Parts and Whole Test 1

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Parts and Whole Test 1

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Question 1
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Which of the following figure is divided into four equal parts ?

A

B

C

D

Solution

From the given images we can observe that figure in option $$D$$ is divided into $$4$$ equal parts.
Question 2
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Which model is shaded to show a fraction equivalent to $$\displaystyle{\frac{3}{6}}$$ ?

A

B

C

D

Solution

In the first image, there are $$4$$ parts and the ratio of the area of shaded part with the whole area is $$1:4$$

In second image, there are $$8$$ parts and the ratio of area of shaded part with compare to the whole area is $$3:8$$

Similarly, the third figure has the ratio of $$3:5$$

But in the fourth image, there are two parts, one shaded and another unshaded.
So, the ratio of the area of the shaded part with the whole area will be $$1:2$$ which is equivalent to $$3:6$$.
Hence, option D is correct.
Question 3
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What fraction of the children in the following group are girls?

A
$$\displaystyle \frac {3}{4}$$

B
$$\displaystyle \frac {4}{3}$$

C
$$\displaystyle \frac {3}{7}$$

D
$$\displaystyle \frac {4}{7}$$

Solution

In a group there are, total $$4$$ boys, $$3$$ girls
$$\therefore $$ total number of students $$= 7$$
Fraction of girls to total students $$=\displaystyle \frac { 3 }{ 7 } $$
Question 4
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The following diagram represents how many shaded parts?

A
$${\frac{3}{2}}$$

B
$${2\frac{1}{3}}$$

C
$${2\frac{1}{2}}$$

D
$${3\frac{1}{2}}$$

Solution

Out of three 2 are completely shaded and one is half shaded so total shahded area will be $$2+\frac{1}{2}$$
=$$2\frac{1}{2}$$
So correct answer is option C
Question 5
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Asha and Usha shared a pizza. Asha ate $$\displaystyle{\frac{1}{8}}$$ of the pizza and Usha ate $$\displaystyle{\frac{1}{2}}$$ of the pizza. Which picture shows how much pizza was left ?

A

B

C

D

Solution

The fractional part of the pizza left = $$1-(\displaystyle{\frac{1}{8}}+\dfrac{1}{2})$$
$$=1-(\cfrac{1}{8}+\dfrac{4}{8})$$
$$=1-\cfrac{5}{8}$$
$$=\cfrac{8}{8}-\dfrac{5}{8}$$
$$=\cfrac{3}{8}$$
$$\therefore$$ $$\dfrac{3}{8}$$ represents option $$A$$.
Question 6
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The shaded part ofthe following strip shows

A
$$\displaystyle \frac {2}{7}\, -\, \displaystyle \frac {1}{7}\, +\, \displaystyle \frac {2}{7}\, =\, \displaystyle \frac {3}{7}$$

B
$$\displaystyle \frac {2}{7}\, +\, \displaystyle \frac {1}{7}\, -\, \displaystyle \frac {2}{7}\, =\, \displaystyle \frac {1}{7}$$

C
$$\displaystyle \frac {2}{7}\, +\, \displaystyle \frac {1}{7}\, =\, \displaystyle \frac {3}{7}$$

D
$$\displaystyle \frac {2}{7}\, +\, \displaystyle \frac {1}{7}\, +\, \displaystyle \frac {2}{7}\, =\, \displaystyle \frac {5}{7}$$

Solution

Shaded part with checks is $$2$$ parts out of $$7$$ parts
Shaded part with oblique lines from top right to bottom left is $$2$$ parts out of $$7$$ parts
Shaded part with vertical lines is $$1$$ part out of $$7$$ parts
Hence, fraction of the shaded region to unshaded part is $$\displaystyle \frac { 2 }{ 7 } +\frac { 1 }{ 7 } +\frac { 2 }{ 7 } =\frac { 5 }{ 7 } $$
Question 7
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The following figure represents

A
$$1\dfrac {1}{4}$$

B
$$3\dfrac {1}{4}$$

C
$$1\dfrac {1}{2}$$

D
$$2\dfrac {1}{4}$$

Solution

Consider one large square to be $$1$$ unit.

Then from the figure, two squares are fully painted.

Third square is $$ \displaystyle \frac {1}{4}th$$ painted.

$$\therefore $$ The fraction that the squares are shaded is given by $$2\displaystyle \frac { 1 }{ 4 } $$
Question 8
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$$\displaystyle 1\dfrac{3}{4}$$ is a which type of fraction?

A
proper

B
improper

C
mixed

D
none

Solution

$$1\dfrac 34$$ is a mixed fraction.
Option C is correct.
Question 9
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In which of the following does the shaded part represent one third of its whole?

A

B

C

D

Solution

Ans-option D
in the figure of option D there are 3 square in which 1 square is shaded
Question 10
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In which figure does the shaded part represent $$\displaystyle{\frac{1}{3}}$$ ?

A

B

C

D

Solution

In the figure of option $$B$$ figure is divided in to $$3$$ equal parts in which one part is shaded . So this shaded part in option $$B$$ is $$\dfrac{1}{3}$$ of the whole shape. Hence option $$B$$ is answer.