Parts And Whole - Class 5 Maths - Extra Questions

Multiply the following. 
$$15\times \cfrac { 2 }{ 5 } $$

$$15\times \dfrac{2}{5}$$

Can be written as

$$= 3 \times 2$$

$$= 6$$



Find:
$$\cfrac { 2 }{ 5 } $$ of $$15$$

$$= \dfrac 25 \times 15$$
$$= 6$$


Find
$$\cfrac { 1 }{ 3 } $$ of $$12$$

$$= \dfrac 13 \times 12$$
$$=4$$


$$\dfrac {7}{50}$$ of a kilogram = ? grams

$$1$$kg=$$1000$$gms 
$$\dfrac{7}{50}\times 1000=140$$gms


Saroj plants $$6$$ mango trees in row in her garden. The distance between two adjacent mango trees is $$\dfrac{5}{4}m$$. Find the distance between the first and the last mango tree.

$$\therefore$$ Distance between first & last $$=5\times \dfrac{5}{4}=\dfrac{25}{4}$$m.
1029631_1054308_ans_c9ab6651aabc4268bf6a089fc4435d0b.png


Rani says that the shaded portion in the given figure represents $$\dfrac{1}{4}$$. Do you agree with her? Give the reason to support your answer?
1041858_54e5b6e18a024225a80f2ca858b2ca3f.png

From the symmetry of the figure we can say that the shaded part represents $$\dfrac{1}{4}$$ the portion of circle.


(ii)$$\dfrac {5}{6}$$ of a day=______hrs

$$1$$ day = $$24$$ hrs. 
$$\dfrac{5}{6}\times 24=20$$ hrs.


Find $$\dfrac {3}{10}$$ of a kilogram. 

$$1$$ kg =$$1000$$ gms

$$\dfrac{3}{10}\times 1000=300$$ gms


Ramesh had $$20$$ pencils, Sheelu had $$50$$ pencils and Jamaal had $$80$$ pencils. After $$4$$ months. Ramesh used up $$10$$ pencils, Sheelu used up $$25$$ pencils and Jamaal used up $$40$$ pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils?

Ramesh $$=20$$ pencils
Sheelu $$=50$$ pencils
Jamaal $$=80$$ pencils
After $$4$$ months
Ramesh $$=10$$ pencils used
Sheelu $$=25$$ pencils used
Jamaal $$=40$$ pencils used
Fraction of pencils used $$=\dfrac{10+25+40}{20+50+80}=\dfrac{75}{150}=\dfrac{1}{2}$$
Ramesh $$=\dfrac{10}{20}=\dfrac{1}{2}$$
Sheelu $$=\dfrac{25}{50}=\dfrac{1}{2}$$
Jamaal $$=\dfrac{40}{80}=\dfrac{1}{2}$$
Hence equal fraction of pencils all used.


$$\dfrac {3}{8}$$ of $$64$$ equals:

$$\cfrac{3}{8} \text{ of } 64 = \cfrac{3}{8} \times 64 = 3 \times 8 = 24$$
Hence, the correct answer is 24.


Multiply and write the answer into lowest term $$15 \times \frac{{12}}{{20}}$$

$$=15 \times \cfrac{{12}}{{20}}$$
$$= 15 \times \cfrac{{3}}{{5}}$$
$$= 3 \times 3 $$
$$= 9$$


Solve :

(i) $$4 \times \dfrac{1}{3}$$

(ii) $$2 \times \dfrac{6}{7}$$

(iii) $$11 \times \dfrac{4}{7}$$

(iv) $$20 \times \dfrac{4}{5}$$

i) $$4 \times {1 \over 3}$$

$$ = {{4 \times 1} \over 3}$$

$$4 \times {1 \over 3} = {4 \over 3}$$

$$ = {4 \over 3}$$

ii) $$2 \times {6 \over 7}$$

$$ = {{2 \times 6} \over 7}$$

$$2 \times {6 \over 7} = {{12} \over 7}$$

$$ = {{12} \over 7}$$

iii) $$11 \times {4 \over 7}$$

$$ = {{11 \times 4} \over 7}$$

$$11 \times {4 \over 7} = {{44} \over 7}$$

$$ = {{44} \over 7}$$

iv) $$20 \times {4 \over 5}$$

$$ = {{20 \times 4} \over 5}$$

$$ = {{4 \times 4} \over 1}$$

$$20 \times {4 \over 5} = 16$$

$$ = {{16} \over 1}$$

$$ = 16$$



Solve:
$$\dfrac{7}{5}$$ of $$65\,kg$$

We have,

$$\dfrac{7}{5}$$ of $$65\,kg$$

$$ =\dfrac{7}{5}\times 65 $$

$$ =7\times 13 $$

$$ =91\,kg $$

 

Hence, this is the answer.



Fill in the boxes: (a). ()$$- \dfrac{5}{8} = \dfrac{1}{4}$$, (b). $$() - \dfrac{1}{5} =\dfrac{1}{2}$$, (c). $$()-\dfrac{1}{2}  = \dfrac{1}{6}$$

let boxes$$=\dfrac{x}{y}$$ then,


Solve part (a).

$$ \dfrac{x}{y}-\dfrac{5}{8}=\dfrac{1}{4} $$

$$ \dfrac{x}{y}=\dfrac{1}{4}+\dfrac{5}{8} $$

$$ \dfrac{x}{y}=\dfrac{2+5}{8} $$

$$ \dfrac{x}{y}=\dfrac{7}{8}\,\,\,\,\,\,\,\,ans. $$


Solve part (b).

$$ \dfrac{x}{y}-\dfrac{1}{5}=\dfrac{1}{2} $$

$$ \dfrac{x}{y}=\dfrac{1}{2}+\dfrac{1}{5} $$

$$ \dfrac{x}{y}=\dfrac{5+2}{10} $$

$$ \dfrac{x}{y}=\dfrac{7}{10}\,\,\,\,ans. $$


Solve part (c).

$$ \dfrac{x}{y}-\dfrac{1}{2}=\dfrac{1}{6} $$

$$ \dfrac{x}{y}=\dfrac{1}{6}+\dfrac{1}{2} $$

$$ \dfrac{x}{y}=\dfrac{1+3}{6} $$

$$ \dfrac{x}{y}=\dfrac{4}{6}\,\,\, $$

$$ \dfrac{x}{y}=\dfrac{2}{3}\,\,\,\,\,\,ans. $$



Find $$(i)\ 4\times \dfrac{2}{7}$$

Given that:
$$i)\ 4\times \dfrac{2}{7}=\dfrac{8}{7}$$

Hence, this is the required solution.


Multiply and reduce to lowest form.
(i)  $$7 \times \frac{3}{5}$$
(ii)  $$4 \times \frac{1}{3}$$
(iii)  $$2 \times \frac{6}{7}$$
(iv)  $$5 \times \frac{2}{9}$$

Part $$\left( 1 \right)$$

$$7\times \dfrac{3}{5}$$

$$=\dfrac{21}{5}$$

 

Part $$\left( 2 \right)$$

$$ =4\times \dfrac{1}{3} $$

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

 

Part $$\left( 3 \right)$$

$$ =2\times \dfrac{6}{7} $$

$$ =\dfrac{12}{7} $$

 

Part $$\left( 4 \right)$$

$$ =5\times \dfrac{2}{9} $$

$$ =\dfrac{10}{9} $$

 

Hence, this is the answer.



Simplify:
$$\dfrac{{50}}{{80}} \times 100$$

$$\dfrac{50}{80}\times 100$$
$$\Rightarrow$$  $$\dfrac{50}{8}\times 10$$

$$\Rightarrow$$  $$\dfrac{25}{4}\times 10$$

$$\Rightarrow$$  $$\dfrac{25}{2}\times 5$$

$$\Rightarrow$$  $$\dfrac{125}{2}$$

$$\Rightarrow$$  $$62.5$$


$$\dfrac {5}{20}$$ of $$100$$ is equal to:

Solution:-
$$\cfrac{5}{20} \text{ of } 100 = \cfrac{5}{20} \times 100 = 5 \times 5 = 25$$
Hence, the correct answer is 25.


Solve: $$\dfrac{1}{7}$$ of $$14$$

$$\dfrac{1}{7}$$ of $$14$$
$$=\dfrac{1}{7}\times14$$
$$=\dfrac{14}{7}$$
$$={2}$$


$$5 $$ equal bags of flour weight $$ 35$$  kg,how many bags are required for $$ 7$$  kg of flour ?

