1. 1.3 – Properties of Real Numbers

2. Real Numbers 1.3 – Properties of Real Numbers

3. Real Numbers (R)

4. 1.3 – Properties of Real Numbers Real Numbers (R)

5. 1.3 – Properties of Real Numbers Real Numbers (R) Rational

6. 1.3 – Properties of Real Numbers Real Numbers (R) Rational (⅓)

7. 1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓)

8. 1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓)

9. 1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) Integers

10. 1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) Integers (-6)

11. 1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6)

12. 1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6)

13. 1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) Whole #’s

14. 1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) Whole #’s (0)

15. 1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) (W) Whole #’s (0)

16. 1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) (W) Whole #’s (0)

17. 1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) (W) Whole #’s (0) Natural #’s

18. 1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) (W) Whole #’s (0) Natural #’s (7)

19. 1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) (W) Whole #’s (0) (N) Natural #’s (7)

20. 1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (Z) Integers (-6) (W) Whole #’s (0) (N) Natural #’s (1)

21. 1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) Irrational (Z) Integers (-6) (W) Whole #’s (0) (N) Natural #’s (1)

22. 1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) Irrational √ 5 (Z) Integers (-6) (W) Whole #’s (0) (N) Natural #’s (1)

23. 1.3 – Properties of Real Numbers Real Numbers (R) (Q) Rational (⅓) (I) Irrational √ 5 (Z) Integers (-6) (W) Whole #’s (0) (N) Natural #’s (1)

24. Example 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

39. 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

40. 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

41. 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

42. 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

43. 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

44. 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

45. 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

46. 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

47. 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

48. Example 2

49. Name the property used in each equation.

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

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

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

53. 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

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

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

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

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

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

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

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

61. 1.4 – The Distributive Property

62. a(b+c)=ab+ac and (b+c)a=ba+ca

63. Example 4

64. Simplify 2(5m+n)+3(2m–4n).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

79. 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

80. 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 +

81. 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

82. 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 –

83. 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

84. 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

85. 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

86. 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

87. 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

88. 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