The document discusses properties of real numbers including: - The commutative property of addition and multiplication, where changing the order of terms does not change the result. - The identity properties of addition and multiplication, where adding/multiplying a number and the identity element (0 for addition, 1 for multiplication) does not change the number. - The inverse properties of addition and multiplication, where adding/multiplying a number and its inverse/opposite results in the identity element.

3. 1. identify properties of real numbers;
2. simplify expressions using properties of real
numbers

5. • Closure
• Commutative
• Associative
• Distributive
• Identity (addition and multiplication)
• Inverse (addition and multiplication)

7. The or of any two real number
is a real number.
2 + 3 = 5

8. The or of any two real number
is a real number.
1 + 2 = 3

9. The or of any two real number
is a real number.
6 + 8 = 14

10. The or of any two real number
is a real number.
11 + 22= 33

11. The or of any two real number
is a real number.
2(6) = 12

12. The or of any two real number
is a real number.
3(2) = 6

13. The or of any two real number
is a real number.
8(6) = 48

14. The or of any two real number
is a real number.
5(9) = 45

15. The or of any two real number
is a real number.
2(10)= 20

17. Changing the of the in
or will not change the result.
2 + 3 = 3 + 2
5 5=

18. Changing the of the in
or will not change the result.
11 + 7 = 7 + 11
18 18=

19. Changing the of the in
or will not change the result.
50 + 25 = 25 + 50
75 75=

20. Changing the of the in
or will not change the result.
4(5) = 5(4)
20 20=

21. Changing the of the in
or will not change the result.
3(8) = 8(3)
24 24=

22. Changing the of the in
or will not change the result.
12(12) = 12(12)
144 144=

23. Changing the of the in
or will not change the result.
Other examples:
12 + 14 = 14 + 12

24. Changing the of the in
or will not change the result.
Other examples:
18 + 9 = 9 + 18

25. Changing the of the in
or will not change the result.
Other examples:
2(4) = 4(2)

26. Changing the of the in
or will not change the result.
Other examples:
13(9) = 13(9)

27. Got
questions?

29. 9
Changing the of the in
or will not change the
result.
=
4 + 3 + 2 = 4 + (3 + 2)
7 4+ 2 + 5
=9

30. Changing the of the in
or will not change the
result.
6
=
1 + 2 + 3 = 1 + (2 + 3)
3 1+ 3 + 5
=6

31. Changing the of the in
or will not change the
result.
24
=
(2 • 3) • 4 = 2 • (3 • 4)
6 2• 4 • 12
=24

32. Changing the of the in
or will not change the
result.
60
=
(3 • 4) • 5 = 3 • (4 • 5)
12 3• 5 • 20
=60

33. Other examples:
Changing the of the in
or will not change the
result.
1 + 4 + 3 = 1 + (4 + 3)

34. Other examples:
Changing the of the in
or will not change the
result.
6 + 8 + 7 = 6 + (8 + 7)

35. Other examples:
Changing the of the in
or will not change the
result.
(7 • 4) • 3 =7 • (4 • 3)

36. Other examples:
Changing the of the in
or will not change the
result.
(5 • 6) • 7 = 5 • (6 • 7)

38. =14
Changing the of the in
or will not change the
result.
=
2 ( 3 + 4 ) = 2 3 + 2 4
6 + 8 6 + 8
14

39. Changing the of the in
or will not change the
result.
3 ( 4 + 5 )
12 + 15
27
=
=

40. Changing the of the in
or will not change the
result.
3 ( 4 + 5 )
Other examples:

41. Changing the of the in
or will not change the
result.
5 ( 𝑥 + 3 )
Other examples:

42. Changing the of the in
or will not change the
result.
7 ( 8 − 2 )
Other examples:

43. Changing the of the in
or will not change the
result.
4 ( 𝑥 − 2 )
Other examples:

44. Got
questions?

46. 1. Identity Property of Addition
2. Identity Property of Multiplication

48. Any number added to the
will remained . Zero (0) is the
identity element for .3 = 3+ 0
Identity element of
addition (0).

49. Any number added to the
will remained . Zero (0) is the
identity element for .
99 = 99+ 0
Identity element of
addition (0).