Given:-
Weight of flour in $$5$$ bags $$= 35 \; kg$$
Weight of flour in $$1$$ bag $$= \dfrac{35}{5} = 7 \; kg$$
Therefore,
No. of bags required for $$7 \; kg$$ flour $$= 1$$


Solve the following 
$$6 \times \dfrac {1}{8}=$$

$$ 6\times \dfrac{1}{8} = \dfrac{6}{8} = \dfrac{3}{4} $$
1121238_1165101_ans_d36b9ad2c90c4e22936ac7933bec56d1.jpeg


Solve the following 
$$\dfrac {1}{5}\times 5=$$

$$ 5\times \dfrac{1}{5} = \dfrac{5}{5} = 1 $$ 
1121237_1165097_ans_1959116b37024755a8af31d9d6791416.jpeg


Solve the following
$$\dfrac {1}{10}\times 7=$$

$$\dfrac{1}{10}$$ $$\times7$$

$$\dfrac{7}{10}$$

$$=0.7$$


Solve the following
$$10\times\dfrac {1}{5}=$$

$$ 10\times$$ $$\dfrac{1}{5}$$

$$=\dfrac{10}{5}=2$$


Solve the following
$$4\times \dfrac {1}{4}=$$

$$4\times$$ $$\dfrac{1}{4}$$

$$=\dfrac{4}{4}$$

$$=1$$


Solve the following 
$$\dfrac {1}{4}\times 9=$$

$$\dfrac{1}{4}\times{9}$$

=  $$\dfrac{9}{4}$$



Solve the following 
$$5\times \dfrac {1}{4}=$$

$$5\times$$ $$\dfrac{1}{4}$$

=   $$\dfrac{5}{4}$$



What fraction of $$1$$ $$kg$$ is $$650$$ $$g$$ ?

$$1 \ kg =1000 \ g$$
Required fraction = $$\dfrac{650}{1000}=\dfrac{13}{20}$$


Solve the following
$$10\ \times \dfrac {1}{8}=$$

$$10 \times \dfrac  {1}{8}$$

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

$$=\dfrac  {5}{4}$$




What fraction is
$$Rs\ 33\ of\ Rs\ 100?$$ =

The fraction will be 
$$ = \dfrac {33}{100}$$


Half is symbolically written as?


1338678_1344433_ans_a992bda547f348e581c3645284126a7b.jpg


Find :$$\dfrac{1}{7}$$ of $$14$$  ?

$$\cfrac{1}{7}$$ of $$14$$ $$\Rightarrow$$ $$\cfrac{1}{7}\times 14$$
$$=\cfrac{1}{7}\times \cfrac{14}{1}$$.....multiplication of fractions
$$=\cfrac{1\times 14}{7\times 1}$$
$$=\cfrac{14}{7}=2$$


Kristin received a $$CD$$ player for her birthday. She bought $$3$$ $$CDs$$ and received $$5$$ others as gifts. What fraction of her total $$CDs$$ did she buy and what fraction did she receive as gifts?

$${\textbf{Step  - 1: Listing the information about the CDs}}{\text{.}}$$

                  $${\text{Kristin bought 3 CDs}}{\text{.}}$$

                  $${\text{She received 5 as gifts}}{\text{.}}$$

                  $${\text{So she has a total of 8 CDs with her}}{\text{.}}$$

$${\textbf{Step  - 2: Calculating the fractions}}{\text{.}}$$

                  $${\text{Fraction of CDs she bought = }}\dfrac{{{\text{number of CDs she bought}}}}{{{\text{total number of CDs she has}}}}$$

                                                                      $$ = \dfrac{3}{8}.$$

                  $${\text{Fraction of CDs she received as gift = }}\dfrac{{{\text{number of CDs she received}}}}{{{\text{total number of CDs she has}}}}$$

                                                                                     $$ = \dfrac{5}{8}.$$

$${\textbf{Hence, Kristin bought }}\mathbf{\dfrac{3}{8}{\text{ of the total CDs and received }}\dfrac{5}{8}{\text{ of it as gift}}{\text{.}}}$$



Solve the following
$$2\times\dfrac {1}{3}=$$

$$ 2 \times \dfrac{1}{3} = \dfrac{2}{3}$$
1121249_1165181_ans_a01817c9efc24d73bb7a239d655cddbe.jpeg


Determine $$\cfrac{2}{3}$$ of a collection of $$15$$ books

In order to determine $$\frac{2}{3}$$ of collection of books, we have to determine, $$\frac{2}{3} \times 15=10 books$$


Determine $$\cfrac{3}{11}$$ of a collection of $$88$$ apples.

In order to determine $$\dfrac{3}{11}$$ of 88 apples, $$\dfrac{3}{11} \times 88=24 apples$$


Solve the following
$$5\times\dfrac {1}{5}$$

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


What fraction is $$Rs.\ 10$$ of $$Rs.\ 100?$$ 

The fraction will be $$ = \dfrac {10}{100}$$
                                 $$ = \dfrac {1}{10}$$

Hence, the required fraction is  $$ \dfrac {1}{10}$$


(a) How many quarters are there in one whole?
(b) How many halves make one whole?
(c) How many one-third parts make one whole?

(a) $$4$$ quarters makes one whole.
Thus $$4$$ quarters are there in one whole.
(b) $$2$$ halves make one whole.
(c) $$3$$ one-third parts make one whole.


Multiply and write your answer in the lowest form .
$$\dfrac{2}{7} \times 3$$

Now,
$$\dfrac{2}{7} \times 3$$
$$=$$ $$\dfrac{6}{7} $$.
This is the required lowest form.


Multiply and write your answer in the lowest form .
$$\dfrac{3}{8} \times 7$$

We have,
$$\dfrac{3}{8} \times 7$$
$$=\dfrac{21}{8}$$.
This is the required lowest form.


Multiply and write your answer in the lowest form .
$$\dfrac{1}{4} \times 3$$

We've,
$$\dfrac{1}{4} \times 3$$
$$=\dfrac{3}{4} $$.
This is the required lowest form.


Three fourth of a kilogram .

$$\dfrac 34\times 1000g\\3\times 250=750g$$


Multiply and write your answer in the lowest form .
$$\dfrac{2}{9} \times 3$$

Now,
$$\dfrac{2}{9} \times 3$$
$$=\dfrac{6}{9} $$
$$=\dfrac{2}{3} $$.
This is the required lowest form.


Multiply and write your answer in the lowest form .
$$\dfrac{4}{9} \times 3$$

Now,
$$\dfrac{4}{9} \times 3$$

$$=\dfrac{12}{9} $$

$$=\dfrac{4}{3}$$.
This is the required lowest form.


What is $$\frac { 7 } { 10 } \text { of } 650 ?$$

$$\dfrac{7}{10}$$ of $$650$$ is $$\dfrac{7}{10}\times 650=7\times 65=455$$


Multiply and write your answer in the lowest form .
$$\dfrac{2}{11} \times 4$$

Now, we've,
$$\dfrac{2}{11} \times 4$$
$$=\dfrac{8}{11}$$.
This is the required lowest form.


Multiply and write your answer in the lowest form .
$$\dfrac{1}{3} \times 2$$

We've,
$$\dfrac{1}{3} \times 2$$
$$=\dfrac{2}{3}$$.
This is the required lowest form.


Find $$\dfrac{3}{4}$$ of $$8$$ flowers.

$$\dfrac{3}{4}$$ of $$8$$ flowers
$$=\dfrac{3}{4}\times 8$$
$$=3\times 2=6$$ flowers


Shade $$\dfrac{4}{9}$$ on the given figure:
1777562_b8b03e7f16444fd68809589d4bd8ba18.PNG

$$\therefore$$ Above figure represents the shaded region $$\dfrac{4}{9}$$ of the hole figure.
1630995_1777562_ans_80b5e6dc282449649eaf1004c7bcf0ba.PNG


Write the fraction representing the shaded portion:
1777538_0673315ce1844e5c97c2d386c257ce34.PNG

Total parts $$= 8$$
Shaded region $$= 3$$
Hence, the shaded portion of the region is $$3$$ part of the whole figure $$\therefore  3 / 8 $$


Which of the drawings (a) to (d) show:
$$3\times \dfrac {1}{4}$$.
1645685_657d1127aeec4c23a4dab5840b43e6b4.png

Fig(c) shows $$3\times\dfrac{1}{4}$$
As it has three squares and each square 's one -fourth part is shaded.


