Parts and Whole Test 5

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Parts and Whole Test 5

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following is true for the shaded parts of models shown?
P: Shaded part of model 1, Q:shaded part of model 2

A
$$P=Q$$

B
$$P< Q$$

C
$$P\le Q$$

D
$$P> Q$$

Solution

Shaded part of model $$1$$ has $$4.5$$ black shaded square and model $$2$$ has $$3$$ black shaded square.
So, $$ P>Q $$
Option D is correct.
Question 2
1 / -0

In which figure does the shaded portion represent the fraction $$\dfrac{1}{2}$$?

A

B

C

D

Solution

For op-(A)
Total number of equal parts$$=4$$
Number of shaded parts $$= 2$$
Fraction of shaded portion $$=\dfrac{2}{4}=\dfrac{1}{2}$$

For op-(B)
Total number of equal parts$$=3$$
Number of shaded parts $$= 2$$
Fraction of shaded portion $$=\dfrac{2}{3}$$

For op-(C)
Total number of equal parts$$=4$$
Number of shaded parts $$= 3$$
Fraction of shaded portion $$=\dfrac{3}{4}$$

For op-(D)
Total number of equal parts$$=6$$
Number of shaded parts $$= 4$$
Fraction of shaded portion $$=\dfrac{4}{6}=\dfrac{2}{3}$$

Hence, $$Op-A$$ is correct.
Question 3
1 / -0

Find the value of $$P, Q, R$$ and $$S$$ respectively.

A
$$1\dfrac {2}{5}, 1.4, 2\dfrac {1}{2}, 2.5$$

B
$$1\dfrac {3}{5}, 1.6, 2\dfrac {1}{2}, 2.5$$

C
$$1\dfrac {2}{5}, 1.4, 3\dfrac {1}{2}, 2.5$$

D
$$1\dfrac {3}{5}, 1.6, 3\dfrac {1}{2}, 3.5$$

Solution

Shaded fraction of first figure is $$P = 1 + \dfrac {6}{10}$$

$$ = \dfrac {16}{10} = \dfrac {8}{5}$$

$$ = 1\dfrac {3}{5}$$

In decimal form, $$Q = 1.6$$

Shaded fraction of second figure $$R = 1 + 1 + 1 + \dfrac {5}{10}$$

$$= 3 + \dfrac {1}{2} = \dfrac {7}{2}$$

$$ = 3\dfrac {1}{2}$$

In decimal form, $$S = 3.5$$.
Question 4
1 / -0

What is the sum of the shaded parts if shaded parts are expressed in fractions?

A
$$1\cfrac { 2 }{ 9 } $$

B
$$1\cfrac { 1 }{ 9 } $$

C
$$1\cfrac { 3 }{ 9 } $$

D
$$1\cfrac { 5 }{ 9 } $$

Solution

Total parts in each square $$=9$$
Shaded parts in first $$=5$$

Fraction of shaded part $$=\dfrac{5}{9}$$

Shaded part in second $$=6$$

Fraction of shaded part $$=\dfrac{6}{9}$$

Total shaded part $$=\dfrac{5}{9}+\dfrac{6}{9}=1\dfrac{2}{9}$$
Question 5
1 / -0

In which figure does the shaded part represents $$\cfrac { 1 }{ 3 } $$?

A

B

C

D

Solution

In option $$B$$
Total numbers of parts in which circle is divided $$=3$$
Shaded part $$=1$$
So fraction of shaded part $$=\dfrac{1}{3}$$
So, option B is correct.
Question 6
1 / -0

Anushka drew the following figure on a piece of paper. What fraction of the figure is unshaded?

A
$$\dfrac {1}{3}$$

B
$$\dfrac {3}{10}$$

C
$$\dfrac {3}{5}$$

D
$$\dfrac {2}{3}$$

Solution

Total number of equal parts $$= 27$$
Number of unshaded parts $$= 18$$
$$\therefore$$ Required fraction $$= \dfrac {18}{27} = \dfrac {2}{3}$$.
Question 7
1 / -0

What fraction of the figure is shaded?

A
$$\dfrac {3}{8}$$

B
$$\dfrac {5}{6}$$

C
$$\dfrac {5}{9}$$

D
$$\dfrac {4}{11}$$

Solution

Let us assume side of larger Square $$=4$$ units
It is divided into $$16$$ small squares of side $$1$$ unit each
Base of shaded Triangle $$=\sqrt{2}$$ units $$=$$ diagonal of square of $$1$$ unit side
Height of shaded Triangle $$=\sqrt{2}+\dfrac{\sqrt{2}}{2}$$ units
Area of 4 shaded triangles $$=4 \times \dfrac{1}{2}\times \sqrt{2}\times (\sqrt{2}+\dfrac{\sqrt{2}}{2}) = 6$$ $$\text{unit}^{2}$$
Area of Larger Square $$=$$ Total Area
Total Area $$= 4^{2} = 16$$ $$\text{unit}^{2}$$
Fraction of the figure is shaded $$= \dfrac{6}{16}$$ $$= \dfrac{3}{8}$$.
Question 8
1 / -0

Which of the following is true for the shaded parts of models shown?
P: Shaded part of model -1
Q: Shaded part of model -2

A
P =Q

B
P<Q

C
P>Q

D
None of these

Solution

For model-1,
Total number of equal parts =12
Number of shaded parts =9
Therefore shaded fraction =P=$$\dfrac{9}{12}$$=$$\dfrac{3}{4}$$
For model-2,
Total number of equal parts =6
Number of shaded parts = 3
Shaded fraction = Q= $$\dfrac{3}{6}$$=$$\dfrac{1\times 2}{2\times2}$$=$$\dfrac{2}{4}$$
Now, $$\dfrac{3}{4}$$>$$\dfrac{2}{4}$$
P>Q
Question 9
1 / -0

In the multiplication of $$\dfrac{2}{3}$$ with $$4$$, the numerator will be :

A
$$2$$

B
$$8$$

C
$$4$$

D
$$12$$

Solution

Given multiplication of $$\dfrac{2}{3}$$ with $$4$$
$$\dfrac{2}{3}\times 4=\dfrac{2\times4}{3}=\dfrac{8}{3}$$
The numerator of the fraction is $$8$$
Question 10
1 / -0

What fraction of the figure is shaded?

A
$$\dfrac{7}{8}$$

B
$$\dfrac{5}{8}$$

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

D
$$\dfrac{3}{4}$$

Solution

Total number of equal triangles = $$8$$
There are $$2$$ smallest parts, $$2$$ medium parts and $$2$$ largest parts left unshaded. So combining them we will get $$2$$ unshaded triangles.
Number of shaded triangles = $$6$$
$$\therefore$$ Shaded fraction = $$\dfrac{6}{8}$$ = $$\dfrac{3}{4}$$