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

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• 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
Example 1-1a
Answer 52
5
Example 1-1b
Answer 30
6
Example 1-1c
7
Example 1-2a
Real Life Example Recreation North Country
Rivers of York, Maine, offers one-day white-water
rafting trips on the Kennebec River. The trip
costs 69 per person, and wet suits are 15
each. Write two equivalent expressions to find
the total cost of one trip for a family of four
if each person uses a wet suit.
Method 1 Find the cost for 1 person, then
multiply by 4.
8
Example 1-2a
Method 2 Find the cost of 4 trips and 4 wet
suits. Then add.
9
Example 1-2b
Evaluate either expression to find the total cost.
Answer The total cost is 336.
Check You can check your results by evaluating
4(84).
10
Example 1-2c
Movies The cost of a movie ticket is 7 and the
cost of a box of popcorn is 2. a. Write two
equivalent expressions to find the total cost
for a family of five to go to the movies if
each member of the family gets a box of
popcorn. b. Find the total cost.
Answer 45
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Example 1-3a
12
Example 1-3b
13
Example 1-3c
14
Example 1-4a
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Example 1-4b
16
Example 1-4c
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Real-Life Example 2Mental Math
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The distributive property is mental math strategy
that can be used when multiplying.
43 x 5 ?
19
Break apart the double-digit number.
43 x 5 ?
40 3

20
Then multiply each part by 5.
43 x 5 ?
40 3

x 5 x 5
21
Then multiply each part by 5.
43 x 5 ?
40 3

x 5 x 5
200 15
22
Finally, sum your two products
43 x 5 215
40 3

x 5 x 5
200 15

215
23
Lets look at another example.
53 x 6 ?
24
Break apart the double-digit number.
53 x 6 ?
25
Break apart the double-digit number.
53 x 6 ?
50 3

26
Multiply each part by 6.
53 x 6 ?
50 3

x 6 x 6
27
Multiply each part by 6.
53 x 6 ?
50 3

x 6 x 6
300 18
28
Sum the two products.
53 x 6 318
50 3

x 6 x 6
300 18 318
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The word distribute means to give out.
30
Distribute the cubes to the girls.
31
Distribute the cubes to the girls.
32
Distribute the cubes to the girls.
33
Distribute the cubes to the girls.
34
Distribute the cubes to the girls.
35
Distribute the cubes to the girls.
36
In this example, the 5 was distributed.
5 x 38 5 x (30 8) (5 x 30) (5 x 8)
37
In this example, the 7 was distributed.
7 x 46 7 x (40 6) (7 x 40) (7 x 6)
38
Find the area of the rectangle.Area length x
width
6 ft
24 ft
39
Find the area of the rectangle.Area length x
width
6 ft
24 ft
40
Find the area of the rectangle.Area length x
width
6 ft
20 ft 4 ft
41
Find the area of the rectangle.Area length x
width
6 ft
20 ft 4 ft
42
Find the area of the rectangle.Area length x
width
6 ft
6 ft
20 ft 4 ft
43
Find the area of the rectangle.Area length x
width
Find the area of each rectangle.
6 ft
6 ft
20 ft 4 ft
44
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
45
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
46
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
47
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
48
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
49
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
50
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
51
Find the area of the rectangle.Area length x
width
Now put the two rectangles back together.
6 ft
144 sq ft
24 ft
52
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
53
Break the pool into a deep end and a shallow end.
deepwater
8 yds
8 yds
shallow water
10 yds
5 yds
54
Find the area of the deep end.
deepwater
8 yds
8 yds
shallow water
10 yds
5 yds
55
Find the area of the deep end.
8 x 5 40
8 yds
8 yds
shallow water
10 yds
5 yds
56
Find the area of the shallow end.
8 x 5 40
8 yds
8 yds
shallow water
10 yds
5 yds
57
Find the area of the shallow end.
8 x 5 40
8 yds
8 yds
8 x 10 80
10 yds
5 yds
58
Now sum the two areas together.
8 x 5 40
8 yds
8 yds
8 x 10 80
10 yds
5 yds
59
Now sum the two areas together.
80
40

8 yds
10 yds
5 yds
60
40 80 120 square yards
40
80
8 yds
5 yds
10 yds
61
Write an expression that shows how to find the
area of the rectangle and uses the distributive
property.
9 yds
5 yds
20 yds
62
Find the areas for each individual rectangle.
9 yds
5 yds
20 yds
63
Find the areas for each individual rectangle.
9 yds
(9 x 5)
5 yds
20 yds
64
Find the areas for each individual rectangle.
9 yds
(9 x 5)
(9 x 20)
5 yds
20 yds
65
Sum the two areas.
9 yds

(9 x 5)
(9 x 20)
5 yds
20 yds
66
(9 x 5) (9 x 20) area
9 yds
(9 x 5)
(9 x 20)
5 yds
20 yds
67
Practice Time
68
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)
69
1) Which of the following expressions shows the
distributive property for 5 x (3 7)?
Correct!
(5 x 3) (5 x 7)
70
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)
71
2) Which of the following expressions shows the
distributive property for 3 x (9 4) ?
(3 x 9) (3 x 4)
Correct!
72
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)
73
3) Which of the following expressions is
equivalent to2 3 2 3 and uses the
distributive property.
2 x (2 3)
Correct!
74
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)
75
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)
77
5) Which of the following expressions is
equivalent to(5 x 9) (5 x 3) ?
5 x (9 3)
Correct!
78
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
79
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
80
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
81
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
82
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
83
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
84
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
85
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
86
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
87
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
88
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
89
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
90
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
91
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
92
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
93
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
94
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
95
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
96
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
97
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
98
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
99
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
100
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
101
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
102
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
103
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
104
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
105
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
106
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
107
11) Which expression is equivalent to 3(x 7)?
x 10
x 21
3x 7
3x 21
108
11) Which expression is equivalent to 3(x 7)?
Correct!
3x 21
109
12) Which expression is equivalent to 4(x 5)?
x 9
4x 20
4x 5
9x
110
12) Which expression is equivalent to 4(x 5)?
4x 20
Correct!
111
13) Which expression is equivalent to 8(x 2)?
10x
8x 2
8x 16
8x 10
112
13) Which expression is equivalent to 8(x 2)?
8x 16
Correct!
113
14) Which expression is equivalent to 2(x 3)?
2x 6
2x 5
2x 3
2x 2
114
14) Which expression is equivalent to 2(x 3)?
2x 6
Correct!
115
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