Find $$\dfrac{3}{4}$$ of $$(i)\ 44\ (ii)\ 64\ (iii)\ 128$$

$$\cfrac{3}{4}$$
(1)
$$=\cfrac{3}{4}\times 44$$
$$=33$$

(2) 
$$=\cfrac{3}{4}\times 64$$
$$=48$$

(3)
$$=\cfrac{3}{4}\times 128$$
$$=3\times 32=96$$


Write the fraction representing the shaded portion:
1777525_a8cddeb0a0a74787a1f91cb3548ed383.PNG

Total parts $$= 4$$
Shaded region $$= 1$$
Hence, the shaded portion of the region is $$1$$ part of the whole figure $$\therefore  1 / 4$$


Write the fraction representing the shaded portion:
1777530_70870d0088af40a3987bff042b6df9d1.PNG

Total parts $$= 3$$
Shaded region $$= 2$$
Hence, the shaded portion of the region is $$2$$ part of the whole figure $$\therefore  2 / 3 $$


Write the fraction representing the shaded portion:
1777536_1fa829f8ce5a499d8c9a18df53be4f2a.PNG

Total parts $$= 9$$
Shaded region $$= 4$$
Hence, the shaded portion of the region is $$4$$ part of the whole figure $$\therefore  4 / 9 $$


What is the two - third of  42 ? 

The two third of $$42$$ is $$\dfrac{2}{3}\times 42$$

                                $$=\dfrac{2\times 42}{3}$$

                                $$=\dfrac{84}{3}$$

                                $$=\dfrac{3\times 28}{3}$$

                                $$=28$$


Write the fraction representing the shaded portion:
1777533_ffba52921ea74970acaeb9e1a152ea06.PNG

Total parts $$= 10$$
Shaded region $$= 3$$
Hence, the shaded portion of the region is $$3$$ part of the whole figure 
$$\therefore 3 / 10 $$


Write the fraction representing the shaded portion:
1777517_d451e92b1c4e4590858bbe1b3f056988.PNG

Total parts $$= 4$$
Shaded region $$= 3$$
Hence, the shaded portion of the region is $$3$$ pans of the whole figure $$\therefore 3/4$$


In the given figure, if we say that the shaded region is $$\dfrac14$$, then identify the error in it.
1777574_9d80b8bc56c64386865d64a13ab66cfe.PNG

The given rectangle has not been divided into $$4$$ equal parts hence, the shaded region is not equal to $$\dfrac14.$$


Write a fraction for the following:
One-eighth

The fraction for one- eighth is $$1 / 8$$


Find the product:
$$\dfrac25 \times15$$

By the rule of Multiplication of fraction,
$$\text{Product of fraction}=\dfrac{\text{product of numerator}}{\text{product of denominator}}$$

$$\therefore \dfrac25 \times15=\dfrac{2\times15}{5\times 1}=\dfrac{30}5=6$$


Write a fraction for the following:
Five$$-$$sixth

The fraction for five$$ - $$sixths is $$\dfrac{5 }{ 6}$$ .


Write a fraction for the following:
Seven-twelfths

The fraction for seven - twelfths is $$\dfrac{7}{12}$$


Write a fraction for the following:
Three- fourths

The fraction for three - fourths is $$3 / 4$$


Write a fraction for the following:
Two - fifths

The fraction for two fifths is $$2 / 5$$


Find the product:
$$\dfrac58\times 1000$$

By the rule of Multiplication of fraction,
$$\text{Product of fraction}=\dfrac{\text{product of numerator}}{\text{product of denominator}}$$

$$\therefore \dfrac58\times 1000$$
$$=\dfrac{5 \times 1000}{8 \times1}$$
$$=\dfrac{5000}{8}$$
$$=625$$ 


Write the shaded portions are fractions. Arrange them in ascending order using appropriate sign between fractions :
1788087_c5567097dcf34a239bf334fe1dd1c6e7.PNG


1726783_1788087_ans_6d5d312963474f4c9926dcae91556b3e.png


Simplify:
$$\dfrac{3}{4} \times 6$$

$$\dfrac{3}{4}\times 6$$

$$= \dfrac{18}{4}$$

$$= \dfrac{9}{2}$$

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


Evaluate the following :
$$(i) \dfrac{2}{3} \times 60$$
$$(ii) \dfrac{4}{7} \times 280 $$

$$(i) \dfrac{2}{3} \times 60 = 2 \times 20 = 40$$
$$(ii) \dfrac{4}{7} \times 280 $$
$$= 4 \times 40 = 160 $$



$$24 \times 25= 24 \times \dfrac{ \square }{4}=600$$

Let the missing number be $$K$$
$$24 \times 25=24 \times \dfrac{K}{4}=600$$

$$K=\dfrac{600 \times 4}{24} =\dfrac{\not {2400}}{\not{24}}=100$$

$$K=100$$


Write the fractions representing the shaded regions and pair up the equivalent fractions from each row :
1787317_e02cdd5b58e94642a811fb66b593643f.PNG

The fractions representing the shaded regions are as follows: 
$$(i)\ \dfrac{1}{2}\qquad\qquad(ii)\ \dfrac {4}{6} \Rightarrow \dfrac{2}{3}\qquad(iii)\ \dfrac{3}{9} \Rightarrow \dfrac{1}{3}\\(iv)\ \dfrac{2}{8} \Rightarrow \dfrac{1}{4}\qquad(v)\ \dfrac{3}{4}$$

$$(a)\ \dfrac{4}{8} \Rightarrow \dfrac{1}{4} \qquad (b)\ \dfrac{8}{12} \Rightarrow \dfrac{2}{3}\qquad(c)\ \dfrac{12}{16} \Rightarrow \dfrac{3}{4}\\ (d)\ \dfrac{4}{8} \Rightarrow \dfrac{1}{2}\qquad(e)\  \dfrac{6}{18} \Rightarrow \dfrac{1}{3}$$

Equivalent fractions are :
$$\left(i\right) \leftrightarrow \left(d\right)$$
$$\left(ii\right) \leftrightarrow \left(b\right)$$
$$\left(iii\right) \leftrightarrow \left(e\right)$$
$$\left(iv\right) \leftrightarrow \left(a\right)$$
$$\left(v\right) \leftrightarrow \left(c\right)$$


Simplify:
$$\dfrac{2}{3} \times 15$$

$$\dfrac{2}{3} \times{15}$$

$$= \dfrac{30}{3}=10$$


Find the value of:
$$\dfrac{3}{5}$$ of 1 hour

$$1$$ hour $$= 60$$ minutes
$$\dfrac{3}{5}$$ of an hour = $$\dfrac{3}{5}$$ $$\times{60} minutes$$
$$= 3 × 12$$ minutes
$$= 36$$ minutes.


Find the value of:
$$= \dfrac{1}{2}$$ of $$10$$ kg

$$\dfrac{1}{2} \times {10}kg$$

$$= \dfrac{10}{2}=5 kg$$


Multiply the following.
$$\cfrac { 3 }{ 6 } \times 10$$

$$\begin{aligned}{}\frac{3}{6} \times 10& = \frac{1}{2} \times 10\\ &= 5\end{aligned}$$


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

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 $$2\dfrac{1}{3}$$


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.

