2. ➤ It is a way to organize information.
Why Use Venn Diagrams?
Adapted Thoughtful dog avatar by Schade is licensed by Public Domain.
3. ➤ It is a way to organize information.
➤ It shows the relationship between 2 or 3 sets of items.
Why Use Venn Diagrams?
Adapted Thoughtful dog avatar by Schade is licensed by Public Domain.
4. ➤ It is a way to organize information.
➤ It shows the relationship between 2 or 3 sets of items.
➤ It is easier to see similarities and differences between items.
Why Use Venn Diagrams?
Adapted Thoughtful dog avatar by Schade is licensed by Public Domain.
5. ➤ It’s a way to organize information.
➤ It shows the relationship between 2 or 3 sets of items.
➤ It is easier to see similarities and differences between items.
➤ It can be used to easily answer questions.
Why Use Venn Diagrams?
Adapted Thoughtful dog avatar by Schade is licensed by Public Domain.
6. The Problem
➤ A survey is conducted to find out who has visited
Spain, Canada, and/or Germany. 27% of people
visited Spain, 67% have been to Canada, and
36% to Germany. 13% of people have been to
Spain and Germany, 21% of people have been to
Canada and Germany, and 3% of people have
been to Spain and Canada but not Germany. 4%
of people have been to all 3 countries.
Spain by mireille is licensed by Public Domain.
Canada by tgm is licensed
by Public Domain.
Germany by GDJ is licensed by Public Domain.
9. Organize Known Information
➤ Visited all 3 countries
➤ 4% visited Spain, Germany and Canada
➤ Visited 2 Countries
10. Organize Known Information
➤ Visited all 3 countries
➤ 4% visited Spain, Germany and Canada
➤ Visited 2 Countries
➤ 13% visited Spain and Germany
11. Organize Known Information
➤ Visited all 3 countries
➤ 4% visited Spain, Germany and Canada
➤ Visited 2 Countries
➤ 13% visited Spain and Germany
➤ 21% visited Canada and Germany
12. Organize Known Information
➤ Visited all 3 countries
➤ 4% visited Spain, Germany and Canada
➤ Visited 2 Countries
➤ 13% visited Spain and Germany
➤ 21% visited Canada and Germany
➤ 3% visited Spain and Canada but not Germany
13. Organize Known Information
➤ Visited all 3 countries
➤ 4% visited Spain, Germany and Canada
➤ Visited 2 Countries
➤ 13% visited Spain and Germany
➤ 21% visited Canada and Germany
➤ 3% visited Spain and Canada but not Germany
➤ Visited each Country
14. Organize Known Information
➤ Visited all 3 countries
➤ 4% visited Spain, Germany and Canada
➤ Visited 2 Countries
➤ 13% visited Spain and Germany
➤ 21% visited Canada and Germany
➤ 3% visited Spain and Canada but not Germany
➤ Visited each Country
➤ 27% visited Spain
15. Organize Known Information
➤ Visited all 3 countries
➤ 4% visited Spain, Germany and Canada
➤ Visited 2 Countries
➤ 13% visited Spain and Germany
➤ 21% visited Canada and Germany
➤ 3% visited Spain and Canada but not Germany
➤ Visited each Country
➤ 27% visited Spain
➤ 67% visited Canada
16. Organize Known Information
➤ Visited all 3 countries
➤ 4% visited Spain, Germany and Canada
➤ Visited 2 Countries
➤ 13% visited Spain and Germany
➤ 21% visited Canada and Germany
➤ 3% visited Spain and Canada but not Germany
➤ Visited each Country
➤ 27% visited Spain
➤ 67% visited Canada
➤ 36% visited Germany
22. Place Known Information For All
➤ Start with the inner most piece, which is who
visited all 3 countries.
Spain
Canada
Germany
23. Place Known Information For All
➤ Start with the inner most piece, which is who
visited all 3 countries.
➤ From the known information, 4% visited all 3
countries.
Spain
Canada
Germany
24. Place Known Information For All
➤ Start with the inner most piece, which is who
visited all 3 countries.
➤ From the known information, 4% visited all 3
countries.
➤ Place 4% in the piece where all 3 circles
overlap.
Spain
Canada
Germany
4%
26. Place Known Information For 2 Pieces
➤ Use the known information about those visiting 2
countries. It doesn’t matter which is done first.
Spain
Canada
Germany
4%
27. Place Known Information For 2 Pieces
➤ Use the known information about those visiting 2
countries. It doesn’t matter which is done first.
➤ 13% visited Spain and Germany
Spain
Canada
Germany
4%
28. Place Known Information For 2 Pieces
➤ Use the known information about those visiting 2
countries. It doesn’t matter which is done first.
