The Distributive Property

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The Distributive Property
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The distributive property is mental math strategy
that can be used when multiplying.
43 x 5 ?
3
Break apart the double-digit number.
43 x 5 ?
40 3

4
Then multiply each part by 5.
43 x 5 ?
40 3

x 5 x 5
5
Then multiply each part by 5.
43 x 5 ?
40 3

x 5 x 5
200 15
6
Finally, sum your two products
43 x 5 215
40 3

x 5 x 5
200 15

215
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Lets look at another example.
53 x 6 ?
8
Break apart the double-digit number.
53 x 6 ?
9
Break apart the double-digit number.
53 x 6 ?
50 3

10
Multiply each part by 6.
53 x 6 ?
50 3

x 6 x 6
11
Multiply each part by 6.
53 x 6 ?
50 3

x 6 x 6
300 18
12
Sum the two products.
53 x 6 318
50 3

x 6 x 6
300 18 318
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There are three steps to the distributive
property.
4 x 28
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There are three steps to the distributive
property.
4 x 28
1) Break apart the double-digit number.
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There are three steps to the distributive
property.
4 x 28 4 x (20 8)
1) Break apart the double-digit number.
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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)

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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)

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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.

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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.

20
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.

21
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.

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The word distribute means to give out.
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Distribute the cubes to the girls.
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Distribute the cubes to the girls.
25
Distribute the cubes to the girls.
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Distribute the cubes to the girls.
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Distribute the cubes to the girls.
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Distribute the cubes to the girls.
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In this example, the 5 was distributed.
5 x 38 5 x (30 8) (5 x 30) (5 x 8)
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In this example, the 7 was distributed.
7 x 46 7 x (40 6) (7 x 40) (7 x 6)
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Find the area of the rectangle.Area length x
width
6 ft
24 ft
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Find the area of the rectangle.Area length x
width
6 ft
24 ft
33
Find the area of the rectangle.Area length x
width
6 ft
20 ft 4 ft
34
Find the area of the rectangle.Area length x
width
6 ft
20 ft 4 ft
35
Find the area of the rectangle.Area length x
width
6 ft
6 ft
20 ft 4 ft
36
Find the area of the rectangle.Area length x
width
Find the area of each rectangle.
6 ft
6 ft
20 ft 4 ft
37
Find the area of the rectangle.Area length x
width
Find the area of each rectangle.
6 ft
6 ft
6 x 20 120 sq ft
20 ft 4 ft
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Find the area of the rectangle.Area length x
width
Find the area of each rectangle.
6 ft
6 ft
6 x 20 120 sq ft
6 x 4 24 sq ft
20 ft 4 ft
39
Find the area of the rectangle.Area length x
width
Find the area of each rectangle.
6 ft
6 ft
120 sq ft
24 sq ft
20 ft 4 ft
40
Find the area of the rectangle.Area length x
width
Now put the two rectangles back together.
6 ft
6 ft
120 sq ft
24 sq ft
20 ft 4 ft
41
Find the area of the rectangle.Area length x
width
Now put the two rectangles back together.
6 ft
120 sq ft
24 sq ft
20 ft 4 ft
42
Find the area of the rectangle.Area length x
width
Now put the two rectangles back together.
6 ft
120 sq ft
24 sq ft
20 ft 4 ft
43
Find the area of the rectangle.Area length x
width
Now put the two rectangles back together.
6 ft
120 sq ft
24 sq ft
24 ft
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Find the area of the rectangle.Area length x
width
Now put the two rectangles back together.
6 ft
144 sq ft
24 ft
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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
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Break the pool into a deep end and a shallow end.
deepwater
8 yds
8 yds
shallow water
10 yds
5 yds
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Find the area of the deep end.
deepwater
8 yds
8 yds
shallow water
10 yds
5 yds
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Find the area of the deep end.
8 x 5 40
8 yds
8 yds
shallow water
10 yds
5 yds
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Find the area of the shallow end.
8 x 5 40
8 yds
8 yds
shallow water
10 yds
5 yds
50
Find the area of the shallow end.
8 x 5 40
8 yds
8 yds
8 x 10 80
10 yds
5 yds
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Now sum the two areas together.
8 x 5 40
8 yds
8 yds
8 x 10 80
10 yds
5 yds
52
Now sum the two areas together.
80
40

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

(9 x 5)
(9 x 20)
5 yds
20 yds
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(9 x 5) (9 x 20) area
9 yds
(9 x 5)
(9 x 20)
5 yds
20 yds
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Practice Time
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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)
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1) Which of the following expressions shows the
distributive property for 5 x (3 7)?
Correct!
(5 x 3) (5 x 7)
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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)
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2) Which of the following expressions shows the
distributive property for 3 x (9 4) ?
(3 x 9) (3 x 4)
Correct!
65
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)
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3) Which of the following expressions is
equivalent to2 3 2 3 and uses the
distributive property.
2 x (2 3)
Correct!
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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)
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4) Which of the following expressions is
equivalent to(4 x 3) (4 x 8) ?
Correct!
4 x (3 8)
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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)
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5) Which of the following expressions is
equivalent to(5 x 9) (5 x 3) ?
5 x (9 3)
Correct!
71
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
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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
73
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
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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
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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
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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
77
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
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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
79
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
80
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
81
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
82
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
83
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
84
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
85
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
86
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
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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
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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
89
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
90
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
91
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
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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
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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
94
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
95
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
96
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
97
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
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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
99
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
100
11) Which expression is equivalent to 3(x 7)?
x 10
x 21
3x 7
3x 21
101
11) Which expression is equivalent to 3(x 7)?
Correct!
3x 21
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12) Which expression is equivalent to 4(x 5)?
x 9
4x 20
4x 5
9x
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12) Which expression is equivalent to 4(x 5)?
4x 20
Correct!
104
13) Which expression is equivalent to 8(x 2)?
10x
8x 2
8x 16
8x 10
105
13) Which expression is equivalent to 8(x 2)?
8x 16
Correct!
106
14) Which expression is equivalent to 2(x 3)?
2x 6
2x 5
2x 3
2x 2
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14) Which expression is equivalent to 2(x 3)?
2x 6
Correct!
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The End.
109
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.
110
Sorry!

• Try again.