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,’

Angela, Subhalakshmi, Balakrishnan.



$$\cfrac{3}{8}\,of\,74 = $$

$$\cfrac { 3 }{ 8 } \times 74=\cfrac { 3\times 37 }{ 4 } =\cfrac { 111 }{ 4 } $$



Express the following as mixed fraction
$$\dfrac{20}{3}$$.

$$\dfrac{20}{3}=\dfrac{18+2}{3}$$
       $$=6+\dfrac{2}{3}$$
       $$=6\dfrac{2}{3}$$


Find: $$\dfrac{9}{3}\,$$ of 5


1320589_1078771_ans_ddaf7fbd1b084f5297774c092e321504.jpg


Find:
(a) $$\displaystyle {1 \over 2}$$ of (i) $$24$$ (ii) $$46$$ 

(b) $$\displaystyle {2 \over 3}$$ of (i) $$18$$ (ii) $$27$$

(c) $$\displaystyle {3 \over 4}$$ of (i) $$16$$ (ii) $$36$$ 

(d) $$\displaystyle {4 \over 5}$$ of (i) $$20$$ (ii) $$35$$

$$(a)\ (i)\ \cfrac { 1 }{ 2 } \times 24=12\quad \quad \quad \quad \quad (ii)\ \cfrac { 1 }{ 2 } \times 46=23$$

$$(b)\ (i)\ \cfrac { 2 }{ 3 }  \times 18=12\quad \quad \quad \quad \quad (ii)\ \cfrac { 2 }{ 3 } \times 27=18$$

$$(c)\ (i)\ \cfrac { 3 }{ 4 } \times 16=12\quad \quad \quad \quad \quad (ii)\ \cfrac { 3 }{ 4 } \times 36=27$$

$$(d)\ (i)\ \cfrac { 4 }{ 5 } \times 20=16\quad \quad \quad \quad \quad (ii)\ \cfrac { 4 }{ 5 } \times 35=28$$


Evaluate $$\dfrac{3}{6} \times 24$$

$$\dfrac { 3 }{ 6 } \times 24=3\times4 $$

$$=12$$




Evaluate:
$$\dfrac{1}{{8}}\,of\,246  $$

$$\cfrac{1}{8}$$ of $$246=\cfrac{1}{8}\times 2\times 123=\cfrac{123}{4}$$


Choose the correct option to complete the sentences . 
$$67%$$ of students said they were learning english for their education . $$17%$$ said they were learning  for fun . 
Education was __________    reason students gave for learning english . 
a) nearly the four times most popular 
b) by far the most popular 
c) the much more popular 

a):- nearly the four times most popular.


$$\cfrac{7}{8}\,of\,74 = $$

$$\cfrac { 7 }{ 8 } \times 74=\cfrac { 7\times 37 }{ 4 } =\cfrac { 259 }{ 4 } $$


$$\cfrac{5}{{12}}\,of\,150 = $$

$$\cfrac{5}{12} \times 150=\cfrac{125}{2}$$



$$\cfrac{7}{{8}}\,of\,246 = $$

$$\cfrac{7}{8}$$ of $$246=\cfrac{7}{8}\times 246=\cfrac{7}{8}\times 2\times123=\cfrac{861}{4}$$



Write the fraction representing the shaded portion.
1643852_641fbf6c5b4a4df2996d4cdfe6584bde.png

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


Write the fraction representing the shaded portion.
1643848_577f74a54ca242c29a27dce32225fb3c.png

The given figure represents $$8$$ shaded parts out of $$9$$ equal parts.
Hence, $$\dfrac {8}{9}$$.


Evaluate:
$$\dfrac{5}{{8}}\,of\,246  $$

$$\cfrac{5}{8}$$ of $$246=\cfrac{5}{8}\times 246=\cfrac{5}{8}\times 2\times 123=\cfrac{5}{4}\times 123 =\dfrac{615}{4}$$ 


Kristin received a $$CD$$ player for her birthday. She bought $$3\ CDs$$ and received $$5$$ other as gifts. What fraction of her total $$CDs$$ did she buy and what fraction did she receive as gifts ?


$${\textbf{Step  - 1: Listing the information about the CDs}}{\text{.}}$$

                  $${\text{Kristin bought 3 CDs}}{\text{.}}$$

                  $${\text{She received 5 as gifts}}{\text{.}}$$

                  $${\text{So she has a total of 8 CDs with her}}{\text{.}}$$

$${\textbf{Step  - 2: Calculating the fractions}}{\text{.}}$$

                  $${\text{Fraction of CDs she bought = }}\dfrac{{{\text{number of CDs she bought}}}}{{{\text{total number of CDs she has}}}}$$

                                                                      $$ = \dfrac{3}{8}.$$

                  $${\text{Fraction of CDs she received as gift = }}\dfrac{{{\text{number of CDs she received}}}}{{{\text{total number of CDs she has}}}}$$

                                                                                     $$ = \dfrac{5}{8}.$$

$${\textbf{Hence, Kristin bought }}\mathbf{\dfrac{3}{8}{\text{ of the total CDs and received }}\dfrac{5}{8}{\text{ of it as gift}}{\text{.}}}$$



$$\cfrac{1}{{11}}\,of\,90 = $$

$$\cfrac{1}{11} \times 90=8\cfrac{2}{11}$$



Write the fraction representing the shaded portion.
1643849_4b3835ce577347c0b2614c5774506c0f.png

The given figure represents $$4$$ shaded parts out of $$8$$ equal parts.
Hence, $$\dfrac {4}{8}$$=$$\dfrac{1}{2}$$


Write the fraction representing the shaded portion.
1643847_c4056d2c47f24dc09a945e6d1b9ed73b.png

The given figure represents $$2$$ shaded parts out of $$4$$ equal parts.
Hence, $$\dfrac {2}{4}$$=$$\dfrac{1}{2}$$


Write the fraction representing the shaded portion.
1643850_3a19a4cbd3844d1384d1a7a438355305.png

The given figure represents $$1$$ shaded parts out of $$4$$ equal parts.
Hence, $$\dfrac {1}{4}$$.


Write the fraction representing the shaded portion.
1643851_771c8b3e68194fe3943e60f6a2874aa9.png

The given figure represents $$3$$ shaded parts out of $$7$$ equal parts.
Hence, $$\dfrac {3}{7}$$.


Write these fractions appropriately as addition or subtractions.
1658022_75ae78339f244e6990e51e02f00c32db.png

$$\dfrac {3}{6} + \dfrac {2}{6} = \dfrac {5}{6}$$
1501807_1658022_ans_7d4e9ef423cb45af85926f58dddf7a54.png


Find :
$$\dfrac{7}{11}$$ of $$Rs\ 330$$


1590774_1676035_ans_acf3a76ec1a34e83aa8b06c26603c12c.jpg


Find :
$$\dfrac{1}{12}$$ of an hour (in mins.)


1516005_1676047_ans_8e28f821a43b496194f33000e97bf870.jpg


Find :
$$\dfrac{3}{7}$$ of $$42\ litres$$


1590776_1676042_ans_0790940e74b74dc2ad16de1938091a5c.jpg


Replace $$\square$$ in each of the following by the correct number.
$$\dfrac {45}{60} = \dfrac {15}{\square}$$


1501643_1657962_ans_ca0a73a09aac4ac88e8b84739253115e.jpg


Write the fraction representing the shaded portion.
1643853_dad94d5631914701aa5f9e17fa3f0688.png

The given figure represents $$10$$ shaded parts out of $$10$$ equal parts.
Hence, $$\dfrac {10}{10}$$.


Write the fraction representing the shaded portion.
1643854_9bb2eebacf7b467599261de0e79d0592.png

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


Multiply :
$$\dfrac{3}{5}$$ by $$25$$


1498978_1675956_ans_34d16d8208644a32bc423c8059c64e2c.jpg


Find :
$$\dfrac{5}{9}$$ of $$108\ metres$$

We have, $$\dfrac{5}{9}$$ of $$108\space\mathrm{m}$$
$$=\dfrac{5}{9}\times108\space\mathrm{m}$$
$$=5\times12\space\mathrm{m}$$
$$=60\space\mathrm{m}$$


Replace $$\square$$ in each of the following by the correct number.
$$\dfrac {4}{5} = \dfrac {\square}{20}$$


1501642_1657961_ans_4dba31a0ceea42dc9c1f96d4ec030b93.jpg


Multiply:
$$\cfrac76$$ by $$(24)$$

The product of two rational number = $$\cfrac{( \ product\  of\  their\  numerator\ )}{ (\  product\  of\  their\  denominator\ )}$$

$$24$$ can be written as $$\cfrac{24}{1}$$
Therefore given question can be written as $$\cfrac76\times \cfrac{24}1$$
So, we have,
$$=\cfrac76\times \cfrac{24}1$$
$$=\cfrac{7\times 24}{6\times 1}$$
$$=\cfrac{7\times 4}{1\times 1}$$
$$=28$$


Find :
$$\dfrac{5}{6}$$ of a day (in hours)

We know, 
$$1$$ day $$=24$$ hours
So, $$\dfrac{5}{6}$$ of a day $$=24\times\dfrac{5}{6}$$ hours $$=20$$ hours


Find the cost of $$3\dfrac25 \text{ m}$$ of cloth at $$\text{Rs. } 66 \dfrac {3}{4}$$ per meter.

