1. Chapter 1

2. Solving Equations and Inequalities

3. 1.1 – Expressions and Formulas

4. Order of Operations

5. 1.1 – Expressions and Formulas Order of Operations Parentheses

6. 1.1 – Expressions and Formulas Order of Operations Parentheses Exponents

7. 1.1 – Expressions and Formulas Order of Operations Parentheses Exponents Multiplication

8. 1.1 – Expressions and Formulas Order of Operations Parentheses Exponents Multiplication Division

9. 1.1 – Expressions and Formulas Order of Operations Parentheses Exponents Multiplication Division Addition

10. 1.1 – Expressions and Formulas Order of Operations Parentheses Exponents Multiplication Division Addition Subtraction

11. 1.1 – Expressions and Formulas Order of Operations ParenthesesPlease Exponents Multiplication Division Addition Subtraction

12. 1.1 – Expressions and Formulas Order of Operations ParenthesesPlease ExponentsExcuse Multiplication Division Addition Subtraction

13. 1.1 – Expressions and Formulas Order of Operations ParenthesesPlease ExponentsExcuse MultiplicationMy Division Addition Subtraction

14. 1.1 – Expressions and Formulas Order of Operations ParenthesesPlease ExponentsExcuse MultiplicationMy DivisionDear Addition Subtraction

15. 1.1 – Expressions and Formulas Order of Operations ParenthesesPlease ExponentsExcuse MultiplicationMy DivisionDear AdditionAunt Subtraction

16. 1.1 – Expressions and Formulas Order of Operations ParenthesesPlease ExponentsExcuse MultiplicationMy DivisionDear AdditionAunt SubtractionSally

17. Example 1

18. Find the value of [2(10 - 4) 2 + 3] ÷ 5.

19. Example 1 Find the value of [2(10 - 4) 2 + 3] ÷ 5. [2(10 - 4) 2 + 3] ÷ 5 =

20. Example 1 Find the value of [2(10 - 4) 2 + 3] ÷ 5. [2(10 - 4) 2 + 3] ÷ 5 = [2(6) 2 + 3] ÷ 5

21. Example 1 Find the value of [2(10 - 4) 2 + 3] ÷ 5. [2(10 - 4) 2 + 3] ÷ 5 = [2(6) 2 + 3] ÷ 5 [2(36) + 3] ÷ 5

22. Example 1 Find the value of [2(10 - 4) 2 + 3] ÷ 5. [2(10 - 4) 2 + 3] ÷ 5 = [2(6) 2 + 3] ÷ 5 [2(36) + 3] ÷ 5 [72 + 3] ÷ 5

23. Example 1 Find the value of [2(10 - 4) 2 + 3] ÷ 5. [2(10 - 4) 2 + 3] ÷ 5 = [2(6) 2 + 3] ÷ 5 [2(36) + 3] ÷ 5 [72 + 3] ÷ 5 75 ÷ 5

24. Example 1 Find the value of [2(10 - 4) 2 + 3] ÷ 5. [2(10 - 4) 2 + 3] ÷ 5 = [2(6) 2 + 3] ÷ 5 [2(36) + 3] ÷ 5 [72 + 3] ÷ 5 75 ÷ 5 15

25. Example 2

26. Evaluate x 2 – y(x + y) if x = 8 and y = 1.5.

27. Example 2 Evaluate x 2 – y(x + y) if x = 8 and y = 1.5. x 2 – y(x + y) =

28. Example 2 Evaluate x 2 – y(x + y) if x = 8 and y = 1.5. x 2 – y(x + y) = 8 2 – 1.5(8 + 1.5)

29. Example 2 Evaluate x 2 – y(x + y) if x = 8 and y = 1.5. x 2 – y(x + y) = 8 2 – 1.5(8 + 1.5) 8 2 – 1.5(8 + 1.5)

30. Example 2 Evaluate x 2 – y(x + y) if x = 8 and y = 1.5. x 2 – y(x + y) = 8 2 – 1.5(8 + 1.5) 8 2 – 1.5(8 + 1.5) 8 2 – 1.5(9.5)

31. Example 2 Evaluate x 2 – y(x + y) if x = 8 and y = 1.5. x 2 – y(x + y) = 8 2 – 1.5(8 + 1.5) 8 2 – 1.5(8 + 1.5) 8 2 – 1.5(9.5) 64 – 1.5(9.5)

32. Example 2 Evaluate x 2 – y(x + y) if x = 8 and y = 1.5. x 2 – y(x + y) = 8 2 – 1.5(8 + 1.5) 8 2 – 1.5(8 + 1.5) 8 2 – 1.5(9.5) 64 – 1.5(9.5) 64 – 14.25

33. Example 2 Evaluate x 2 – y(x + y) if x = 8 and y = 1.5. x 2 – y(x + y) = 8 2 – 1.5(8 + 1.5) 8 2 – 1.5(8 + 1.5) 8 2 – 1.5(9.5) 64 – 1.5(9.5) 64 – 14.25 49.75