➤ 13% visited Spain and Germany
➤ This is those who visited both countries. Notice it
does not say if they visited Canada or not.
Because this information isn’t given, it is assumed
that some may have visited Canada as well.
Spain
Canada
Germany
4%
29. Place Known Information For 2 Pieces
➤ Use the known information about those visiting 2
countries. It doesn’t matter which is done first.
➤ 13% visited Spain and Germany,
➤ This is those who visited both countries. Notice it
does not say if they visited Canada or not.
Because this information isn’t given, it is assumed
that some may have visited Canada as well.
➤ Because 4% was already filled in to account for
those who visited Canada, this needs subtracted
from 13% to fill in the missing piece.
Spain
Canada
Germany
4%
30. Place Known Information For 2 Pieces (Con’t)
➤ Identify the overlap.
Spain
Canada
Germany
4%
31. Place Known Information For 2 Pieces (Con’t)
➤ Identify the overlap.
Spain
Canada
Germany
4%
32. Place Known Information For 2 Pieces (Con’t)
➤ Identify the overlap.
➤ Because 4% was already filled in to account for
those who visited Canada, this needs subtracted from
13% to fill in the missing piece.
Spain
Canada
Germany
4%
33. Place Known Information For 2 Pieces (Con’t)
➤ Identify the overlap.
➤ Because 4% was already filled in to account for
those who visited Canada, this needs subtracted from
13% to fill in the missing piece.
➤ Missing piece: 13% - 4%
Spain
Canada
Germany
4%
13%
- 4%
34. Place Known Information For 2 Pieces
➤ Identify the overlap.
➤ Because 4% was already filled in to account for
those who visited Canada, this needs subtracted from
13% to fill in the missing piece.
➤ Missing piece: 13% - 4%
➤ = 9%
Spain
Canada
Germany
4%
9%
35. Place Known Information For 2 Pieces (Con’t)
➤ 21% visited Canada and Germany
Spain
Canada
Germany
9%
4%
36. Place Known Information For 2 Pieces (Con’t)
➤ 21% visited Canada and Germany
➤ Identify the overlap.
Spain
Canada
Germany
9%
4%
37. Place Known Information For 2 Pieces (Con’t)
➤ 21% visited Canada and Germany
➤ Identify the overlap.
➤ Find the missing piece by subtracting 4% from
the total who visited both countries.
Spain
Canada
Germany
9%
4%
38. Place Known Information For 2 Pieces (Con’t)
➤ 21% visited Canada and Germany
➤ Identify the overlap.
➤ Find the missing piece by subtracting 4% from
the total who visited both countries.
➤ Missing piece: 21% - 4%
Spain
Canada
Germany
9%
4%
21%
- 4%
39. Place Known Information For 2 Pieces (Con’t)
➤ 21% visited Canada and Germany
➤ Identify the overlap.
➤ Find the missing piece by subtracting 4% from
the total who visited both countries.
➤ Missing piece: 21% - 4%
➤ = 17%
Spain
Canada
Germany
9%
4%
17%
40. Place Known Information For 2 Pieces (Con’t)
➤ 3% visited Spain and Canada but not Germany
Spain
Canada
Germany
17%9%
4%
41. Place Known Information For 2 Pieces (Con’t)
➤ 3% visited Spain and Canada but not Germany
➤ Because this amount has excluded the people who
visited Germany, it is just placed into the piece
where only Spain and Canada overlap.
Spain
Canada
Germany
17%9%
4%
42. Place Known Information For 2 Pieces (Con’t)
➤ 3% visited Spain and Canada but not Germany
➤ Because this amount has excluded the people who
visited Germany, it is just placed into the piece
where only Spain and Canada overlap.
Spain
Canada
Germany
4%
17%9%
3%
44. Place Known Information For Each Country
➤ The only pieces remaining are those who
visited only one country.
Spain
Canada
Germany
4%
17%
3%
9%
45. Place Known Information For Each Country
➤ The only pieces remaining are those who
visited only one country.
➤ The totals for each country are known.
Spain
Canada
Germany
4%
17%
3%
9%
46. Place Known Information For Each Country
➤ The only pieces remaining are those who
visited only one country.
➤ The totals for each country are known.
➤ To find the missing pieces, subtract the
pieces previously filled in from the total to
find those who visited only one country.
Spain
Canada
Germany
4%
17%
3%
9%
47. Place Known Information For Each Country
➤ The only pieces remaining are those who
visited only one country.
➤ The totals for each country are known.
➤ To find the missing pieces, subtract the
pieces previously filled in from the total to
find those who visited only one country.
