Q: What fraction does the shaded part represent?

In the given object, there are a total of \$10\$ rectangles and \$3\$ rectangles are shaded amongst them. Therefore, the ratio of shaded rectangles to the total number of rectangles is:\$\dfrac {Shaded}{Total}=\dfrac {3 }{ 10 }\$Hence, the fraction of the shaded part is \$\dfrac { 3 }{ 10 }\$

Q: 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

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.

Q: What fraction of an hour is \$45 \$ minutes ?

An hour \$\left(1 hour\right) = 60\, minutes\$\$\therefore\$ Requird fraction \$= \dfrac{45}{60}=\dfrac{3}{4}\$

Q: What fraction of the figure is shaded?

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}\$

Q: Pictorial representation of \$3\times \displaystyle \frac{2}{3}\$ is?

We have given Pictorial representation of \$3\times \dfrac{2}{3}\$\$\Rightarrow\$ \$3\times \dfrac{2}{3}=\dfrac{2}{3}+\dfrac{2}{3}+\dfrac{2}{3}\$\$\therefore\$ Option \$B\$ is correct answer.

Q: Write the fraction representing the shaded portion.

The given figure represents \$3\$ shaded parts out of \$12\$ equal parts.Hence, \$\dfrac {9}{12}\$=\$\dfrac{3}{4}\$

Q: The following figure represents:

The given figure has \$3\$ large squares with \$4\$ parts in each square. In the first square, all \$\dfrac4 4\$ parts are colored. In the second square also all \$\dfrac4 4\$ parts are colored. In the third square, only \$\dfrac1 4\$ is colored.So we can say that the given figures are \$1+1+\dfrac 1 4= 2\$ whole \$\dfrac1 4\$Option D is the correct answer.

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

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 1

What fraction does the shaded part represent?

Accepted Answer

In the given object, there are a total of $10$ rectangles and $3$ rectangles are shaded amongst them. Therefore, the ratio of shaded rectangles to the total number of rectangles is:$\dfrac {Shaded}{Total}=\dfrac {3 }{ 10 }$Hence, the fraction of the shaded part is $\dfrac { 3 }{ 10 }$

Question 2

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

Accepted Answer

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 3

What fraction of an hour is $45 $ minutes ?

Accepted Answer

An hour $\left(1 hour\right) = 60\, minutes$$\therefore$ Requird fraction $= \dfrac{45}{60}=\dfrac{3}{4}$

Question 4

What fraction of the figure is shaded?

Accepted Answer

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 = $\dfrac{6}{8}$ = $\dfrac{3}{4}$

Question 5

Convert the following improper fraction into mixed fraction.$\displaystyle\frac{7}{3}$

Accepted Answer

Mixed fraction :- A mixed fraction is a number with a combination of an integer & a proper fraction.For example :- $\dfrac{7}{3}$$3)7(2$    $6$_______    $1$_______So the mixed fraction of $\dfrac{7}{3}$ is $2\dfrac{1}{3}$

Question 6

Pictorial representation of $3\times \displaystyle \frac{2}{3}$ is?

Accepted Answer

We have given Pictorial representation of $3\times \dfrac{2}{3}$$\Rightarrow$   $3\times \dfrac{2}{3}=\dfrac{2}{3}+\dfrac{2}{3}+\dfrac{2}{3}$$\therefore$    Option $B$ is correct answer.

Question 7

Write the fraction representing the shaded portion.

Accepted Answer

The given figure represents $3$ shaded parts out of $12$ equal parts.Hence, $\dfrac {9}{12}$=$\dfrac{3}{4}$

Question 8

The following figure represents:

Accepted Answer

The given figure has $3$ large squares with $4$ parts in each square. In the first square, all $\dfrac4 4$ parts are colored. In the second square also all $\dfrac4 4$ parts are colored. In the third square, only $\dfrac1 4$ is colored.So we can say that the given figures are $1+1+\dfrac 1 4= 2$ whole $\dfrac1 4$Option D is the correct answer.

Question 9

The teacher asked the students to read as much as possible of a particular book during the weekend. Balakrishnanread $\dfrac{1}{2}$ of the book. Angela read $\dfrac{5}{6}$ of the book and Subhalakshmi read $\dfrac{2}{3}$ of the book. Arrange the three names in the order from the one who read the most of the least.

Accepted Answer

Compare the fractions by making the denominators of all the fractions same.Book read by Balakrishnan is,$\dfrac{1}{2} = \dfrac{1}{2} \times \dfrac{3}{3}$$ = \dfrac{3}{6}$Book read by Subhalakshmi is,$\dfrac{2}{3} = \dfrac{2}{3} \times \dfrac{2}{2}$$ = \dfrac{4}{6}$Book read by Angela is $\dfrac{5}{6}$.The order of reading the book can be arranged as,$\dfrac{3}{6} < \dfrac{4}{6} < \dfrac{5}{6}$Therefore, the order from the one who read the book most of the least is,&#8217;Angela, Subhalakshmi, Balakrishnan.

Question 10

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

Accepted Answer

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, $S = 3.5$.