6th Grade Math Textbook, Fundamentals

Lesson 8-9 for exercise sets. &KDSWHU 

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Draw a Venn diagram to illustrate the following.

1.Al’s class has 18 stamp collectors, 14 coin collectors, and 12 CD collectors.

One student collects all three, 7 collect stamps and coins but not CDs, 5 collect

coins and CDs but not stamps, and 5 collect stamps and CDs but not coins.

How many students in Al’s class collect only coins? Only stamps? Only CDs?

2.Show the factors of 9, 16, and 24, including their common factors.

3.Discuss and Write In Example 1 above, which numbers that are given

in the problem do not appear in the Venn diagram? Explain.

There are 96 students at Kennedy Middle School

who play instruments. Of these, 23 students in all

play the trumpet; 20 students in all play the clarinet;

and 18 students in all play the guitar. Of the students

who play one or more of these three instruments,

4 students play the trumpet and the guitar but not

the clarinet; 2 students play the clarinet and the

trumpet but not the guitar; and 3 students play the

guitar and the clarinet but not the trumpet. Only

1 student plays all three instruments. How many

students play onlythe trumpet? How many play only

the guitar? How many play onlythe clarinet?

To answer these questions, use a Venn diagram.

Draw and label three overlapping circles, one for each data set.

Add to find the number of trumpet players who also play

one or more other instruments: 4  1  2 7 students.

Since the total number of trumpet players is 23, subtract 7

from 23 to find that there are 16 students who play only the

trumpet. Follow this procedure for each instrument.

So 16 students play only the trumpet, 10 students play only the

guitar, and 14 students play only the clarinet.

Trumpet

Clarinet

Guitar













1

Trumpet only:

23 (4  1 2)

 23  7

 16

Guitar only:

18 (4  1 3)

 18  8

 10

Clarinet only:

20 (2  1 3)

 20  6

 14