Distributive Property: Advanced Problems

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Distributive PropertyAdvanced Problems

• It may be necessary to review the basic
  distributive property problems in the number
  property introduction PowerPoint presentation

2

• Recall the distributive property of
  multiplication over addition . . .
• symbolically
• a (b c) a b a c
• and pictorially (rectangular array area model)

b
c
a b
a c
a
3

• 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
4
Find the area of the rectangle.Area length x
width
6 ft
24 ft
5
Find the area of the rectangle.Area length x
width
6 ft
20 ft 4 ft
6
Find the area of the rectangle.Area length x
width
6 ft
20 ft 4 ft
7
Find the area of the rectangle.Area length x
width
6 ft
6 ft
20 ft 4 ft
8
Find the area of the rectangle.Area length x
width
Find the area of each rectangle.
6 ft
6 ft
20 ft 4 ft
9
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
10
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
11
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
12
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
13
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
14
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
15
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
16
Find the area of the rectangle.Area length x
width
Now put the two rectangles back together.
6 ft
144 sq ft
24 ft
17
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
18
Break the pool into a deep end and a shallow end.
deepwater
8 yds
8 yds
shallow water
10 yds
5 yds
19
Find the area of the deep end.
deepwater
8 yds
8 yds
shallow water
10 yds
5 yds
20
Find the area of the deep end.
8 x 5 40
8 yds
8 yds
shallow water
10 yds
5 yds
21
Find the area of the shallow end.
8 x 5 40
8 yds
8 yds
shallow water
10 yds
5 yds
22
Find the area of the shallow end.
8 x 5 40
8 yds
8 yds
8 x 10 80
10 yds
5 yds
23
Now sum the two areas together.
8 x 5 40
8 yds
8 yds
8 x 10 80
10 yds
5 yds
24
Now sum the two areas together.
80
40

8 yds
10 yds
5 yds
25
40 80 120 square yards
40
80
8 yds
5 yds
10 yds
26
Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
9 yds
5 yds
20 yds
27
Find the areas for each individual rectangle.
9 yds
5 yds
20 yds
28
Find the areas for each individual rectangle.
9 yds
(9 x 5)
5 yds
20 yds
29
Find the areas for each individual rectangle.
9 yds
(9 x 5)
(9 x 20)
5 yds
20 yds
30
Sum the two areas.
9 yds

(9 x 5)
(9 x 20)
5 yds
20 yds
31
(9 x 5) (9 x 20) area
9 yds
(9 x 5)
(9 x 20)
5 yds
20 yds
32
Practice Time
33
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)
34
1) Which of the following expressions shows the
distributive property for 5 x (3 7)?
Correct!
(5 x 3) (5 x 7)
35
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)
36
2) Which of the following expressions shows the
distributive property for 3 x (9 4) ?
(3 x 9) (3 x 4)
Correct!
37
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)
38
3) Which of the following expressions is
equivalent to2 3 2 3 and uses the
distributive property.
2 x (2 3)
Correct!
39
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)
40
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)
42
5) Which of the following expressions is
equivalent to(5 x 9) (5 x 3) ?
5 x (9 3)
Correct!
43
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
44
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
45
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
46
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
47
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
48
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
49
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
50
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
51
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
52
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
53
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
54
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
55
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
56
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
57
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
58
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
59
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
60
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
61
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
62
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
63
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
64
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
65
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
66
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
67
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
68
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
69
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
70
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
71
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
72
11) Which expression is equivalent to 3(x 7)?
x 10
x 21
3x 7
3x 21
73
11) Which expression is equivalent to 3(x 7)?
Correct!
3x 21
74
12) Which expression is equivalent to 4(x 5)?
x 9
4x 20
4x 5
9x
75
12) Which expression is equivalent to 4(x 5)?
4x 20
Correct!
76
13) Which expression is equivalent to 8(x 2)?
10x
8x 2
8x 16
8x 10
77
13) Which expression is equivalent to 8(x 2)?
8x 16
Correct!
78
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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81
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