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NCERT Solutions for Class 7 Maths Chapter 2: Fractions and Decimals - Exercise 2.2

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NCERT Solutions for Class 7 Maths Chapter 2 (EX 2.2)

NCERT Solutions for Class 7 Maths Chapter exercise 2.2 can be easily availed and be quickly downloaded from Vedantu in secure PDF format. The subject is complicated for the young minds and can often lead to confusion; hence, the provided Solutions for exercise 2.2 Class 7 Maths becomes very important to help when required a reference. The experts from Vedantu have utilized their years of teaching experience to help students in need in the format of PDF, which can be downloaded in simple steps from their website. Subjects like Science, Maths, English will become easy to study if you have access to NCERT Solution for Class 7 Science, Maths solutions and solutions of other subjects. You can also download NCERT Solutions for Class 7 Maths to help you to revise complete syllabus and score more marks in your examinations.


Class:

NCERT Solutions for Class 7

Subject:

Class 7 Maths

Chapter Name:

Chapter 2 - Fractions and Decimals

Exercise:

Exercise - 2.2

Content-Type:

Text, Videos, Images and PDF Format

Academic Year:

2023-24

Medium:

English and Hindi

Available Materials:

  • Chapter Wise

  • Exercise Wise

Other Materials

  • Important Questions

  • Revision Notes

Access NCERT Solutions for Class 7 Maths Chapter 2 – Fractions and Decimals

Exercise - 2.2

1. Which of the drawings (a) to (d ) show: 

(i) $2 \times \dfrac{1}{5} $ 

(ii) $2 \times \dfrac{1}{2} $

(iii) $3 \times \dfrac{2}{3}$   

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

(a)


$2 \times \dfrac{1}{5} $


(b)


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


(c)


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


(d)


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


Ans:

(i) Given: $2 \times \dfrac{1}{5} $

We need to find which figure represent  the above expression.

We can write it as  

$2 \times \dfrac{1}{5} = \dfrac{1}{5} + \dfrac{1}{5}$

Fig(d)  represents two figures in which each figure  have\[1\] shaded part out of \[5\] equal parts .

So, we have $\dfrac{1}{5}$shaded part from both figures.

$ \Rightarrow \dfrac{1}{5} + \dfrac{1}{5} = 2 \times \dfrac{1}{5} $

Hence, Fig (d) represents $2 \times \dfrac{1}{5} $.


(ii) Given: $2 \times \dfrac{1}{2} $

We need to find which figure represent  the above expression.

We can write it as  

$2 \times \dfrac{1}{2} = \dfrac{1}{2} + \dfrac{1}{2}$

Fig(b) represents two figures in which each figure have 1 shaded part out of 2 equal parts.

So, we have $\dfrac{1}{2}$ shaded part from both figures.

$ \Rightarrow \dfrac{1}{2} + \dfrac{1}{2} = 2 \times \dfrac{1}{2}$

Hence, Fig(b) represents $2 \times \dfrac{1}{2}$.


(iii) Given: $3 \times \dfrac{2}{3}$

We need to find which figure represent  the above expression.

We can write it as  

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

Fig(a)  represents three figures in which each figure have \[2\] shaded parts out of \[3\]equal  parts .

So, we have $\dfrac{2}{3}$ shaded part from each figure.

$ \Rightarrow \dfrac{2}{3} + \dfrac{2}{3} + \dfrac{2}{3} = 3 \times \dfrac{2}{3}$

Hence, Fig (a) represents $3 \times \dfrac{2}{3}$.


(iv) Given: $3 \times \dfrac{1}{4}$

We need to find which figure represent  the above expression.

We can write it as  

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

Fig(c)  represents three figures in which each figure have \[1\] shaded part out of \[4\] equal parts .

So, we have $\dfrac{1}{4}$ shaded part from each figure.

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

Hence, Fig (c) represents $3 \times \dfrac{1}{4}$.


