6th Grade Math Textbook, Progress

Make a Venn diagram and list the facts.

Let A represent black bowling balls.

Let B represent speckled bowling balls.

Let C represent black speckled bowling balls.

To find the number of bowling balls that are

both black and speckled (C), subtract 27 from

the sum of 12 and 24. (12 
24)  27 C

Then write a fraction to show the number of

black speckled bowling balls out of all the balls.



2

C

7



number of black speckled

total number of bowling balls

Add the number of bowling balls in each region:

A 
B 
C 27 A 
C 12 C 
B 24

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Visualize yourself in the problem above as

you reread it. List the facts and the question.

Facts: 27 bowling balls

12 are black

24 are speckled

Question:What fractional part of the bowling balls

are both black and speckled?

Problem-Solving Strategy:

Use a Diagram

8-17

(12 
24)  27 C

36  27  9

One third of the bowling balls are both

black and speckled.

There are 27 bowling balls for rent that are black, speckled,

or both. If 12 are black and 24 are speckled, what fractional

part of the bowling balls are both black and speckled?

A C B

12 Black 24 Speckled

27 C ?



2

9

7

^1

3



Think

3 
 15 
 9 27 3 
 9 12 9 
 15 24

27  27 12  12 24  24

Your answer checks.

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12

• 9
  3

24

• 9
  15

9

Black

12

Speckled

24

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