34. Example 3

35. Evaluate a 3 + 2bc if a = 2, b = -4, and c = -3. c 2 – 5

36. Example 3 Evaluate a 3 + 2bc if a = 2, b = -4, and c = -3. c 2 – 5 a 3 + 2bc = c 2 – 5

37. Example 3 Evaluate a 3 + 2bc if a = 2, b = -4, and c = -3. c 2 – 5 a 3 + 2bc = 2 3 + 2(-4)(-3) c 2 – 5

38. Example 3 Evaluate a 3 + 2bc if a = 2, b = -4, and c = -3. c 2 – 5 a 3 + 2bc = 2 3 + 2(-4)(-3) c 2 – 5 (-3) 2 – 5

39. Example 3 Evaluate a 3 + 2bc if a = 2, b = -4, and c = -3. c 2 – 5 a 3 + 2bc = 2 3 + 2(-4)(-3) c 2 – 5 (-3) 2 – 5 = 8 + 2(-4)(-3)

40. Example 3 Evaluate a 3 + 2bc if a = 2, b = -4, and c = -3. c 2 – 5 a 3 + 2bc = 2 3 + 2(-4)(-3) c 2 – 5 (-3) 2 – 5 = 8 + 2(-4)(-3) 9 – 5

41. Example 3 Evaluate a 3 + 2bc if a = 2, b = -4, and c = -3. c 2 – 5 a 3 + 2bc = 2 3 + 2(-4)(-3) c 2 – 5 (-3) 2 – 5 = 8 + 2(-4)(-3) 9 – 5 = 8 + 24 9 – 5

42. Example 3 Evaluate a 3 + 2bc if a = 2, b = -4, and c = -3. c 2 – 5 a 3 + 2bc = 2 3 + 2(-4)(-3) c 2 – 5 (-3) 2 – 5 = 8 + 2(-4)(-3) 9 – 5 = 8 + 24 9 – 5 = 32 4

43. Example 3 Evaluate a 3 + 2bc if a = 2, b = -4, and c = -3. c 2 – 5 a 3 + 2bc = 2 3 + 2(-4)(-3) c 2 – 5 (-3) 2 – 5 = 8 + 2(-4)(-3) 9 – 5 = 8 + 24 9 – 5 = 32 = 8 4

44. Example 4

45. Find the area of the following trapezoid. 16 in. 10 in. 52 in.

46. Example 4 Find the area of the following trapezoid. 16 in. A = ½h(b 1 + b 2 ) 10 in. 52 in.

47. Example 4 Find the area of the following trapezoid. 16 in. A = ½h(b 1 + b 2 ) 10 in. 52 in. A = ½h(b 1 + b 2 )

48. Example 4 Find the area of the following trapezoid. 16 in. A = ½h(b 1 + b 2 ) 10 in. = h 52 in. A = ½h(b 1 + b 2 )

49. Example 4 Find the area of the following trapezoid. 16 in. = b 1 A = ½h(b 1 + b 2 ) 10 in. = h 52 in. A = ½h(b 1 + b 2 )

50. Example 4 Find the area of the following trapezoid. 16 in. = b 1 A = ½h(b 1 + b 2 ) 10 in. = h 52 in. = b 2 A = ½h(b 1 + b 2 )

51. Example 4 Find the area of the following trapezoid. 16 in. A = ½h(b 1 + b 2 ) 10 in. 52 in. A = ½h(b 1 + b 2 ) = ½10(16 + 52)

52. Example 4 Find the area of the following trapezoid. 16 in. A = ½h(b 1 + b 2 ) 10 in. 52 in. A = ½h(b 1 + b 2 ) = ½10(16 + 52) = ½10(68)

53. Example 4 Find the area of the following trapezoid. 16 in. A = ½h(b 1 + b 2 ) 10 in. 52 in. A = ½h(b 1 + b 2 ) = ½10(16 + 52) = ½10(68) = 5(68)

54. Example 4 Find the area of the following trapezoid. 16 in. A = ½h(b 1 + b2) 10 in. 52 in. A = ½h(b 1 + b 2 ) = ½10(16 + 52) = ½10(68) = 5(68) = 340

55. 1.2 – Properties of Real Numbers

56. Real Numbers

57. 1.2 – Properties of Real Numbers Real Numbers (R)

58. 1.2 – Properties of Real Numbers Real Numbers (R)

59. 1.2 – Properties of Real Numbers Real Numbers (R) Rational

60. 1.2 – Properties of Real Numbers Real Numbers (R) Rational (⅓)

61. 1.2 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓)

62. 1.2 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓)

63. 1.2 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) Integers

64. 1.2 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) Integers (-6)

65. 1.2 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6)

66. 1.2 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6)

67. 1.2 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) Whole #’s

68. 1.2 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) Whole #’s (0)

69. 1.2 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) (W) Whole #’s (0)

70. 1.2 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) (W) Whole #’s (0)

71. 1.2 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) (W) Whole #’s (0) Natural #’s

72. 1.2 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) (W) Whole #’s (0) Natural #’s (7)

73. 1.2 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) (W) Whole #’s (0) (N) Natural #’s (7)

74. 1.2 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) (W) Whole #’s (0) (N) Natural #’s (1)