2. Some pictures (a) to (c) are given below. Tell which of them show:

(i)$3 \times \dfrac{1}{5} = \dfrac{3}{5}$         (ii) $2 \times \dfrac{1}{3} = \dfrac{2}{3}$       (iii) $3 \times \dfrac{3}{4} = 2\dfrac{1}{4}$

(a)


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


(b)


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


(c)


$3 \times \dfrac{3}{4} = 2\dfrac{1}{4}$


Ans: (i)Given:  $3 \times \dfrac{1}{5} = \dfrac{3}{5} $

We need to find which figure represent  the above expression.

We can write it as  

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

Fig(c)  represents three figures in which each figure have  $1 $ shaded part out of  $5 $ equal parts .

So, we have $\dfrac{1}{5}$ shaded part from each figure.

 $ \Rightarrow \dfrac{1}{5} + \dfrac{1}{5} + \dfrac{1}{5} = 3 \times \dfrac{1}{5} = \dfrac{3}{5} $

Hence, Fig (c) represents  $3 \times \dfrac{1}{5} = \dfrac{3}{5} $.


(ii) Given:  $2 \times \dfrac{1}{3} = \dfrac{2}{3} $

We need to find which figure represent  the above expression.

We can write it as  

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

Fig(a) represents two figures in which each figure have 1 shaded part out of  $3 $equal parts.

So, we have $\dfrac{1}{3} $ shaded part from both figures.

 $ \Rightarrow \dfrac{1}{3} + \dfrac{1}{3} = 2 \times \dfrac{1}{3} = \dfrac{2}{3} $

Hence, Fig(a) represents  $2 \times \dfrac{1}{3} = \dfrac{2}{3} $.


(iii) Given:  $3 \times \dfrac{3}{4} = 2\dfrac{1}{4} $

We need to find which figure represent  the above expression.

We can write it as  

 $ \Rightarrow 3 \times \dfrac{3}{4} = \dfrac{3}{4} + \dfrac{3}{4} + \dfrac{3}{4} $

Fig(b)  represents three figures in which each figure have  $3 $ shaded parts out of  $4 $ equal  parts .

So, we have $\dfrac{3}{4} $ shaded part from each figure.

 $ \Rightarrow \dfrac{3}{4} + \dfrac{3}{4} + \dfrac{3}{4} = 3 \times \dfrac{3}{4} $

Hence, Fig (b) represents  $3 \times \dfrac{3}{4} = 2\dfrac{1}{4} $.


3. Multiply and reduce to lowest form and convert into a mixed fraction:

(i)  $7 \times \dfrac{3}{5} $

Ans: Given:  $7 \times \dfrac{3}{5} $

We need to convert the given expression into a mixed fraction.

 Multiplication of Fraction rule is given by

Product of fraction  $ =  $(product of numerator)/(product of denominator)

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

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

 $ = \dfrac{7 \times 3}{5 \times 1}$   

 $= \dfrac{21}{5}$   

 $= 4\dfrac{1}{5}  $  $ \text{(because multiplication of fraction rule)} $


(ii)  $4 \times \dfrac{1}{3} $

Ans: Given:  $4 \times \dfrac{1}{3} $

We need  to convert given expression  into mixed fraction.

Multiplication of Fraction rule is given by

Product of fraction  $ =  $(product of numerator)/(product of denominator)

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

 $ = \dfrac{4 \times 1}{3}   $

 $= \dfrac{4}{3}   $

 $ = 1\dfrac{1}{3} $   $ \text{(because multiplication of fraction rule)} $


(iii)  $2 \times \dfrac{6}{7} $

Ans: Given:  $2 \times \dfrac{6}{7} $

We need  to convert given expression  into mixed fraction.

