Solved Examples and Worksheet for Dividing Region into Equal Parts using Models

Q1Ursula cut an apple into 2 equal parts and ate 1 of them. What fraction of the apple did she eat?

A. 23
B. 13
C. 12
D. 25

Solutions
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Step: 1
Number of parts the apple was cut into = 2.
Step: 2
Number of parts Ursula ate = 1.
Step: 3
Fraction of apple Ursula ate = Number of parts she ateTotal number of parts
= 12
Step: 4
Ursula ate 12of the whole apple.
Correct Answer is :   12
Q2What is the area of the each square formed a square is cut into 4 equal parts shown below?

A. one-third the area of the whole
B. one-fourth the area of the whole
C. equal to the area of the whole
D. one-half the area of the whole

Solutions
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Step: 1
When a square is cut into four equal parts, 4 squares are formed and area of each square is equal to one- fourth the area of the whole.
Correct Answer is :   one-fourth the area of the whole
Q3What is the area of the each triangle formed a hexagon is cut into 6 equal parts shown below.


A. one-fourth the area of the whole
B. one-third the area of the whole
C. one-sixth the area of the whole
D. equal to the area of the whole

Solutions
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Step: 1
When a hexagon is cut into six equal parts, 6 triangles are formed and area of each triangle is equal to one- sixth the area of the whole.
Correct Answer is :   one-sixth the area of the whole
Q4What is the area of the each triangle formed when a circle is cut into 4 equal parts?

A. one-third the area of the circle
B. one-fourth the area of the circle
C. equal to the area of the circle
D. one-half the area of the circle

Solutions
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Step: 1
When a circle is cut into four equal parts, 4 triangles are formed and area of each triangle is equal to one- fourth the area of the circle.
Correct Answer is :   one-fourth the area of the circle
Q5What is the area of the each rectangle formed a rectangle is cut into 6 equal parts shown below?


A. one-sixth the area of the whole
B. one-half the area of the whole
C. equal to the area of the whole
D. one-third the area of the whole

Solutions
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Step: 1
When a rectangle is cut into six equal parts, 6 rectangles are formed.
Step: 2
The area of each small rectangle is one-sixth the area of the whole.
Step: 3
Here, one small rectangle is shaded.
Step: 4
So, area of the small shaded rectangle is one- sixth the area of the whole.
Correct Answer is :   one-sixth the area of the whole
Q6What is the area of the each triangle formed a square is cut into 8 equal parts shown below?


A. one-sixth the area of the square
B. one-fourth the area of the square
C. equal to the area of the square
D. one-eighth the area of the square

Solutions
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Step: 1
When a square is cut into eight equal parts, 8 triangles are formed and area of each triangle is equal to one- eighth the area of the square.
Correct Answer is :   one-eighth the area of the square
Q7Which of the following figures shows "the area of the each rectangle is one-twelfth the area of the whole"?


A. Figure 2
B. Figure 4
C. Figure 1
D. Figure 3

Solutions
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Step: 1
Figure 2 is divided into 8 equal parts. So, it shows that "the area of each rectangle is one-eighth the area of the whole".
Step: 2
: Figure 3 is divided into 4 equal parts. So, it shows that "the area of each rectangle is one-fourth the area of the whole".
Step: 3
Figure 4 is divided into 9 equal parts. So, it shows that "the area of each rectangle is one-nineth the area of the whole".
Step: 4
Figure 1 is divided into 12 equal parts. So, it shows that "the area of each rectangle is one-twelfth the area of the whole".
Step: 5
So, Figure 1 is the right answer.
Correct Answer is :   Figure 1
Q8How much area of the circle is shaded?


A. one-eighth the area of the circle
B. one-half the area of the circle
C. one-fourth the area of the circle
D. equal to the area of the circle

Solutions
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Step: 1
The given circle is divided into 8 equal parts and 1 part is shaded.
Step: 2
Here, the area of each part of the circle is one-eighth the area of the circle.
Step: 3
So, the area of the shaded part of the given circle is one-eighth the area of the circle.
Correct Answer is :   one-eighth the area of the circle
Q9How much area of the circle is unshaded?


A. equal to the area of the circle
B. one-eighth the area of the circle
C. one-fourth the area of the circle
D. one-half the area of the circle

Solutions
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Step: 1
The given circle is divided into 2 equal parts and 1 part is shaded.
Step: 2
Here, the area of each part of the circle is one-half the area of the circle.
Step: 3
So, the area of the un shaded part of the given circle is one-half the area of the circle.
Correct Answer is :   one-half the area of the circle
Q10What is the area of the shaded part of the given square?


A. equal to the area of the whole
B. one-sixteenth the area of the whole
C. one-eighteenth the area of the whole
D. one-twelfth the area of the whole

Solutions
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Step: 1
The given square is divided into 16 equal parts and 1 part is shaded.
Step: 2
Here, the area of each part of the square is one-sixteenth the area of the whole.
Step: 3
So, the area of the shaded part of the given square is one-sixteenth the area of the whole.
Correct Answer is :   one-twelfth the area of the whole

HighSchool Math