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## The Distributive Property

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### Title: The Distributive Property Author: Current User Indians Hill Exe Last modified by: Owner (Owner) Created Date: 12/4/2010 8:48:19 AM Document presentation format – PowerPoint PPT presentation

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Title: The Distributive Property

1
The Distributive Property
2
The distributive property is mental math strategy
that can be used when multiplying.
24 x 6 ?
3
Think of an array with a length of 24 and a width
of 6
6
24
4
How can you break the array apart to make 24 a
friendlier number?
6
24
5
Break the length into 20 and 4.
6
20 4
6
Think of them as separate arrays.
6
20 4
7
Now you have 6 x 20 and 6 times 4.
6
6
20 4
8
What is the total of each array?
6
6
20 4
9
6 x 20 is 6 x 2 tens or 12 tens which is 120.
6
6
6 x 20 120
20 4
10
6 x 4 is 24.
6
6
6 x 20 120
6 x 4 24
20 4
11
Now, put the two arrays back together.
6
120
24
20 4
12
Here they are together again.
6
120
24
20 4
13
Add the two arrays together. 120 24 144.
6
120
24
24
14
So the answer to 6 x 24 is 144.
6
144
24
15
Lets look at it in an equation.
16
Break apart the double-digit number.
24 x 6 ?
20 4

17
Then multiply each part by 5.
24 x 6 ?
20 4

x 6 x 6
18
Then multiply each part by 5.
24 x 6 ?
20 4

x 6 x 6
120 24
19
24 x 6 144
20 4

x 6 x 6
120 24

144
20
Lets look at another example.
53 x 6 ?
21
Break apart the double-digit number.
53 x 6 ?
22
Break apart the double-digit number.
53 x 6 ?
50 3

23
Multiply each part by 6.
53 x 6 ?
50 3

x 6 x 6
24
Multiply each part by 6.
53 x 6 ?
50 3

x 6 x 6
300 18
25
53 x 6 318
50 3

x 6 x 6
300 18 318
26
There are three steps to the distributive
property.
4 x 28
27
There are three steps to the distributive
property.
4 x 28
1) Break apart the double-digit number.
28
There are three steps to the distributive
property.
4 x 28 4 x (20 8)
1) Break apart the double-digit number.
29
There are three steps to the distributive
property.
4 x 28 4 x (20 8)
1. Break apart the double-digit number.
2. Multiply each part by 4. (distribute the 4)

30
There are three steps to the distributive
property.
4 x 28 4 x (20 8) (4 x 20) (4 x 8)
1. Break apart the double-digit number.
2. Multiply each part by 4. (distribute the 4)

31
There are three steps to the distributive
property.
4 x 28 4 x (20 8) (4 x 20) (4 x 8)
1. Break apart the double-digit number.
2. Multiply each part by 4. (distribute the 4)
3. Sum the two products.

32
There are three steps to the distributive
property.
4 x 28 4 x (20 8) 80 (4 x 8)
1. Break apart the double-digit number.
2. Multiply each part by 4. (distribute the 4)
3. Sum the two products.

33
There are three steps to the distributive
property.
4 x 28 4 x (20 8) 80 32
1. Break apart the double-digit number.
2. Multiply each part by 4. (distribute the 4)
3. Sum the two products.

34
There are three steps to the distributive
property.
4 x 28 4 x (20 8) 80 32 112
1. Break apart the double-digit number.
2. Multiply each part by 4. (distribute the 4)
3. Sum the two products.

35
The word distribute means to give out.
36
Distribute the cubes to the girls.
37
Distribute the cubes to the girls.
38
Distribute the cubes to the girls.
39
Distribute the cubes to the girls.
40
Distribute the cubes to the girls.
41
Distribute the cubes to the girls.
42
In this example, the 5 was distributed.
5 x 38 5 x (30 8) (5 x 30) (5 x 8)
43
In this example, the 7 was distributed.
7 x 46 7 x (40 6) (7 x 40) (7 x 6)
44
A swimming pool has a shallow end and a deep end.
Find the surface area of the pool.
deepwater
8 yds
shallow water
5 yds
10 yds
45
Break the pool into a deep end and a shallow end.
deepwater
8 yds
8 yds
shallow water
10 yds
5 yds
46
Find the area of the deep end.
deepwater
8 yds
8 yds
shallow water
10 yds
5 yds
47
Find the area of the deep end.
8 x 5 40
8 yds
8 yds
shallow water
10 yds
5 yds
48
Find the area of the shallow end.
8 x 5 40
8 yds
8 yds
shallow water
10 yds
5 yds
49
Find the area of the shallow end.
8 x 5 40
8 yds
8 yds
8 x 10 80
10 yds
5 yds
50
Now sum the two areas together.
8 x 5 40
8 yds
8 yds
8 x 10 80
10 yds
5 yds
51
Now sum the two areas together.
80
40

8 yds
10 yds
5 yds
52
40 80 120 square yards
40
80
8 yds
5 yds
10 yds
53
Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
9 yds
5 yds
20 yds
54
Find the areas for each individual rectangle.
9 yds
5 yds
20 yds
55
Find the areas for each individual rectangle.
9 yds
(9 x 5)
5 yds
20 yds
56
Find the areas for each individual rectangle.
9 yds
(9 x 5)
(9 x 20)
5 yds
20 yds
57
Sum the two areas.
9 yds

