Property

1
Property 5

• The Distributive Property
• of Multiplication

2
The Distributive Property

• Background
• The word distributive comes from the verb to
  distribute.
• Definition on dictionary.com
• Distributing refers to passing things out or
  delivering things to people

3
The Distributive Property
a(b c) (a b) (a c)
A times the sum of b and c a times b plus a
times c
Lets plug in some numbers first. Remember that
to distribute means delivering items, or handing
them out. Here is how this property works
5(2 3) (5 2) (5 3)
4
You have sold many items for the fundraiser!
You went to two houses on one street and three
houses on a different street. Every family bought
5 items!
5(2 3) (5 2) (5 3)
You went to two houses on one street and three
houses on a different street. Every family bought
5 items!
5
You will be distributing 5 items to each house.
2
3
5
4
1
6
5(2 3) (5 2) (5 3)
You distributed (delivered) these all in one
trip. There are (23) five houses all together.
You need to deliver 5 gifts to each house. You
need to put 25 items on your wagon at one time.
5 items x 5 houses 25 items all together
7
5(2 3) (5 2) (5 3)
and
10
You distributed your items in two trips (). On
the first trip you distributed 5 items to each of
2 houses (5 x 2 10). On the second trip you
distributed 5 items to each of 3 houses (5 x 3
15). That means you distributed (delivered) 10
items plus 15 items. That makes 25 items
altogether.

15
25
8
The Distributive Property
Make 1 trip. You have 5 houses. You need to bring
5 items to each house. You need 25 items on your
wagon.
DISTRIBUTION CENTER
5(2 3)
9
The Distributive Property
Make 2 trips. You have 2 houses for your first
trip and you need to bring 5 items to each house.
You have 3 houses on your second trip and need to
bring 5 items to each house. When your second
trip is over, you will have distributed 25 items.
DISTRIBUTION CENTER
(5 2) (5 3)
10

• An example 6 x 13
• using your mental math skills . . .
• symbolically
• 6 (10 3) 6 10 6 3
• and pictorially (rectangular array area model)

10
3
6 10
6 3
6
11
How do I tell the properties apart?

• Commutative
• Numbers switch places
• Associative
• Parentheses on both sides
• Only multiplication on each side
• Identity
• Multiply by 1
• Zero Property
• Multiply by zero
• Distributive
• Parentheses on each side
• One side has a multiplication sign AND a plus sign

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Lets practice !
Look at the problem. Identify which property it
represents.
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4(5 6) (4 5) (4 6)
The Distributive Property of Multiplication

• 3 numbers on one side4 on the other
• Multiplication AND addition
• 3 sets of parentheses

14
987 1 987
The Identity Property of Multiplication

• Times 1

15
3 0 0
Zero Property of Multiplication

• Times zero

16
(1 2) 3 1 (2 3)
The Associative Property of Multiplication

• Same 3 numbers
• Multiplication only
• 2 sets of parentheses

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6 11 11 6
The Commutative Property of Multiplication

• Same 2 numbers
• Numbers switched places

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9 7 7 9
The Commutative Property of Multiplication

• Same 2 numbers
• Numbers switched places

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12 0 0
Zero Property of Multiplication

• Times zero

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(9 8) 7 9 (8 7)
The Associative Property of Multiplication

• Same 3 numbers
• Multiplication only
• 2 sets of parentheses

21
9(8 7) (9 8) (9 7)
The Distributive Property of Multiplication

• 3 numbers on one side4 on the other
• Multiplication AND addition
• 3 sets of parentheses

22
9 1 9
The Identity Property of Multiplication

• Times 1

23
a 1 a
The Identity Property of Multiplication
24
a b b a
The Commutative Property of Multiplication
25
(a b) c a (b c)
The Associative Property of Multiplication
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a 0 0
The Zero Property of Multiplication
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a(b c) (a b) (a c)
The Distributive Property of Multiplication