions

81. Which Property?
51/7 + 0 = 51/7

82. Identity Property of Addition
Which Property?
51/7 + 0 = 51/7
Identity Property of Addition

83. Which Property?
3/4 – 6/7 = – 6/7 + 3/4

84. Commutative Property of Addition
Which Property?
3/4 – 6/7 = – 6/7 + 3/4
Commutative Property of Addition

85. Which Property?
12/5 • 1 = 12/5

86. Identity Property of Multiplication
Which Property?
12/5 • 1 = 12/5
Identity Property of Multiplication

87. Which Property?
-8 2/5 + 0 = -8 2/5

88. Identity Property of Addition
Which Property?
-8 2/5 + 0 = -8 2/5
Identity Property of Addition

89. Which Property?
[(-2/3)(5)]9 = -2/3[(5)(9)]

90. Associative Property of Multiplication
Which Property?
[(-2/3)(5)]9 = -2/3[(5)(9)]
Associative Property of Multiplication

91. Properties Using
Variables

92. Which Property?
6(3 – 2n) = 18 – 12n

93. Distributive Property
Which Property?
6(3 – 2n) = 18 – 12n
Distributive Property

94. Which Property?
2x + 3 = 3 + 2x

95. Commutative Property of Addition
Which Property?
2x + 3 = 3 + 2x
Commutative Property of Addition

96. Which Property?
ab = ba

97. Commutative Property of Multiplication
Which Property?
ab = ba
Commutative Property of Multiplication

98. Which Property?
a + 0 = a

99. Identity Property of Addition
Which Property?
a + 0 = a
Identity Property of Addition

100. Which Property?
a(bc) = (ab)c

101. Associative Property of Multiplication
Which Property?
a(bc) = (ab)c
Associative Property of Multiplication

102. Which Property?
a•1 = a

103. Identity Property of Multiplication
Which Property?
a•1 = a
Identity Property of Multiplication

104. Which Property?
a +b = b + a

105. Commutative Property of Addition
Which Property?
a +b = b + a
Commutative Property of Addition

106. Which Property?
a(b + c) = ab + ac

107. Distributive Property
Which Property?
a(b + c) = ab + ac
Distributive Property

108. Which Property?
a + (b + c) = (a +b) + c

109. Associative Property of Addition
Which Property?
a + (b + c) = (a +b) + c
Associative Property of Addition

110. Which Property?
a + (-a) = 0

111. Inverse Property of Addition
Which Property?
a + (-a) = 0
Inverse Property of Addition

112. Properties of Real Numbers
Commutative
Associative
Distributive
Identity + ×
Inverse + ×