Numeric Properties

1
Numeric Properties

• Commutative, Associative, Identity,
  Multiplication of 0

2
This slide show will introduce you to the names
of various properties. Most likely, you are
already familiar with the concepts behind these
properties.
3
The commutative property states that you can add
numbers in any order you want.
2 3 4 9 3 4 2 9 4 2 3 9
4
The commutative property can make your life
easier if you are trying to add compatible
numbers.
1 2 3 4 5 6 7 8 9
5
The commutative property can make your life
easier if you are trying to add compatible
numbers.
1 2 3 4 5 6 7 8 9
Reordering the numbers can be helpful.
6
The commutative property can make your life
easier if you are trying to add compatible
numbers.
1 2 3 4 5 6 7 8 9
Reordering the numbers can be helpful.
1 9 2 8 3 7 4 6 5
7
The commutative property can make your life
easier if you are trying to add compatible
numbers.
1 2 3 4 5 6 7 8 9
Reordering the numbers can be helpful.
1 9 2 8 3 7 4 6 5
10 10 10 10 5 45
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The commutative property also works for
multiplication.
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You can multiply in any order you want, and you
will get the same answer.
2 x 3 x 4 24 3 x 4 x 2 24 4 x 2 x 3 24
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Again, this can be helpful if there are
compatible numbers.
2 x 4 x 5 x 25
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Again, this can be helpful if there are
compatible numbers.
2 x 4 x 5 x 25
Reordering the numbers can be helpful.
12
Again, this can be helpful if there are
compatible numbers.
2 x 4 x 5 x 25
Reordering the numbers can be helpful.
2 x 5 x 4 x 25
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Again, this can be helpful if there are
compatible numbers.
2 x 4 x 5 x 25
Reordering the numbers can be helpful.
2 x 5 x 4 x 25
10 x 100 1000
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The associative property states that you can
group any numbers you want in an addition problem.
(1 2) (3 4) 10 1 (2 3) 4 10 (1
2 3) 4 10 1 (2 3 4) 10
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The associative property also works for
multiplication problems.
(5 x 6) x (10 x 100) 30,0005 x (6 x 10) x 100
30,000 (5 x 6 x 10) x 100 30,0005 x (6 x 10
x 100) 30,000
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The identity of addition property states that you
can add zero to any number, and you will not
change the value of the number.
24 0 24 -56 0 -56 256 0 256 R 0 R
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The identity of multiplication property states
that you can multiply any number by 1, and you
will not change the value of the number .
75 x 1 75 -24(1) -24 (502)(1) 502 1R R
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The multiplication of zero property states that
if you multiply any number by 0, then the product
is 0.
675 x 0 0 -135(0) 0 (0)(0) 0 H(0) 0
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Practice Time!
20
Name the property displayed by each equation.

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

21
1
221 22

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

22
1
221 22

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

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2
633 336

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

24
2
633 336

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

25
3
8cd 8dc

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

26
3
8cd 8dc

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

27
4
0 9 9 0

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

28
4
0 9 9 0

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

29
5
(7a)(b) (7)(ab)

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

30
5
(7a)(b) (7)(ab)

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

31
6
1m m

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

32
6
1m m

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

33
7
(19)(12) (12)(19)

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

34
7
(19)(12) (12)(19)

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

35
8
(3)(7)(0) 0

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

36
8
(3)(7)(0) 0

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

37
9
x (2y z) (2y z) x

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

38
9
x (2y z) (2y z) x

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

39
10
x (2y z) (x 2y) z

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

40
10
x (2y z) (x 2y) z

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

41
11
A x B x 0 0

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

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11
A x B x 0 0

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

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12
Q x R x 0 R x Q x 0

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

44
12
Q x R x 0 R x Q x 0

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

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13
1 x (25 x M) (1 x 25) x M

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

46
13
1 x (25 x M) (1 x 25) x M

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

47
14
(35 Y) 0 35 Y

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

48
14
(35 Y) 0 35 Y

• Commutative
• Associative
• Identity of Addition
• Identity of Multiplication
• Multiplication of Zero

49
Rewrite the expression using the commutative
property.
15
5 9
50
15
Rewrite the expression using the commutative
property.
5 9
9 5
51
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Rewrite the expression using the commutative
property.
8a 6
52
16
Rewrite the expression using the commutative
property.
8a 6
6 8a
53
17
Rewrite the expression using the commutative
property.
9 18w
54
17
Rewrite the expression using the commutative
property.
9 18w
18w 9
55
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Rewrite the expression using the associative
property.
(2 R) 5
56
18
Rewrite the expression using the associative
property.
(2 R) 5
2 (R 5)
57
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Rewrite the expression using the associative
property.
A x (B x C)
58
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Rewrite the expression using the associative
property.
A x (B x C)
(A x B) x C
59
20
Rewrite the expression using the associative
property.
(1 2) (3 4)
60
20
Rewrite the expression using the associative
property.
(1 2) (3 4)
1 (2 3) 4
61
Explain why you could not use the commutative
property on the following expression.
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15 5
62
21
Explain why you could not use the commutative
property on the following expression.
15 5 10
Different Answers
5 15 -10
63
22
Explain why you could not use the commutative
property on the following expression.
8 4
64
22
Explain why you could not use the commutative
property on the following expression.
8 4 2
Different Answers
4 8 ½
65
The End!