Given:-
Cost of the cloth per meter is equal to $$\text{Rs. }. 66 \dfrac {3}{4}$$
Total length of the cloth required is equal to $$ 3 \dfrac 25 \text{ m}.$$

Total cost of cloth $$=$$ Cost of the cloth per meter $$\times$$ Total cloth required
                               $$=  66\dfrac {3}{4} \times 3 \dfrac 25$$

                               $$=\dfrac  {267} {4}\times \dfrac {17}5$$

                               $$=\text{Rs. } \dfrac {4335}{20}$$

Further we can divide by $$5$$ we get,
$$\dfrac {4335}{20} = \dfrac {867}{4}$$
            $$ =\text{Rs. } 216\dfrac {3}{4}$$

$$\therefore$$ Cost of the cloth is $$\text{Rs. }216 \dfrac {3}{4}$$.


Write a fraction for the following:
Eight- ninths

The fraction for eight - ninths is $$8 / 9$$


Find the product:
$$2 \cfrac{4}{15} \times (12)$$

By the rule Multiplication of fraction,
Product of fraction=$$\cfrac{product\ of\ numerator}{product\ of\ denominator}$$
$$1^{st}$$ we will convert mixed fraction into improper fraction.
$$2\cfrac{4}{15}=\cfrac{2\times 15+4}{15}=\cfrac{34}{15}$$
And, $$12$$ can be written as $$\cfrac{12}{1}$$
Then,
$$2 \cfrac{4}{15} \times (12)=\cfrac{34}{15}\times \cfrac{12}{1}$$
$$=\cfrac{(34\times 12)}{(15\times 1)}$$
$$=\cfrac{(34\times 4)}{(5\times 1)}$$
$$=\cfrac{136}{5}$$
$$=\cfrac{27\times 5+1}{5}$$
$$=27+\cfrac{1}{5}$$
$$=27\cfrac{1}{5}$$



Find :
$$\dfrac{3}{20}$$ of a kg (in grams)

We know, 
$$1\space\mathrm{kg}=1000\space\mathrm{gm}$$
Then, $$\dfrac{3}{20}\space\mathrm{kg}=1000\times\dfrac{3}{20}\space\mathrm{gm}=150\space\mathrm{gm}$$


Find :
$$\dfrac{5}{6}$$ of an year (in months)


1516007_1676050_ans_392a5fc2c2c54b5f8c27acd4e01d2c1c.jpg


Find :
$$\cfrac{1}{3}$$ of $$24$$

$$24$$ can also be written as $$\cfrac{24}{1}$$
$$\therefore$$ We have:
$$\cfrac{1}{3}$$ of $$\cfrac{24}{1}$$
This can be written as,
$$\cfrac{1}{3}\times \cfrac{24}{1}$$
By the rule Multiplication of fraction,
Product of fraction=$$\cfrac{product\ of\ numerator}{product\ of\ denominator}$$
So,
$$\cfrac{1}{3}\times \cfrac{24}{1}=\cfrac{(1\times 24)}{(3\times 1)}$$
$$=8$$



Find :
$$\dfrac{7}{20}$$ of a litre (in ml)


1516033_1676098_ans_6a7bcb8caca44c128bdc5c68d6aa16ca.jpg


Find :
$$\dfrac{2}{7}$$ of a week (in days)


1590794_1676111_ans_152bfba61770403ab47cc48957f293bf.jpg


Find :
$$\cfrac{3}{4}$$ of $$32$$

$$32$$ can also be written as $$\cfrac{32}{1}$$
$$\therefore$$ We have:
$$\cfrac{3}{4}$$ of $$\cfrac{32}{1}$$
This can be written as,
$$\cfrac{3}{4}\times \cfrac{32}{1}$$
By the rule Multiplication of fraction,
Product of fraction=$$\cfrac{product\ of\ numerator}{product\ of\ denominator}$$
So,
$$\cfrac{3}{4}\times \cfrac{32}{1}=\cfrac{(3\times 32)}{(4\times 1)}$$
$$=\cfrac{(3\times 8)}{(1\times 1)}$$
$$=24$$



Find :
$$\cfrac{5}{11}$$ of $$Rs.220$$

$$220$$ can also be written as $$\cfrac{220}{1}$$
$$\therefore$$ We have:
$$\cfrac{5}{11}$$ of $$\cfrac{220}{1}$$
This can be written as,
$$\cfrac{5}{11}\times \cfrac{220}{1}$$
By the rule Multiplication of fraction,
Product of fraction=$$\cfrac{product\ of\ numerator}{product\ of\ denominator}$$
So,
$$\cfrac{5}{11}\times \cfrac{220}{1}=\cfrac{(5\times 220)}{(11\times 1)}$$
$$=\cfrac{(5\times 20)}{(1\times 1)}$$
$$=100$$
$$\cfrac{5}{11}$$ of $$220$$ is $$100$$
So, 
$$\cfrac{5}{11}$$ of $$Rs.220$$ is $$Rs100$$



Find :
$$\cfrac{6}{7}$$ of $$35\ liters$$

$$35$$ can also be written as $$\cfrac{35}{1}$$
$$\therefore$$ We have:
$$\cfrac{6}{7}$$ of $$\cfrac{35}{1}$$
This can be written as,
$$\cfrac{6}{7}\times \cfrac{35}{1}$$
By the rule Multiplication of fraction,
Product of fraction=$$\cfrac{product\ of\ numerator}{product\ of\ denominator}$$
So,
$$\cfrac{6}{7}\times \cfrac{35}{1}=\cfrac{(6\times 35)}{(7\times 1)}$$
$$=\cfrac{(6\times 5)}{(1\times 1)}$$
$$=30$$
$$\cfrac{6}{7}$$ of $$35$$ is $$30$$
So, 
$$\cfrac{6}{7}$$ of $$35\ liters$$ is $$30\ liters$$


Find :
$$\cfrac{3}{20}$$ of $$1020$$

$$1020$$ can also be written as $$\cfrac{1020}{1}$$
$$\therefore$$ We have:
$$\cfrac{3}{20}$$ of $$\cfrac{1020}{1}$$
This can be written as,
$$\cfrac{3}{20}\times \cfrac{1020}{1}$$
By the rule Multiplication of fraction,
Product of fraction=$$\cfrac{product\ of\ numerator}{product\ of\ denominator}$$
So,
$$\cfrac{3}{20}\times \cfrac{1020}{1}=\cfrac{(3\times 1020)}{(20\times 1)}$$
$$=\cfrac{(3\times 51)}{(1\times 1)}$$
$$=153$$



Find :
$$\cfrac{7}{10}$$ of a metre

A metre contains $$100$$ centimetre (cm).
$$100$$ can also be written as $$\cfrac{100}{1}$$
$$\therefore$$ We have:
$$\cfrac{7}{10}$$ of $$\cfrac{100}{1}$$
This can be written as,
$$\cfrac{7}{10}\times \cfrac{100}{1}$$
By the rule Multiplication of fraction,
Product of fraction=$$\cfrac{product\ of\ numerator}{product\ of\ denominator}$$
So,
$$\cfrac{7}{10}\times \cfrac{100}{1}=\cfrac{(7\times 100)}{(10\times 1)}$$
$$=\cfrac{(7\times 100)}{(1\times 1)}$$
$$=70$$
$$\cfrac{7}{10}$$ of  $$1000$$ is $$70$$
So, 
$$\cfrac{7}{10}$$ of a metre is $$70\ cm$$


Find :
$$\cfrac{4}{9}$$ of $$54\ meters$$ 

$$54$$ can also be written as $$\cfrac{54}{1}$$
$$\therefore$$ We have:
$$\cfrac{4}{9}$$ of $$\cfrac{54}{1}$$
This can be written as,
$$\cfrac{4}{9}\times \cfrac{54}{1}$$
By the rule Multiplication of fraction,
Product of fraction=$$\cfrac{product\ of\ numerator}{product\ of\ denominator}$$
So,
$$\cfrac{4}{9}\times \cfrac{54}{1}=\cfrac{(4\times 54)}{(9\times 1)}$$
$$=\cfrac{(4\times 6)}{(1\times 1)}$$
$$=24$$
$$\cfrac{4}{9}$$ of $$54$$ is $$24$$
So, 
$$\cfrac{4}{9}$$ of $$54\ meters$$ is $$24\ meters$$