➤ It doesn’t matter which you find first.
Spain
Canada
Germany
4%
17%
3%
9%
50. Place Known Information For Spain
➤ 27% visited Spain
➤ 4 pieces make up Spain
Spain
Canada
Germany
4%
17%
3%
9%
51. Place Known Information For Spain
➤ 27% visited Spain
➤ 4 pieces make up Spain
Spain
Canada
Germany
4%
17%
3%
9%
52. Place Known Information For Spain
➤ 27% visited Spain
➤ 4 pieces make up Spain
Spain
Canada
Germany
4%
17%9%
3%
53. Place Known Information For Spain
➤ 27% visited Spain
➤ 4 pieces make up Spain
Spain
Canada
Germany
4%
17%
3%
9%
54. Place Known Information For Spain
➤ 27% visited Spain
➤ 4 pieces make up Spain
Spain
Canada
Germany
17%
3%
9%
4%
55. Place Known Information For Spain
➤ 27% visited Spain
➤ 4 pieces make up Spain
➤ Subtract the known pieces from 27% to
find the missing piece.
Spain
Canada
Germany
17%
3%
9%
4%
56. Place Known Information For Spain
➤ 27% visited Spain
➤ 4 pieces make up Spain
➤ Subtract the known pieces from 27% to
find the missing piece.
➤ 27% - 3%
Spain
Canada
Germany
17%
3%
9%
4%
57. Place Known Information For Spain
➤ 27% visited Spain
➤ 4 pieces make up Spain
➤ Subtract the known pieces from 27% to
find the missing piece.
➤ 27% - 3% - 4%
Spain
Canada
Germany
17%
3%
9%
4%
58. Place Known Information For Spain
➤ 27% visited Spain
➤ 4 pieces make up Spain
➤ Subtract the known pieces from 27% to
find the missing piece.
➤ 27% - 3% - 4% - 9%
Spain
Canada
Germany
17%
3%
9%
4%
59. Place Known Information For Spain
➤ 27% visited Spain
➤ 4 pieces make up Spain
➤ Subtract the known pieces from 27% to
find the missing piece.
➤ 27% - 3% - 4% - 9%
➤ = 11%
Spain
Canada
Germany
17%
3%
9%
4%
11%
61. Place Known Information For Canada
➤ 67% visited Canada
Spain
Canada
Germany
11%
9%
3%
4%
17%
62. Place Known Information For Canada
➤ 67% visited Canada
➤ 4 pieces make up Canada
Spain
Canada
Germany
11%
9%
3%
4%
17%
63. Place Known Information For Canada
➤ 67% visited Canada
➤ 4 pieces make up Canada
Spain
Canada
Germany
11%
9%
3%
4%
17%
64. Place Known Information For Canada
➤ 67% visited Canada
➤ 4 pieces make up Canada
Spain
Canada
Germany
11%
9%
3%
4%
17%
65. Place Known Information For Canada
➤ 67% visited Canada
➤ 4 pieces make up Canada
Spain
Canada
Germany
11%
9%
3%
4%
17%
66. Place Known Information For Canada
➤ 67% visited Canada
➤ 4 pieces make up Canada
Spain
Canada
Germany
11%
9%
3%
4%
17%
67. Place Known Information For Canada
➤ 67% visited Canada
➤ 4 pieces make up Canada
➤ Subtract the known pieces from 67% to
find the missing piece.
Spain
Canada
Germany
11%
9%
3%
4%
17%
68. Place Known Information For Canada
➤ 67% visited Canada
➤ 4 pieces make up Canada
➤ Subtract the known pieces from 67% to
find the missing piece.
➤ 67% - 3%
Spain
Canada
Germany
11%
9%
3%
4%
17%
69. Place Known Information For Canada
➤ 67% visited Canada
➤ 4 pieces make up Canada
➤ Subtract the known pieces from 67% to
find the missing piece.
➤ 67% - 3% - 4%
Spain
Canada
Germany
11%
9%
3%
4%
17%
70. Place Known Information For Canada
➤ 67% visited Canada
➤ 4 pieces make up Canada
➤ Subtract the known pieces from 67% to
find the missing piece.
➤ 67% - 3% - 4% - 17%
Spain
Canada
Germany
11%
9%
3%
4%
17%
71. Place Known Information For Canada
➤ 67% visited Canada
➤ 4 pieces make up Canada
➤ Subtract the known pieces from 67% to
find the missing piece.
