Transcript Venn Diagrams - Barry University

Katelyn Donovan
MAT 202
Dr. Carol Marinas
January 23, 2006
Sunday Night Television Shows
The Problem
In a Math Class with 27 students, 20 watch
Desperate Housewives, 9 watch both Desperate
Housewives and Grey’s Anatomy, and 3 watch
neither Desperate Housewives nor Grey’s
Anatomy. How many students watch Grey’s
Anatomy only?
Drawing the Venn Diagram
1. Draw one circle to represent
the number of students who
watch Desperate
Housewives.
2. Draw another circle to
represent the number of
students who watch Grey’s
Anatomy.
3. The intersection of the two
circles represents the number
of students who watch both
Desperate Housewives and
Grey’s Anatomy.
4. Label the circles accordingly.
U
Desperate
Housewives
Grey’s Anatomy
Plan of Attack
1. Fill in any given
numbers into its correct
place (see chart on
right)
2. Find the missing values
arithmetically.
3. Fill in the missing
values.
4. Check: when all values
are added, the sum
should equal the total
number of students.
U
Number of
students
who watch
DH
# of
students
who
watch
both DH
and GA
Number of
students
who watch
GA
Desperate
Housewives
Number of
students
who watch
neither DH
nor GA
Grey’s Anatomy
Key
D H = Desperate Housewives
G A = Grey’s Anatomy
What Do We Know?
In a Math Class with 27
students, 20 students
watch Desperate
Housewives,
9 students watch both
Desperate Housewives
and Grey’s Anatomy, and 3
students watch neither
Desperate Housewives nor
Grey’s Anatomy.
U
3
9
Desperate
Housewives
Grey’s Anatomy
What Do We Need to Know?
1. How many students
watch Desperate
Housewives only?
2. How many students
watch Grey’s
Anatomy only?
U
3
?
Desperate
Housewives
9
?
Grey’s Anatomy
Finding the Missing Values 1
1. We know there are 20 students
who watch Desperate
Housewives. There are 9 that
watch both DH and GA.
2. To find how many students watch
DH only, subtract the number who
watch both DH and GA (9) from
the total number who watch DH
(20).
3. 20 – 9 = 11
4. 11 is the number of students who
watch DH only.
5. Fill values into Venn Diagram.
U
3
11
Desperate
Housewives
9
Grey’s Anatomy
Finding the Missing Values 2
1. We are missing the number of students who watch
Grey’s Anatomy only.
2. To find this number, sum the number of students who
watch DH (11), the number who watch both DH and GA
(9), and the number who watch neither DH nor GA (3).
3. 11 + 9 + 3 = 23
4. Subtract the sum from the total number of students (27)
to get the number of students who watch G A only.
5. 27 – 23 = 4
6. 4 Students watch G A only.
7. Fill in value to complete the Venn Diagram
Does Your Venn Diagram Look Like
Mine?
U
3
11
Desperate
Housewives
9
4
Grey’s Anatomy
Always Check Your Answer!
Does the sum of all values in the Venn Diagram equal the
total number of students (27)?
Let’s Check:
11 watch DH
+ 9 watch both DH and GA
+ 3 watch neither DH nor GA
+ 4 watch GA only
27 total students
It checks!!
Are We Done?
NO!!!!!!!!
We did not re-read the question and
answer it properly!
If you look back to the original problem, it
asks “How many students watch Grey’s
Anatomy only?”
The final answer is 4
Pay attention to what the problem is asking!