Find :
$$\cfrac{5}{9}$$ of $$45$$

$$45$$ can also be written as $$\cfrac{45}{1}$$
$$\therefore$$ We have:
$$\cfrac{5}{9}$$ of $$\cfrac{45}{1}$$
This can be written as,
$$\cfrac{5}{9}\times \cfrac{45}{1}$$
By the rule Multiplication of fraction,
Product of fraction=$$\cfrac{product\ of\ numerator}{product\ of\ denominator}$$
So,
$$\cfrac{5}{9}\times \cfrac{45}{1}=\cfrac{(5\times 45)}{(9\times 1)}$$
$$=\cfrac{(5\times 5)}{(1\times 1)}$$
$$=25$$



Find :
$$\cfrac{7}{10}$$ of a kg

A kilogram (kg) contains $$1000$$ grams.
$$1000$$ can also be written as $$\cfrac{1000}{1}$$
$$\therefore$$ We have:
$$\cfrac{7}{10}$$ of $$\cfrac{1000}{1}$$
This can be written as,
$$\cfrac{7}{10}\times \cfrac{1000}{1}$$
By the rule Multiplication of fraction,
Product of fraction=$$\cfrac{product\ of\ numerator}{product\ of\ denominator}$$
So,
$$\cfrac{7}{10}\times \cfrac{1000}{1}=\cfrac{(7\times 1000)}{(10\times 1)}$$
$$=\cfrac{(7\times 100)}{(1\times 1)}$$
$$=700$$
$$\cfrac{7}{10}$$ of  $$1000$$ is $$700$$
So, 
$$\cfrac{7}{10}$$ of a kg is $$700\ grams$$


Find :
$$\cfrac{1}{6}$$ of an hour 

An hour contains $$60$$ minutes
$$60$$ can also be written as $$\cfrac{60}{1}$$
$$\therefore$$ We have:
$$\cfrac{1}{6}$$ of $$\cfrac{60}{1}$$
This can be written as,
$$\cfrac{1}{6}\times \cfrac{60}{1}$$
By the rule Multiplication of fraction,
Product of fraction=$$\cfrac{product\ of\ numerator}{product\ of\ denominator}$$
So,
$$\cfrac{1}{6}\times \cfrac{60}{1}=\cfrac{(1\times 60)}{(6\times 1)}$$
$$=\cfrac{(1\times 10)}{(1\times 1)}$$
$$=10$$
$$\cfrac{1}{6}$$ of  $$60$$ is $$10$$
So, 
$$\cfrac{1}{6}$$ of an hour is $$10\ minutes$$


Find :
$$\cfrac{7}{50}$$ of $$1000$$

$$1000$$ can also be written as $$\cfrac{1000}{1}$$
$$\therefore$$ We have:
$$\cfrac{7}{50}$$ of $$\cfrac{1000}{1}$$
This can be written as,
$$\cfrac{7}{50}\times \cfrac{1000}{1}$$
By the rule Multiplication of fraction,
Product of fraction=$$\cfrac{product\ of\ numerator}{product\ of\ denominator}$$
So,
$$\cfrac{7}{50}\times \cfrac{1000}{1}=\cfrac{(7\times 1000)}{(50\times 1)}$$
$$=\cfrac{(7\times 20)}{(1\times 1)}$$
$$=140$$



In the adjoining figure, if we say that the shaded region is $$\dfrac{1}{4}$$ of the whole region, then identify the error in it.
1786719_2daedb2cb8a140af93040a37e43a6431.PNG

The whole rectangle is not divided into four equal parts.


Find :
$$\cfrac{7}{50}$$ of a litre

A litre contains $$1000$$ mililitres.
$$1000$$ can also be written as $$\cfrac{1000}{1}$$
$$\therefore$$ We have:
$$\cfrac{7}{50}$$ of $$\cfrac{1000}{1}$$
This can be written as,
$$\cfrac{7}{50}\times \cfrac{1000}{1}$$
By the rule Multiplication of fraction,
Product of fraction=$$\cfrac{product\ of\ numerator}{product\ of\ denominator}$$
So,
$$\cfrac{7}{50}\times \cfrac{1000}{1}=\cfrac{(7\times 1000)}{(50\times 1)}$$
$$=\cfrac{(7\times 20)}{(1\times 1)}$$
$$=140$$
$$\cfrac{7}{50}$$ of  $$1000$$ is $$140$$
So, 
$$\cfrac{7}{50}$$ of a litre is $$140\ mililitres$$


Find :
$$\cfrac{7}{8}$$ of a day

A day contains $$24$$ hours.
$$24$$ can also be written as $$\cfrac{24}{1}$$
$$\therefore$$ We have:
$$\cfrac{7}{8}$$ of $$\cfrac{24}{1}$$
This can be written as,
$$\cfrac{7}{8}\times \cfrac{24}{1}$$
By the rule Multiplication of fraction,
Product of fraction=$$\cfrac{product\ of\ numerator}{product\ of\ denominator}$$
So,
$$\cfrac{7}{8}\times \cfrac{24}{1}=\cfrac{(7\times 24)}{(8\times 1)}$$
$$=\cfrac{(7\times 3)}{(1\times 1)}$$
$$=21$$
$$\cfrac{7}{8}$$ of  $$24$$ is $$21$$
So, 
$$\cfrac{7}{8}$$ of a day is $$21\ hours$$


Write the fraction represented by the shaded portion of the adjoining figure:
1788556_fd886d3a5a9343de995196ebd4b331b2.png

The figure shows that the number of total equal parts is $$ 8 $$ and out of these $$ 7 $$ parts is shaded.
$$ \therefore $$ the fraction of shaded part is $$ \dfrac {7}{8} $$


Ali divided one fruit cake equally among six persons. What part of the cake he gave to each person?

Ali has to divide one fruit cake equally among $$ 6 $$ persons
$$ \therefore $$ Each person will get $$  \dfrac {1}{6} $$ th part.


Shade the parts of the following figures according to given fractions:
1786707_77d6b5b96876427eaaa8db4cad88a555.PNG


1747528_1786707_ans_fef19dfe041d48b783fb85f4b3ed8950.PNG


A rectangle is divided into a certain number of equal parts. If 16 of the parts so formed represent the fraction $$ \frac{1}{4} $$, find the number of parts in which the rectangle has been divided. 

Let the number of parts in which the rectangle has been divided be $$ x $$
According to the question $$ \Rightarrow \frac { 16}{x} = \frac {1}{4} $$
Cross-multiplication  $$ \Rightarrow 16 \times  4 = 1 \times x $$
$$ \Rightarrow x = 64 $$
$$ 64  $$ are the parts in which the rectangle has been divided


What is the fraction of each of the following shaded parts ?
1786698_2fc6a89b7207416684b6a196b22ee527.PNG

$$(i) \dfrac{4}{7}$$    $$(ii)  \dfrac{3}{8}$$   $$(iii)  \dfrac{1}{8}$$
$$(iv) \dfrac{1}{4}$$  $$(v) \dfrac{1}{6}$$   $$(vi) \dfrac{3}{10}$$
$$(vii) \dfrac{3}{7}$$   $$(viii) \dfrac{2}{4}$$  $$(ix) \dfrac{4}{9}$$


Find :
$$\cfrac{3}{7}$$ of a week

A week contains $$7$$ days
$$7$$ can also be written as $$\cfrac{7}{1}$$
$$\therefore$$ We have:
$$\cfrac{3}{7}$$ of $$\cfrac{7}{1}$$
This can be written as,
$$\cfrac{3}{7}\times \cfrac{7}{1}$$
By the rule Multiplication of fraction,
Product of fraction=$$\cfrac{product\ of\ numerator}{product\ of\ denominator}$$
So,
$$\cfrac{3}{7}\times \cfrac{7}{1}=\cfrac{(3\times 7)}{(7\times 1)}$$
$$=\cfrac{(3\times 1)}{(1\times 1)}$$
$$=3$$
$$\cfrac{3}{7}$$ of  $$7$$ is $$3$$
So, 
$$\cfrac{3}{7}$$ of a week is $$3\ days$$


Where money goesFraction of allowance
 Manavi Kuber
 Saving Account $$\dfrac{1}{2}$$ $$\dfrac{1}{3}$$
 Spend at mall $$\dfrac{1}{4}$$ $$\dfrac{3}{5}$$
 Left over ? ?
Manavi and Kuber each receives an equal allowance. The table shows the fraction of their allowance each deposits into his/her saving account and the fraction each spends at the mall. If allowance of each is $$Rs.1260$$ find the amount left with each.

