Properties of Real Numbers

1
Properties of Real Numbers

• Commutative
• Associative
• Distributive
• Identity
• Inverse

2
Commutative Properties

• Changing the order of the numbers in addition or
  multiplication will not change the result.
• Commutative Property of Addition states 2 3
  3 2 or a b b a.
• Commutative Property of Multiplication states 4
  5 5 4 or ab ba.

3
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)

4
Distributive Property

• Multiplication distributes over addition.

5
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.

6
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.

7
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.

8
Multiplicative Inverse Property

• For each real number a there exists a unique real
  number such that their product is 1.

9
Lets play Name that property!
10
State the property or properties that justify the
following.

• 3 2 2 3

11
State the property or properties that justify the
following.

• 3 2 2 3

Commutative Property
12
State the property or properties that justify the
following.

• 10(1/10) 1

13
State the property or properties that justify the
following.

• 10(1/10) 1

Multiplicative Inverse Property
14
State the property or properties that justify the
following.

• 3(x 10) 3x 30

15
State the property or properties that justify the
following.

• 3(x 10) 3x 30

Distributive Property
16
State the property or properties that justify the
following.

• 3 (4 5) (3 4) 5

17
State the property or properties that justify the
following.

• 3 (4 5) (3 4) 5

Associative Property
18
State the property or properties that justify the
following.

• (5 2) 9 (2 5) 9

19
State the property or properties that justify the
following.

• (5 2) 9 (2 5) 9

Commutative Property
20
Which Property?
3 7 7 3
21
Which Property?
3 7 7 3
Commutative Property of Addition
22
Which Property?
8 0 8
23
Which Property?
8 0 8
Identity Property of Addition
24
Which Property?
6 4 4 6
25
Which Property?
6 4 4 6
Commutative Property of Multiplication
26
Which Property?
17 (-17) 0
27
Which Property?
17 (-17) 0
Inverse Property of Addition
28
Which Property?
2(5) 5(2)
29
Which Property?
2(5) 5(2)
Commutative Property of Multiplication
30
Which Property?
(2 1) 4 2 (1 4)
31
Which Property?
(2 1) 4 2 (1 4)
Associative Property of Addition
32
Which Property?
even even even
33
Which Property?
3(2 5) 32 35
34
Which Property?
3(2 5) 32 35
Distributive Property
35
Which Property?
6(78) (67)8
36
Which Property?
6(78) (67)8
Associative Property of Multiplication
37
Which Property?
5 1 5
38
Which Property?
5 1 5
Identity Property of Multiplication
39
Properties Using Negatives
40
Which Property?
(6 3)4 64 34
41
Which Property?
(6 3)4 64 34
Distributive Property
42
Which Property?
1(-9) -9
43
Which Property?
1(-9) -9
Identity Property of Multiplication
44
Which Property?
3 (-3) 0
45
Which Property?
3 (-3) 0
Inverse Property of Addition
46
Which Property?
1 -9 3 1 (-9)
3
47
Which Property?
1 -9 3 1 (-9)
3
Associative Property of Addition
48
Which Property?
-3(6) 6(-3)
49
Which Property?
-3(6) 6(-3)
Commutative Property of Multiplication
50
Which Property?
-8 0 -8
51
Which Property?
-8 0 -8
Identity Property of Addition
52
Which Property?
37 34 3(7 4)
53
Which Property?
37 34 3(7 4)
Distributive Property
54
Which Property?
6 (3 (-2) (6 3) (- 2)
55
Which Property?
6 (3 (-2) (6 3) (- 2)
Associative Property of Addition
56
Which Property?
7 (-5) -5 7
57
Which Property?
7 (-5) -5 7
Commutative Property of Addition
58
Which Property?
(5 4)9 45 36
59
Which Property?
(5 4)9 45 36
Distributive Property
60
Which Property?
-3(5 4) (-3 5)4
61
Which Property?
-3(5 4) (-3 5)4
Associative Property of Multiplication
62
Which Property?
-8(4) 4(-8)
63
Which Property?
-8(4) 4(-8)
Commutative Property of Multiplication
64
Properties Using Fractions
65
Which Property?
51/7 0 51/7
66
Which Property?
51/7 0 51/7
Identity Property of Addition
67
Which Property?
3/4 6/7 6/7 3/4
68
Which Property?
3/4 6/7 6/7 3/4
Commutative Property of Addition
69
Which Property?
12/5 1 12/5
70
Which Property?
12/5 1 12/5
Identity Property of Multiplication
71
Which Property?
-8 2/5 0 -8 2/5
72
Which Property?
-8 2/5 0 -8 2/5
Identity Property of Addition
73
Which Property?
(-2/3)(5)9 -2/3(5)(9)
74
Which Property?
(-2/3)(5)9 -2/3(5)(9)
Associative Property of Multiplication
75
Properties Using Variables
76
Which Property?
6(3 2n) 18 12n
77
Which Property?
6(3 2n) 18 12n
Distributive Property
78
Which Property?
2x 3 3 2x
79
Which Property?
2x 3 3 2x
Commutative Property of Addition
80
Which Property?
ab ba
81
Which Property?
ab ba
Commutative Property of Multiplication
82
Which Property?
a 0 a
83
Which Property?
a 0 a
Identity Property of Addition
84
Which Property?
a(bc) (ab)c
85
Which Property?
a(bc) (ab)c
Associative Property of Multiplication
86
Which Property?
a1 a
87
Which Property?
a1 a
Identity Property of Multiplication
88
Which Property?
a b b a
89
Which Property?
a b b a
Commutative Property of Addition
90
Which Property?
a(b c) ab ac
91
Which Property?
a(b c) ab ac
Distributive Property
92
Which Property?
a (b c) (a b) c
93
Which Property?
a (b c) (a b) c
Associative Property of Addition
94
Which Property?
a (-a) 0
95
Which Property?
a (-a) 0
Inverse Property of Addition
96
Properties of Real Numbers

• Commutative
• Associative
• Distributive
• Identity
• Inverse