75. 1.2 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) Irrational (Z) Integers (-6) (W) Whole #’s (0) (N) Natural #’s (1)

76. 1.2 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) Irrational √ 5 (Z) Integers (-6) (W) Whole #’s (0) (N) Natural #’s (1)

77. 1.2 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (I) Irrational √ 5 (Z) Integers (-6) (W) Whole #’s (0) (N) Natural #’s (1)

78. Real Rational Irrational Integers Whole Natural

79. Example 1

80. Name the sets of numbers to which each apply.

81. Example 1 Name the sets of numbers to which each apply.

82. Example 1 Name the sets of numbers to which each apply.

83. Example 1 Name the sets of numbers to which each apply. (a) √ 16

84. Example 1 Name the sets of numbers to which each apply. (a) √ 16 = 4

85. Example 1 Name the sets of numbers to which each apply. (a) √ 16 = 4 - N

86. Example 1 Name the sets of numbers to which each apply. (a) √ 16 = 4 - N, W

87. Example 1 Name the sets of numbers to which each apply. (a) √ 16 = 4 - N, W, Z

88. Example 1 Name the sets of numbers to which each apply. (a) √ 16 = 4 - N, W, Z, Q

89. Example 1 Name the sets of numbers to which each apply. (a) √ 16 = 4 - N, W, Z, Q, R

90. Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b)-185

91. Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b)-185 - Z

92. Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b)-185 - Z, Q

93. Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b)-185 - Z, Q, R

94. Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b)-185 - Z, Q, R (c)√ 20

95. Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b)-185 - Z, Q, R (c)√ 20 - I, R

96. Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b)-185 - Z, Q, R (c)√ 20 - I, R (d) -⅞

97. Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b)-185 - Z, Q, R (c)√ 20 - I, R (d) -⅞ - Q

98. Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b)-185 - Z, Q, R (c)√ 20 - I, R (d) -⅞ - Q, R

99. Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b)-185 - Z, Q, R (c)√ 20 - I, R (d) -⅞ - Q, R __ (e) 0.45

100. Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b)-185 - Z, Q, R (c)√ 20 - I, R (d) -⅞ - Q, R __ (e) 0.45 - Q

101. Example 1 Name the sets of numbers to which each apply. (a)√ 16 = 4 - N, W, Z, Q, R (b)-185 - Z, Q, R (c)√ 20 - I, R (d) -⅞ - Q, R __ (e) 0.45 - Q, R

102. Properties of Real Numbers PropertyAdditionMultiplication Commutativea + b = b + aa·b = b·a Associative (a+b)+c = a+(b+c) (a · b) · c = a · (b · c) Identitya+0 = a = 0+aa·1 = a = 1·a Inversea+(-a) =0= -a+aa·1 =1= 1·a a a Distributivea(b+c)=ab+ac and (b+c)a=ba+ca

103. Example 2

104. Name the property used in each equation.

105. Example 2 Name the property used in each equation. (a) (5 + 7) + 8 = 8 + (5 + 7)

106. Example 2 Name the property used in each equation. (a) (5 + 7) + 8 = 8 + (5 + 7) Commutative Addition

107. Example 2 Name the property used in each equation. (a) (5 + 7) + 8 = 8 + (5 + 7) Commutative Addition (b) 3(4x) = (3·4)x

108. Example 2 Name the property used in each equation. (a) (5 + 7) + 8 = 8 + (5 + 7) Commutative Addition (b) 3(4x) = (3·4)x Associative Multiplication

109. Example 3 What is the additive and multiplicative inverse for -1¾?

110. Example 3 What is the additive and multiplicative inverse for -1¾? Additive: -1¾

111. Example 3 What is the additive and multiplicative inverse for -1¾? Additive: -1¾ + = 0

112. Example 3 What is the additive and multiplicative inverse for -1¾? Additive: -1¾ + 1¾ = 0

113. Example 3 What is the additive and multiplicative inverse for -1¾? Additive: -1¾ + 1¾ = 0 Multiplicative: -1¾

114. Example 3 What is the additive and multiplicative inverse for -1¾? Additive: -1¾ + 1¾ = 0 Multiplicative: -1¾ · = 1

115. Example 3 What is the additive and multiplicative inverse for -1¾? Additive: -1¾ + 1¾ = 0 Multiplicative: (-1¾)(- 4 / 7 ) = 1

116. Example 4

117. Simplify 2(5m+n)+3(2m–4n).

118. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n)

119. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n)

120. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)

121. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+

122. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+

123. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)

124. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+

125. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+

126. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)

127. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-

128. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-

129. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n)

130. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m

131. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m +

132. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n

133. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n +

134. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n + 6m

135. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n + 6m –

136. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n + 6m – 12n

137. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n + 6m – 12n

138. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n + 6m – 12n

139. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n + 6m – 12n 10m + 6m + 2n – 12n

140. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n + 6m – 12n 10m + 6m + 2n – 12n 16m

141. Example 4 Simplify 2(5m+n)+3(2m–4n). 2 (5m+n) + 3 (2m–4n) 2(5m)+2(n)+3(2m)-3(4n) 10m + 2n + 6m – 12n 10m + 6m + 2n – 12n 16m – 10n