For Manvi,
Fraction of allowance left over $$=1 - \left(\dfrac{1}{2} + \dfrac{1}{4} \right) = 1 - \dfrac{3}{4} = \dfrac{1}{4}$$
$$\therefore $$  Amount left $$= 1260 \times \dfrac{1}{4} = Rs.\ 315$$

For Kuber,
Fraction of allowance left over $$=1 - \left(\dfrac{1}{3} + \dfrac{3}{5}  \right) = 1 -  \dfrac{14}{15} = \dfrac{1}{15}$$
$$\therefore $$  Amount left $$= 1260 \times \dfrac{1}{15} = Rs.\ 84$$


Write the fraction representing the total number of natural numbers in the collection of numbers $$ -3, -2, -1 , 0 , 1, 2, 3 $$ What fraction will it be for whole numbers ? what fraction will it be for integers ?

Total collection of numbers $$ -3,-2,-1,0,1,2,3 $$ and out of these $$ 1,2,$$ and $$ 3 $$ is natural number and $$ 0,1,2 $$ and $$ 3 $$ are whole number and $$ -3,-2,-1,0,1,2,3 $$ are integers.


Find the fraction that represents the number of natural numbers to total numbers in the collection $$ 0 , 1, 2, 3, 4, 5 $$ what fraction will it be for whole numbers ?

From the collection $$ 0,1,2,3,4,5 \rightarrow 1,2,3,4,5 $$ is natural numbers
$$ \therefore $$ Fraction that represents the number of natural numbers to total numbers $$ = \dfrac {5}{6} $$ and $$ ( 0, 1 , 2 ,3, 4, 5 $$ is whole numbers)
$$ \therefore$$  that represents the number of natural numbers to whole numbers $$ = \dfrac{6}{6} $$


In the figure what is the ratio of the areas of shaded portions I and II taken together and shaded portion III?



1789726_a127a3d57838486e9e40ccfd662a1ade.png

$$\textbf{Step 1: Calculate the area of region I}$$
                                    Region $$\mathrm{I}$$ is in the shape of a square.
                                    Side of the square $$=5 \mathrm{~cm}$$
                                    Area of the region $$\mathrm{I}=$$ Area of the square
                                                                                  $$=$$ Side $$\times$$ side
                                                                                  $$=5 \mathrm{~cm} \times 5 \mathrm{~cm}$$
                                                                                  $$=25 \mathrm{sq} \mathrm{cm}$$

$$\textbf{Step 2 : Calculate the area of region III}$$
                                  $$\begin{aligned}\text { Area of the region III }=& \text { Area of the rectangle } \\&=\text { Length } \times \text { Breadth } \\&=7 \mathrm{~cm} \times 5 \mathrm{~cm} \\&=35 \mathrm{sq} \mathrm{cm}\end{aligned}$$

$$\textbf{Step 3: Calculate the area of region II}$$
Area of the shaded portion II $$=$$ Total Area- (Area of shaded portion I + Area of shaded portion III) 
                                               $$\begin{aligned}&=(10 \times 10) \mathrm{sqcm}-(35+25) \mathrm{sqcm} \\&=(100-60) \mathrm{sqcm} \\&=40 \mathrm{~sqcm}\end{aligned}$$

$$\Rightarrow \text{Ratio of area I + II  to III =} \dfrac{40+25}{35}=\dfrac{65}{35}=\dfrac{13}{7}$$

$$\therefore \textbf{Ratio of the combined areas of  shaded portion I and II to shaded portion III is 13 : 7}$$


What fraction of a straight angle is a right angle ?

We know that angle of straight line is $$ 180^0 $$
Angle of right angle is $$ 90^0 $$
$$ \therefore $$ required fraction $$ \Rightarrow \dfrac {90^0}{180^0} = \dfrac  { 90^0 \div  90^0}{ 180^0 \div 90^0 } = \dfrac {1}{2} $$


Animals: The label on a bottle of pet vitamins lists dosage guidelines. What dosage would you give to each of these animals? 
(a) a 18 kg adult dog
(b) a 6 kg cat
(c) a 18 kg pregnant dog


1903313_1790221_ans_a8eb75d30b964baba5175d2a2551e3e1.jpg


In the figure what is the ratio of the areas of shaded portion II to shaded portion III?



1789725_e513a7ac9b27490f8670354284d08bb8.png

$$\textbf{Step 1: Calculate the area of region I}$$
                                    Region $$\mathrm{I}$$ is in the shape of a square.
                                    Side of the square $$=5 \mathrm{~cm}$$
                                    Area of the region $$\mathrm{I}=$$ Area of the square
                                                                                  $$=$$ Side $$\times$$ side
                                                                                  $$=5 \mathrm{~cm} \times 5 \mathrm{~cm}$$
                                                                                  $$=25 \mathrm{sq} \mathrm{cm}$$

$$\textbf{Step 2 : Calculate the area of region III}$$
                                  $$\begin{aligned}\text { Area of the region III }=& \text { Area of the rectangle } \\&=\text { Length } \times \text { Breadth } \\&=7 \mathrm{~cm} \times 5 \mathrm{~cm} \\&=35 \mathrm{sq} \mathrm{cm}\end{aligned}$$

$$\textbf{Step 3: Calculate the area of region II}$$
Area of the shaded portion II $$=$$ Total Area- (Area of shaded portion I + Area of shaded portion III) 
                                               $$\begin{aligned}&=(10 \times 10) \mathrm{sqcm}-(35+25) \mathrm{sqcm} \\&=(100-60) \mathrm{sqcm} \\&=40 \mathrm{~sqcm}\end{aligned}$$

$$\begin{aligned}\text { Required ratio }=& \frac{\text { Area of region II } }{\text { Area of region III }} \\&=\frac{40 \mathrm{~sq} \mathrm{cm}}{35 \mathrm{~sq} \mathrm{cm}} \\&=\frac{8}{7}\end{aligned}$$

$$\therefore \textbf{Ratio of the areas of  shaded portion II to shaded portion III is 8 : 7}$$


In the figure what is the ratio of the areas of shaded portion I to shaded portion II?



1789724_c6fd78ba702f4f43a16c3e01fe3de999.png

$$\textbf{Step 1: Calculate the area of region I}$$
                                    Region $$\mathrm{I}$$ is in the shape of a square.
                                    Side of the square $$=5 \mathrm{~cm}$$
                                    Area of the region $$\mathrm{I}=$$ Area of the square
                                                                                  $$=$$ Side $$\times$$ side
                                                                                  $$=5 \mathrm{~cm} \times 5 \mathrm{~cm}$$
                                                                                  $$=25 \mathrm{sq} \mathrm{cm}$$

$$\textbf{Step 2 : Calculate the area of region III}$$
                                  $$\begin{aligned}\text { Area of the region III }=& \text { Area of the rectangle } \\&=\text { Length } \times \text { Breadth } \\&=7 \mathrm{~cm} \times 5 \mathrm{~cm} \\&=35 \mathrm{sq} \mathrm{cm}\end{aligned}$$

$$\textbf{Step 3: Calculate the area of region II}$$
Area of the shaded portion II $$=$$ Total Area- (Area of shaded portion I + Area of shaded portion III) 
                                               $$\begin{aligned}&=(10 \times 10) \mathrm{sqcm}-(35+25) \mathrm{sqcm} \\&=(100-60) \mathrm{sqcm} \\&=40 \mathrm{~sqcm}\end{aligned}$$

$$\begin{aligned}\text { Required ratio }=& \frac{\text { Area of region } 1}{\text { Area of region II }} \\&=\frac{25 \mathrm{~sq} \mathrm{cm}}{40 \mathrm{~sq} \mathrm{cm}} \\&=\frac{5}{8}\end{aligned}$$

$$\therefore \textbf{Ratio of the areas of  shaded portion I to shaded portion II is 5 : 8}$$


What fraction of each of the above figure is shaded?
1800545_98d4131f1af247f6b076568c25370e9e.png

(i) Fraction is $$\dfrac{2}{8}=\dfrac{1}{4}$$
(ii) Fraction is $$\dfrac{3}{10}$$
(iii) Fraction is $$\dfrac{5}{12}$$
(iv) Fraction is $$\dfrac{7}{13}$$


Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign <, =, > between the fractions:- 
1866652_dd70fe5933af4c6fa74b8245f23d529e.PNG

a) * Here, $$1^{st}$$ circle represents 3 shaded parts out of 8 equal parts. Therefore, it represents a fraction $$\dfrac{3}{8}$$  
* Here, $$2^{nd}$$ circle represents 6 shaded parts out of 8 equal parts. Therefore, it represents a fraction $$\dfrac{6}{8}$$ 
* Here, $$3^{rd}$$ circle represents 4 shaded parts out of 8 equal parts. Therefore, it represents a fraction $$\dfrac{4}{8}$$ 
* Here, $$4^{th}$$ circle represents 1 shaded parts out of 8 equal parts. Therefore, it represents a 1 fraction $$\dfrac{1}{8}$$ 
Now, these fractions may be arranged as 
$$\dfrac{1}{8} < \dfrac{3}{8} < \dfrac{4}{8} < \dfrac{6}{8}$$

b) * Here, $$1^{st}$$ square represents 8 shaded parts out of 9 equal parts Therefore, it represents a fraction $$\dfrac{8}{9}$$ 
* Here, $$2^{nd}$$ square represents 4 shaded parts out of 9 equal parts Therefore, it represents a fraction $$\dfrac{4}{9}$$ 
* Here, $$3^{rd}$$ square represents 3 shaded parts out of 9 equal parts Therefore, it represents a fraction $$\dfrac{3}{9}$$ 
* Here, $$4^{th}$$ square represents 6 shaded parts out of 9 equal parts Therefore, it represents a 6 fraction $$\dfrac{6}{9}$$ 
Now, these fractions can be arranged as
$$\dfrac{3}{9} < \dfrac{4}{9} < \dfrac{6}{9} < \dfrac{8}{9}$$ 

c) To represent the given fraction
$$\dfrac{2}{6}, \dfrac{4}{6}, \dfrac{8}{6}$$ and $$\dfrac{6}{6}$$ on number line, each unit length should be succeed in 6 equal parts Now, these fractions can be represented as.

$$\dfrac{5}{6} > \dfrac{2}{6}$$ 

$$\dfrac{3}{6} > 0$$

$$\dfrac{1}{6} > \dfrac{6}{6}$$

$$\dfrac{8}{6} > \dfrac{5}{6}$$


Evaluate the following:

$$\ (i) 7 \times \dfrac{3}{5}$$                      $$(ii) \ 21 \times \dfrac{3}{14}$$

$$(iii) \ 3\dfrac{2}{5} \times 8$$                   $$(iv) \ 5 \times 6 \dfrac{3}{4}$$

$$(i) \ 7 \times \dfrac{3}{5} = \dfrac{21}{5} = 4\dfrac{1}{5}$$

$$(ii) \ 21 \times \dfrac{3}{14} = \dfrac{9}{2} = 4\dfrac{1}{2}$$

$$(iii) \ 3 \dfrac{2}{5} \times 8 = \dfrac{17}{5} \times 8= \dfrac{136}{5}= 27 \dfrac{1}{5}$$

$$(iv) \ 5 \times 6 \dfrac{3}{4} = 5 \times \dfrac{27}{4} = \dfrac{135}{4} = 33 \dfrac{3}{4}$$


Write these fractions appropriately as additions or substractions:-
1866699_80141350e0504c5886c250be67ac34e6.png


1879485_1866699_ans_bc694a4960dc41448247bbbc69b3f0b5.png


Identify the error, if any 
1866451_2efd9849ad334e869c68ea26cd709547.png

 The given figures do not represent the given fractions as here each shape is not divided in equal parts. 


Write the fraction representing the shaded portion. 

1866422_c62a3e6642204ec9899d4419885961e3.PNG

i) The given figure represents 2 shaded parts out of 4 equal parts. Hence $$\frac{2}{4}$$
ii) The given figure represents 8 shaded parts out of 9 equal parts. Hence $$\frac{8}{9}$$
ii) The given figure represents 4 shaded parts out of 8 equal parts. Hence $$\frac{4}{8}$$
iv) The given figure represents 1 shaded parts out of 4 equal parts. Hence $$\frac{1}{4}$$
v) The given figure represents 3 shaded parts out of 7 equal parts. Hence $$\frac{3}{7}$$
vi) The given figure represents 3 shaded parts out of 12 equal parts. Hence $$\frac{3}{12}$$
vii) The given figure represents 10 shaded parts out of 10 equal parts. Hence $$\frac{10}{10}$$
viii) The given figure represents 4 shaded parts out of 9 equal parts. Hence $$\frac{4}{9}$$
ix) The given figure represents 4 shaded parts out of 8 equal parts. Hence $$\frac{4}{8}$$
x) The given figure represents 1 shaded parts out of 2 equal parts. Hence $$\frac{1}{2}$$


Write the fractions. Are all the these fractions equivalent?
1866614_c328bec912824b87ac2a3648e2809c9c.png

a) In the given circles, 1 out of 2, 2 out of 4, 3 out of 6, and 4 out of 8 equal part of shaded respectively. Therefore these circles represent. 
Also, all these fractions are equivalent. 
b) In the given rectangles, 4 out of 12, 3 out of 9, 2 out of 6, 1 out of 3, and 6 out of 15 equal parts (i.e, circles) are shaded respectively Therefore these rectangles represent, Not, not all of these fractions are equivalent. 


 What fraction of these circles have X's in them? 
1866499_6116e1eff7e6410a92afd07b3855a956.png

There are 4 circle, out of 8, having X's in them,.

Therefore it represents a fraction $$\dfrac{4}{8}$$

                                                        $$=\dfrac 12$$


Colour the part according to the given fraction.
1866434_af77b59bcda74b439e1bedc0821c0007.png


1877994_1866434_ans_51755dda49054937a26081144d2f2222.png


Write the fractions and pair up the equivalent fractions from each row. 
1866619_b48a2c2beba44f42bb3f77a361b23b94.png

a) Here, 1 parts is shaded out of 2 equal parts ( i,e., rectangle) Hence this, Figure represents a fraction $$\frac{1}{2}$$
b) Here, 4 parts is shaded out of 6 equal parts ( Le., rectangle) Hence this, Figure represents a fraction $$\frac{4}{6} = \frac{2}{3}$$
c) Here, 3 parts is shaded out of 9 equal parts ( he., rectangle) Hence this, Figure represents a fraction $$\frac{3}{9} = \frac{1}{3}$$
d) Here, 2 parts is shaded out of 8 equal parts ( Le., rectangle) Hence this, Figure represents a fraction $$\frac{2}{8} = \frac{1}{4}$$
e) Here,3 parts is shaded out of 4 equal parts ( Le., rectangle) Hence this, Figure represents a fraction $$\frac{3}{4}$$ 
i) Here,6 parts are shaded out of 18 equal parts (i.e, triangles) Hence, this figure represents a fraction $$\frac{6}{18} = \frac{1}{3}$$ 
ii) Here, 4 parts are shaded out of 8 equal parts (i,e, rectangle) Hence, this figure represents a fraction $$\frac{4}{8} = \frac{1}{2}$$
iii) Here, 12 parts are shaded out o f 16 equal parts (i.e , squares) Hence, this figure $$\frac{12}{16} = \frac{3}{6}$$
iv) Here, 8 parts are shaded out of 12 equal parts (i,e . rectangle) Hence, this figure represents a fraction $$\frac{8}{12} = \frac{2}{3}$$
v) Here,4 parts are shaded out of 16 equal parts (i,e , triangles) Hence, this figure represents a fraction $$\frac{4}{16} = \frac{1}{4}$$
Now these figures can be, matched correctly as (a)(ii), (b)(iv), (c)(i), (d)(v), (e)(iii). 


What fraction of a clock wise revolution does the hour hand of a clock turn through, when it goes from $$3$$ to $$9$$.

We may observe that in $$1$$ complete clock wise revolution the hour hand will rotate by $$360^{\circ}$$
When the hour hands goes from $$3$$ to $$9$$ clock wise, it will rotate by $$2$$ right angles or $$180^{\circ}$$
$$Fraction = \dfrac {180^{\circ}}{360^{\circ}} = \dfrac {1}{2}$$

1823256_1867317_ans_d4115f1e72484f07833961c22a574b54.png


Class 5 Maths Extra Questions