(9 x 5)
(9 x 20)
5 yds
20 yds
58
(9 x 5) (9 x 20) area
9 yds
(9 x 5)
(9 x 20)
5 yds
20 yds
59
Practice Time
60
6) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
4 yds
3 yds
9 yds
61
6) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
4 yds
3 yds
9 yds
62
6) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
4 yds
3 yds
9 yds
63
6) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
4 yds
4 yds
3 yds
9 yds
64
6) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
4 yds
4 yds
4 x 3
3 yds
9 yds
65
6) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
4 yds
4 yds
4 x 3
4 x 9
3 yds
9 yds
66
6) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
4 x 3
4 x 9
4 yds
4 yds
3 yds
9 yds
67
6) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
4 x 3
4 x 9
4 yds
3 yds
9 yds
68
6) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
4 x 3
4 x 9
4 yds
3 yds
9 yds
69
6) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
4 x 3
4 x 9
4 yds
3 yds
9 yds
70
7) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
6 yds
4 yds
8 yds
71
7) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
6 yds
4 yds
8 yds
72
7) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
6 yds
4 yds
8 yds
73
7) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
6 yds
6 yds
4 yds
8 yds
74
7) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
6 yds
6 yds
6 x 4
4 yds
8 yds
75
7) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
6 yds
6 yds
6 x 4
6 x 8
4 yds
8 yds
76
7) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
6 x 4
6 x 8
6 yds
6 yds
4 yds
8 yds
77
7) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
6 x 4
6 x 8
6 yds
4 yds
8 yds
78
7) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
6 x 4
6 x 8
6 yds
4 yds
8 yds
79
7) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
6 x 4
6 x 8
6 yds
4 yds
8 yds
80
8) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
5 yds
2 yds
10 yds
81
8) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
5 yds
5 x 2
5 x 10
2 yds
10 yds
82
8) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
5 x 2
5 x 10
5 yds
2 yds
10 yds
83
9) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
8 yds
3 yds
5 yds
84
9) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
8 yds
8 x 3
8 x 5
3 yds
5 yds
85
9) Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
8 x 3
8 x 5
8 yds
3 yds
5 yds
86
10) Write an expression that shows how to find
the area of the rectangle and uses the
distributive property.
5 yds
x yds
10 yds
87
10) Write an expression that shows how to find
the area of the rectangle and uses the
distributive property.
5 yds
5x
5 10
x yds
10 yds
88
10) Write an expression that shows how to find
the area of the rectangle and uses the
distributive property.
5x
5 10
5 yds
x yds
10 yds
89
11) Which expression is equivalent to 3(x 7)?
x 10
x 21
3x 7
3x 21
90
11) Which expression is equivalent to 3(x 7)?
Correct!
3x 21
91
12) Which expression is equivalent to 4(x 5)?
x 9
4x 20
4x 5
9x
92
12) Which expression is equivalent to 4(x 5)?
4x 20
Correct!
93
13) Which expression is equivalent to 8(x 2)?
10x
8x 2
8x 16
8x 10
94
13) Which expression is equivalent to 8(x 2)?
8x 16
Correct!
95
14) Which expression is equivalent to 2(x 3)?
2x 6
2x 5
2x 3
2x 2
96
14) Which expression is equivalent to 2(x 3)?
2x 6
Correct!
97
The End.
98
1) Which of the following expressions shows the
distributive property for 5 x (3 7)?
(5 3) x (5 7)
(5 x 3) x (5 x 7)
(5 x 3) (5 x 7)
99
1) Which of the following expressions shows the
distributive property for 5 x (3 7)?
Correct!
(5 x 3) (5 x 7)
100
2) Which of the following expressions shows the
distributive property for 3 x (9 4) ?
(3 x 9) (3 x 4)
(3 9) (3 4)
(3 9) x (3 4)
101
2) Which of the following expressions shows the
distributive property for 3 x (9 4) ?
(3 x 9) (3 x 4)
Correct!
102
3) Which of the following expressions is
equivalent to2 3 2 3 and shows the
distributive property.
2 2 3 3
2 x (2 3)
3 x (2 3)
103
3) Which of the following expressions is
equivalent to2 3 2 3 and uses the
distributive property.
2 x (2 3)
Correct!
104
4) Which of the following expressions is
equivalent to(4 x 3) (4 x 8) ?
3 x (4 8)
8 x (3 4)
4 x (3 8)
105
4) Which of the following expressions is
equivalent to(4 x 3) (4 x 8) ?
Correct!
4 x (3 8)
106
5) Which of the following expressions is
equivalent to(5 x 9) (5 x 3) ?
3 x (9 5)
5 x (9 3)
9 x (3 5)
107
5) Which of the following expressions is
equivalent to(5 x 9) (5 x 3) ?
5 x (9 3)
Correct!
108
3) Which of the following expressions is
equivalent to2 3 2 3 and uses the
distributive property.
2 2 3 3 This shows the commutative property.
Try again.
109
Sorry!
• Try again.