➤ 67% - 3% - 4% - 17%
➤ = 43%
Spain
Canada
Germany
11%
9%
3%
4%
17%
43%
73. Place Known Information For Germany
➤ 36% visited Germany
Spain
Canada
Germany
4%
17%
3%11% 43%
9%
74. Place Known Information For Germany
➤ 36% visited Germany
➤ 4 pieces make up Germany
Spain
Canada
Germany
4%
17%
3%11% 43%
9%
75. Place Known Information For Germany
➤ 36% visited Germany
➤ 4 pieces make up Germany
Spain
Canada
Germany
3%11% 43%
4%
17%9%
76. Place Known Information For Germany
➤ 36% visited Germany
➤ 4 pieces make up Germany
Spain
Canada
Germany
3%11% 43%
4%
17%9%
77. Place Known Information For Germany
➤ 36% visited Germany
➤ 4 pieces make up Germany
Spain
Canada
Germany
3%11% 43%
4%
17%9%
78. Place Known Information For Germany
➤ 36% visited Germany
➤ 4 pieces make up Germany
Spain
Canada
Germany
3%11%
4%
17%9%
43%
79. Place Known Information For Germany
➤ 36% visited Germany
➤ 4 pieces make up Germany
➤ Subtract the known pieces from 36%.
Spain
Canada
Germany
3%11%
4%
17%9%
43%
80. Place Known Information For Germany
➤ 36% visited Germany
➤ 4 pieces make up Germany
➤ Subtract the known pieces from 36%.
➤ 36% - 9%
Spain
Canada
Germany
3%11% 43%
4%
17%9%
81. Place Known Information For Germany
➤ 36% visited Germany
➤ 4 pieces make up Germany
➤ Subtract the known pieces from 36%.
➤ 36% - 9% - 4%
Spain
Canada
Germany
3%11% 43%
4%
17%9%
82. Place Known Information For Germany
➤ 36% visited Germany
➤ 4 pieces make up Germany
➤ Subtract the known pieces from 36%.
➤ 36% - 9% - 4% - 17%
Spain
Canada
Germany
3%11% 43%
4%
17%9%
83. Place Known Information For Germany
➤ 36% visited Germany
➤ 4 pieces make up Germany
➤ Subtract the known pieces from 36%.
➤ 36% - 9% - 4% - 17%
➤ = 6%
Spain
Canada
Germany
3%11% 43%
4%
17%9%
6%
84. None Of The Countries
➤ All the information is filled in for the 3 countries
but what about those who have not visited any
of the 3 countries?
Spain
Canada
Germany
4%
17%
3%11% 43%
6%
9%
85. None Of The Countries
➤ All the information is filled in for the 3 countries
but what about those who have not visited any
of the 3 countries?
➤ Because this is based on a percent, all those
surveyed must equal 100%. To find those who
did not visited any of these countries, subtract
all who did from 100%.
Spain
Canada
Germany
6%
4%
17%9%
3% 43%11%
86. None Of The Countries (Con’t)
➤ 100 -11%
Spain
Canada
Germany
6%
4%
17%9%
3% 43%11%
87. None Of The Countries (Con’t)
➤ 100 -11% -3%
Spain
Canada
Germany
6%
4%
17%9%
3% 43%11%
88. None Of The Countries (Con’t)
➤ 100 -11% -3% -43%
Spain
Canada
Germany
6%
4%
17%9%
3% 43%11%
89. None Of The Countries (Con’t)
➤ 100 -11% -3% -43% -9%
Spain
Canada
Germany
6%
4%
17%9%
3% 43%11%
90. None Of The Countries (Con’t)
➤ 100 -11% -3% -43% -9% -4%
Spain
Canada
Germany
6%
4%
17%9%
3% 43%11%
91. None Of The Countries (Con’t)
➤ 100 -11% -3% -43% -9% -4% -17%
Spain
Canada
Germany
6%
4%
17%9%
3% 43%11%
92. None Of The Countries (Con’t)
➤ 100 -11% -3% -43% -9% -4% -17% -6%
Spain
Canada
Germany
6%
4%
17%9%
3% 43%11%
93. None Of The Countries (Con’t)
➤ 100 -11% -3% -43% -9% -4% -17% -6%
➤ = 7%
Spain
Canada
Germany
4%
17%
3%11% 43%
6%
9%
None = 7%
94. None Of The Countries (Con’t)
➤ 100 -11% -3% -43% -9% -4% -17% -6%
➤ = 7%
➤ Thus, 7% of those surveyed visited none of
these countries.
Spain
Canada
Germany
4%
17%
3%11% 43%
6%
9%
None = 7%
96. Use Venn Diagram To Answer Questions
➤ What percent visited Canada and Germany
but not Spain?
