Parts and Whole Test 12

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Parts and Whole Test 12

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Weekly Quiz Competition

Question 1
1 / -0

How many more unit squares in the figure must be shaded so that the fraction of shaded squares is $$\displaystyle\frac{7}{9}$$?

A
$$1$$

B
$$3$$

C
$$6$$

D
$$8$$

Solution

Total number of unit square is $$18$$
$$\Rightarrow$$ Let total number of shaded squares be $$x$$.
$$\Rightarrow$$ Fraction of shaded squares is $$\dfrac{7}{9}$$
$$\rightarrow$$ According to the question,
$$\Rightarrow$$ $$\dfrac{7}{9}=\dfrac{x}{18}$$

$$\Rightarrow$$ $$x=\dfrac{7}{9}\times {18}$$

$$\Rightarrow$$ $$x=14$$
$$\Rightarrow$$ Out of these $$14$$ squares $$6$$ are shaded.
$$\therefore$$ We have to shade $$8$$ more squares.
Question 2
1 / -0

What fraction of the figure is shaded?

A
$$\displaystyle\frac{4}{9}$$

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

C
$$\displaystyle\frac{5}{9}$$

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

Solution

If we rearrange the figure then we can conclude that out of $$9$$ squares, $$4.5$$ squares are shaded
So the fraction of figure which is shaded is $$\dfrac{4.5}{9}=\dfrac{1}{2}$$
Question 3
1 / -0

What fraction of the given circles is crossed?

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

B
$$\dfrac{4}{8}$$

C
$$\dfrac{5}{8}$$

D
$$\dfrac{7}{8}$$

Solution

Total number of circle = 8
Number of crossed circles = 5
$$\therefore$$Required fraction = $$\dfrac{5}{8}$$
Question 4
1 / -0

Which of the following options is CORRECT for the fraction of shaded parts in figures $$I$$ and $$II$$?

A
$$I > II$$

B
$$II > I$$

C
$$I = II$$

D
Can't be determined

Solution

Number of equal parts in Figure $$I = 24$$
Number of shaded parts in Figure $$I = 20$$
$$\therefore$$ Required shaded fraction for figure $$I = \dfrac {20}{24} = \dfrac {5}{6}$$
Number of equal parts in figure $$II = 40$$
Number of shaded parts in figure $$II = 32$$
$$\therefore$$ Required shaded fraction for figure $$II = \dfrac {32}{40} = \dfrac {4}{5}$$
Now, $$\dfrac {5}{6} = \dfrac {5\times 5}{6\times 5} = \dfrac {25}{30}$$

and $$\dfrac {4}{5} = \dfrac {4\times 6}{5\times 6} = \dfrac {24}{30}$$

$$\because \dfrac {25}{30} > \dfrac {24}{30}$$

$$\therefore I > II$$.
Question 5
1 / -0

Monthly salary of a person is $$ Rs.15000 $$. The central angle of the sector representing his expenses on food and house rent on a pie chart is $$ 60^o $$. The amount he spend on food and house rent is

A
$$ 5000 $$

B
$$ 2500 $$

C
$$ 6000 $$

D
$$ 9000 $$

Solution

As, total salary= $$ 15000 $$, expenses on food and house rent= $$ 60^o $$
Food and housing expenses from monthly salary= $$ \dfrac{Central\quad angle\quad of\quad the \quad part\quad of \quad pie \quad chart}{ Central\quad angle\quad of \quad the \quad pie \quad chart} $$
Given that,
Part of salary spent on food and house rent= $$ \dfrac{60^o}{360^o}= \dfrac{1}{6}$$
Salary spent in amount on food and housing= $$ \dfrac{1}{6}\times 15000 $$
$$ \therefore 2500 $$ Rs is total amount spent on food and house rent.
Question 6
1 / -0

In the given figure, the shaded region is represented by the fraction:

A
$$\dfrac{4}{12}$$

B
$$\dfrac{5}{12}$$

C
$$\dfrac{5}{24}$$

D
$$\dfrac{4}{24}$$

Solution

Here the shaded triangles represent half of the area of the square.
Therefore, the number of shaded squares are $$=1+0.5+0.5+0.5=2.5$$
The total number of squares are $$=12$$
So, the shaded fraction $$=\dfrac{2.5}{12}=\dfrac{2.5\times2}{12\times2}=\dfrac{5}{24}$$
Question 7
1 / -0

What part of the circle is coloured?

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

B
$$\dfrac{1}{8}$$

C
$$\dfrac{4}{8}$$

D
$$\dfrac{2}{8}$$

Solution

There is 8 parts in circle and 1 part is coloured.
So, total parts=8 (=Denominator)
coloured parts=1 (=numerator)
so, $$fraction=1/8$$
Question 8
1 / -0

Represent the answer in fraction

A
$$\dfrac{2}{4}$$

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

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

D
Both A and C
Question 9
1 / -0

What part of the rectangle is blue and what part is grey?

A
Blue part $$\dfrac{1}{16}$$ Grey part $$\dfrac{3}{16}$$

B
Blue part $$\dfrac{1}{8}$$ Grey part $$\dfrac{4}{32}$$

C
Blue part $$\dfrac{1}{4}$$ Grey part $$\dfrac{3}{4}$$

D
Blue part $$\dfrac{4}{32} $$ Grey part $$\dfrac{3}{32}$$

Solution
Question 10
1 / -0

What part of the circle is coloured?

A
$$\dfrac{2}{8}$$

B
$$\dfrac{1}{8}$$

C
$$\dfrac{3}{8}$$

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

Solution

There is 8 parts in circle and 3 part is coloured.
So, total parts=8 (=Denominator)
coloured parts=3 (=numerator)
so, $$fraction=3/8$$