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Venn Diagrams

Venn Diagrams. A how-to guide by Ms. Walton. Where do we see them?. Venn Diagram Example:. Twenty-four members of Mu Alpha Theta went to a Mathematics conference. One-third of the members ran cross country. One sixth of the members were on the football team .

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Venn Diagrams

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  1. Venn Diagrams A how-to guide by Ms. Walton

  2. Where do we see them?

  3. Venn Diagram Example: Twenty-four members of Mu Alpha Theta went to a Mathematics conference. One-third of the members ran cross country. One sixth of the members were on the football team . Three members were on both cross country and football teams. The rest of the members were in the band. How many were in the band? Hint: Draw a Venn Diagram and take one sentence at a time...

  4. Solution: Twenty-four members of Mu Alpha Theta went to a Mathematics conference. • Three members were on cross country and football teams… CC Football 3 1 5 The above sentence tells you two draw overlapping circles and put 3 in CCF • One-third of the members ran cross country. 24 / 3 = 8; 8 members run cross country. So put 5 in cross country as there are already 3 in cross country. • One sixth of the members were on the football team . 24/6 = 4; 4 members play football. So put 1 in football as there are already 3 in football. Continued….

  5. Example: Continued…… • The rest of the members were in the band. How many were in the band? • Out of 24 members in Mu Alpha Theta, 9 play football or run cross country. • Therefore, 15 are in the band. CC Football Band 3 5 1 15 Mu Alpha Theta

  6. Example #2 • Write a sentence to describe this Venn Diagram Cashews Almonds

  7. Ex #2 answer: • “No cashews are almonds.” • This situation is called mutual exclusivity (the groups have nothing in common!)

  8. Example #3 • In a class of 50 students, 18 take Chorus, 26 take Band, and 2 take both Chorus and Band. • How many students in the class are not enrolled in either Chorus or Band?

  9. #3 solution 50 total chorus band 16 2 24

  10. Example #4 • A veterinarian surveys 26 of his patrons. • He discovers that 14 have dogs, 10 have cats, and 5 have fish. • Four have dogs and cats, 3 have dogs and fish, and one has a cat and fish. • If no one has all three kinds of pets, how many patrons have none of these pets?

  11. #4 solution—how many not accounted for? Cats Dogs 7 4 5 1 3 Fish 1 26-7-4-5-1-1-3= 5

  12. You try #1 • A guidance counselor is planning schedules for 30 students. • Sixteen students say they want to take French, 16 want to take Spanish, and 11want to take Latin. • Five say they want to take both French and Latin, and of these, 3 wanted to take Spanish as well. • Five want only Latin, and 8 want only Spanish. How many students want French only?

  13. You try #2 • In a school of 320 students, 85 students are in the band, 200 students are on sports teams, and 60 students participate in both activities. How many students are involved in either band or sports?

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