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

Commutative Property
11
State the property or properties that justify the
following.

• 10(1/10) 1

Multiplicative Inverse Property
12
State the property or properties that justify the
following.

• 3(x 10) 3x 30

Distributive Property
13
State the property or properties that justify the
following.

• 3 (4 5) (3 4) 5

Associative Property
14
State the property or properties that justify the
following.

• (5 2) 9 (2 5) 9

Commutative Property
15
2.
Which Property?
3 7 7 3
Commutative Property of Addition
16
3.
Which Property?
8 0 8
Identity Property of Addition
17
5.
Which Property?
6 4 4 6
Commutative Property of Multiplication
18
6.
Which Property?
17 (-17) 0
Inverse Property of Addition
19
7.
Which Property?
2(5) 5(2)
Commutative Property of Multiplication
20
1.
Which Property?
(2 1) 4 2 (1 4)
Associative Property of Addition
21
8.
Which Property?
even even even
Closure Property
22
9.
Which Property?
3(2 5) 32 35
Distributive Property
23
10.
Which Property?
6(78) (67)8
Associative Property of Multiplication
24
11.
Which Property?
5 1 5
Identity Property of Multiplication
25
Properties Using Negatives
26
13.
Which Property?
(6 3)4 64 34
Distributive Property
27
14.
Which Property?
1(-9) -9
Identity Property of Multiplication
28
15.
Which Property?
3 (-3) 0
Inverse Property of Addition
29
16.
Which Property?
1 -9 3 1 (-9)
3
Associative Property of Addition
30
17.
Which Property?
-3(6) 6(-3)
Commutative Property of Multiplication
31
18.
Which Property?
-8 0 -8
Identity Property of Addition
32
19.
Which Property?
37 34 3(7 4)
Distributive Property
33
20.
Which Property?
6 (3 (-2) (6 3) (- 2)
Associative Property of Addition
34
21.
Which Property?
7 (-5) -5 7
Commutative Property of Addition
35
22.
Which Property?
(5 4)9 45 36
Distributive Property
36
23.
Which Property?
-3(5 4) (-3 5)4
Associative Property of Multiplication
37
24.
Which Property?
-8(4) 4(-8)
Commutative Property of Multiplication
38
Properties Using Fractions
39
25.
Which Property?
51/7 0 51/7
Identity Property of Addition
40
26.
Which Property?
3/4 6/7 6/7 3/4
Commutative Property of Addition
41
27.
Which Property?
12/5 1 12/5
Identity Property of Multiplication
42
28.
Which Property?
(fraction)(fraction)
fraction
Closure Property
43
29.
Which Property?
-8 2/5 0 -8 2/5
Identity Property of Addition
44
30.
Which Property?
(-2/3)(5)9 -2/3(5)(9)
Associative Property of Multiplication
45
Properties Using Variables
46
31.
Which Property?
6(3 2n) 18 12n
Distributive Property
47
32.
Which Property?
2x 3 3 2x
Commutative Property of Addition
48
33.
Which Property?
ab ba
Commutative Property of Multiplication
49
34.
Which Property?
a 0 a
Identity Property of Addition
50
35.
Which Property?
a(bc) (ab)c
Associative Property of Multiplication
51
36.
Which Property?
a1 a
Identity Property of Multiplication
52
37.
Which Property?
a b b a
Commutative Property of Addition
53
38.
Which Property?
a(b c) ab ac
Distributive Property
54
39.
Which Property?
a (b c) (a b) c
Associative Property of Addition
55
40.
Which Property?
a (-a) 0
Inverse Property of Addition
56
Properties of Real Numbers

• Commutative
• Associative
• Distributive
• Identity
• Inverse