50. Any number added to the
will remained . Zero (0) is the
identity element for .
36 = 36+ 0
Identity element of
addition (0).

51. Any number added to the
will remained . Zero (0) is the
identity element for .
113 = 113+ 0
Identity element of
addition (0).

52. Any number added to the
will remained . Zero (0) is the
identity element for .
0 = 11+ 11
Identity element of
addition (0).

53. Any number added to the
will remained . Zero (0) is the
identity element for .
0 = 78+ 78
Identity element of
addition (0).

54. Any number added to the
will remained . Zero (0) is the
identity element for .
0 = 62+ 62
Identity element of
addition (0).

55. Got
questions?

57. Any number multiplied to the
will remained . One (1)
is the identity element for .8 = 8• 1
Identity element of
multiplication (1).

58. Any number multiplied to the
will remained . One (1)
is the identity element for .
22 = 22• 1
Identity element of
multiplication (1).

59. Any number multiplied to the
will remained . One (1)
is the identity element for .
77 = 77• 1
Identity element of
multiplication (1).

60. Any number multiplied to the
will remained . One (1)
is the identity element for .
1 = 92• 92
Identity element of
multiplication (1).

61. Any number multiplied to the
will remained . One (1)
is the identity element for .
1 = 16• 16
Identity element of
multiplication (1).

62. Any number multiplied to the
will remained . One (1)
is the identity element for .
1 = 43• 43
Identity element of
multiplication (1).

63. Got
questions?

65. 1. Inverse Property of Addition
2. Inverse Property of Multiplication

67. 3 = 0+ (−3)
The of a number and its
(opposite) is the .
Additive Inverse
(opposite)

68. The of a number and its
(opposite) is the .
9 = 0+ (−9)
Additive Inverse
(opposite)

69. The of a number and its
(opposite) is the .
21 = 0+ (−21)
Additive Inverse
(opposite)

70. The of a number and its
(opposite) is the .
15 = 0+ (−15)
Additive Inverse
(opposite)

71. The of a number and its
(opposite) is the .
7 = 0+ (−7)
Additive Inverse
(opposite)

72. The of a number and its
(opposite) is the .
4 = 0+ (−4)
Additive Inverse
(opposite)

73. The of a number and its
(opposite) is the .
22 = 0+ (−22)
Additive Inverse
(opposite)

74. Got
questions?

76. The of a number and its
(reciprocal) is the
.12 = 1•
1
12
Multiplicative Inverse
(reciprocal)

77. The of a number and its
(reciprocal) is the
.
23 = 1•
1
23
Multiplicative Inverse
(reciprocal)

78. The of a number and its
(reciprocal) is the
.
76 = 1•
1
76
Multiplicative Inverse
(reciprocal)

79. The of a number and its
(reciprocal) is the
.
44 = 1•
1
44
Multiplicative Inverse
(reciprocal)

80. The of a number and its
(reciprocal) is the
.
115 = 1•
1
115
Multiplicative Inverse
(reciprocal)

81. The of a number and its
(reciprocal) is the
.
𝑎 = 1•
1
𝑎
Multiplicative Inverse
(reciprocal)

82. The of a number and its
(reciprocal) is the
.
𝑏 = 1•
1
𝑏
Multiplicative Inverse
(reciprocal)

83. The of a number and its
(reciprocal) is the
.
𝑐𝑑 = 1•
1
𝑐𝑑
Multiplicative Inverse
(reciprocal)

84. The of a number and its
(reciprocal) is the
.
𝑥𝑦𝑧 = 1•
1
𝑥𝑦𝑧
Multiplicative Inverse
(reciprocal)

85. Got
questions?

87. 3 + 7 = 7 + 3
Commutative
Property of Addition
2.

88. 8 + 0 = 8
Identity Property of
Addition
3.

89. 6 • 4 = 4 • 6
Commutative Property
of Multiplication
5.

90. 5 • 1 = 5
Identity Property of
Multiplication
11.

91. 51/7 + 0 = 51/7
Identity Property of
Addition
25.

92. a + (-a) = 0
Inverse Property of
Addition
40.

93. E-Math 7
Practice and Application
Test I, II & III
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