Spain
Canada
Germany
4%
17%
3%11% 43%
6%
None = 7%
9%
97. Use Venn Diagram To Answer Questions
➤ What percent visited Canada and Germany
but not Spain?
➤ 17% visited only Canada and Germany
Spain
Canada
Germany
4%
3%11% 43%
6%
None = 7%
9% 17%
98. Use Venn Diagram To Answer Questions
➤ What percent visited Canada and Germany
but not Spain?
➤ 17% visited only Canada and Germany
➤ What percent visited only 2 countries?
Spain
Canada
Germany
4%
9% 17%
3%11% 43%
6%
None = 7%
99. Use Venn Diagram To Answer Questions
➤ What percent visited Canada and Germany
but not Spain?
➤ 17% visited only Canada and Germany
➤ What percent visited only 2 countries?
➤ 9%
Spain
Canada
Germany
4%
11% 43%
6%
None = 7%
17%9%
3%
100. Use Venn Diagram To Answer Questions
➤ What percent visited Canada and Germany
but not Spain?
➤ 17% visited only Canada and Germany
➤ What percent visited only 2 countries?
➤ 9% + 3%
Spain
Canada
Germany
4%
11% 43%
6%
None = 7%
17%9%
3%
101. Use Venn Diagram To Answer Questions
➤ What percent visited Canada and Germany
but not Spain?
➤ 17% visited only Canada and Germany
➤ What percent visited only 2 countries?
➤ 9% + 3% + 17%
Spain
Canada
Germany
4%
11% 43%
6%
None = 7%
17%9%
3%
102. Use Venn Diagram To Answer Questions
➤ What percent visited Canada and Germany
but not Spain?
➤ 17% visited only Canada and Germany
➤ What percent visited only 2 countries?
➤ 9% + 3% + 17%
➤ = 29% visited only 2 countries
Spain
Canada
Germany
4%
11% 43%
6%
None = 7%
17%9%
3%
103. Use Venn Diagram To Answer Questions (Con’t)
Suppose 500 people were surveyed.
Spain
Canada
Germany
4%
9% 17%
3%11% 43%
6%
None = 7%
104. Use Venn Diagram To Answer Questions (Con’t)
Suppose 500 people were surveyed.
➤ How many visited both Spain and Germany?
Spain
Canada
Germany
4%
9% 17%
3%11% 43%
6%
None = 7%
105. Use Venn Diagram To Answer Questions (Con’t)
Suppose 500 people were surveyed.
➤ How many visited both Spain and Germany?
➤ The Venn Diagram gives percents. Find
the percent who visited both.
Spain
Canada
Germany
17%
3%11% 43%
6%
None = 7%
4%
9%
106. Use Venn Diagram To Answer Questions (Con’t)
Suppose 500 people were surveyed.
➤ How many visited both Spain and Germany?
➤ The Venn Diagram gives percents. Find
the percent who visited both.
➤ 9% + 4% = 13%
Spain
Canada
Germany
4%
9% 17%
3%11% 43%
6%
None = 7%
107. Use Venn Diagram To Answer Questions (Con’t)
Suppose 500 people were surveyed.
➤ How many visited both Spain and Germany?
➤ The Venn Diagram gives percents. Find
the percent who visited both.
➤ 9% + 4% = 13%
➤ Use multiplication to find how many people
visited Spain and Germany
Spain
Canada
Germany
4%
9% 17%
3%11% 43%
6%
None = 7%
108. Use Venn Diagram To Answer Questions (Con’t)
Suppose 500 people were surveyed.
➤ How many visited both Spain and Germany?
➤ The Venn Diagram gives percents. Find
the percent who visited both.
➤ 9% + 4% = 13%
➤ Use multiplication to find how many people
visited Spain and Germany
➤ 500 * 13% = 500 * 0.13 =
Spain
Canada
Germany
4%
9% 17%
3%11% 43%
6%
None = 7%
109. Use Venn Diagram To Answer Questions (Con’t)
Suppose 500 people were surveyed.
➤ How many visited both Spain and Germany?
➤ The Venn Diagram gives percents. Find
the percent who visited both.
➤ 9% + 4% = 13%
➤ Use multiplication to find how many people
visited Spain and Germany
➤ 500 * 13% = 500 * 0.13 =
➤ 65 people visited Spain and Germany
Spain
Canada
Germany
4%
9% 17%
3%11% 43%
6%
None = 7%
110. Venn Diagram Recap
➤ Venn Diagrams are useful for organizing information.
➤ Always start at the inner most piece and work your way out to fill in the pieces.
➤ To answer questions, identify all pieces that fit the situation.
➤ Remember that addition, subtraction, and/or multiplication may be needed to answer questions.
Happy Venning!