Multiplication of Fraction rule is given by

Product of fraction  $ =  $(product of numerator)/(product of denominator)

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

     

  $ = \dfrac{{2 \times 6}}{7} $  

     

  $ = \dfrac{12}{7}   $

     

  $ = 1\dfrac{5}{7}   $ $ \text{(because multiplication of fraction rule)} $

(iv)  $5 \times \dfrac{2}{9} $

Ans: Given:  $5 \times \dfrac{2}{9} $

We need to convert the given expression into a mixed fraction.

Multiplication of Fraction rule is given by

Product of fraction  $ =  $(product of numerator)/(product of denominator)

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

     

 $  = \dfrac{5 \times 2}{9}   $

     

  $ = \dfrac{10}{9}   $

     

  $ = 1\dfrac{1}{9}  $   $ \text{(because multiplication of fraction rule)} $


(v)  $\dfrac{2}{3} \times 4$

Ans: Given:  $\dfrac{2}{3} \times 4  $

We need  to convert given expression  into mixed fraction.

Multiplication of Fraction rule is given by

Product of fraction  $ =  $(product of numerator)/(product of denominator)

 $ \Rightarrow \dfrac{2}{3} \times 4   $

     

   $= \dfrac{{2 \times 4}}{3} $ 

   $= \dfrac{8}{3}   $

     

  $ = 2\dfrac{2}{3}  $ $ \text{(because multiplication of fraction rule)} $


(vi)  $ \dfrac{5}{2} \times 6 $

Ans: Given:  $5 \times \dfrac{2}{6} $

We need to convert the given expression into a mixed fraction.

Multiplication of Fraction rule is given by

Product of fraction  $ =  $(product of numerator)/(product of denominator)

 $\Rightarrow \dfrac{5}{2} \times 6$   

   $= 5 \times 3  $

   $ = 15 $  $ \text{(because multiplication of fraction rule)} $


(vii)  $11 \times \dfrac{4}{7} $

Ans: Given:  $11 \times \dfrac{4}{7} $

We need  to convert given expression  into mixed fraction.

Multiplication of Fraction rule is given by

Product of fraction  $ =  $(product of numerator)/(product of denominator)

 $\Rightarrow 11 \times \dfrac{4}{7}  $ 

     

  $ = \dfrac{11 \times 4}{7} $  

     

   $= \dfrac{44}{7} $  

     

  $ = 6\dfrac{2}{7} $ $ \text{(because multiplication of fraction rule)} $


(viii)  $20 \times \dfrac{4}{5} $

Ans: Given:  $20 \times \dfrac{4}{5} $

We need  to convert given expression  into mixed fraction.

Multiplication of Fraction rule is given by

Product of fraction  $ =  $(product of numerator)/(product of denominator)

 $\Rightarrow 20 \times \dfrac{4}{5}  $ 

     

   $= \dfrac{20 \times 4}{5}  $ 

     

  $ = 4 \times 4  $ 

     

  $ = 16 $ $ \text{(because multiplication of fraction rule)} $


(ix)  $13 \times \dfrac{1}{3} $

Ans: Given:  $13 \times \dfrac{1}{3} $

We need  to convert given expression  into mixed fraction.

Multiplication of Fraction rule is given by

Product of fraction  $ =  $(product of numerator)/(product of denominator)

 $\Rightarrow 13 \times \dfrac{1}{3}  $ 

     

  $ = \dfrac{13 \times 1}{3}  $ 

     

  $= \dfrac{13}{3}$   

     

  $ = 4\dfrac{1}{3} $  $ \text{(because multiplication of fraction rule)} $


(x)  $15 \times \dfrac{3}{5} $

Ans: Given : $15 \times \dfrac{3}{5} $

We need  to convert given expression  into mixed fraction.

Multiplication of Fraction rule is given by

Product of fraction  $ =  $(product of numerator)/(product of denominator)

 $\Rightarrow 15 \times \dfrac{3}{5}$   

   $ = \dfrac{{15 \times 3}}{5}$    

   $ = 3 \times 3$ 

   $ = 9 $  $ \text{(because multiplication of fraction rule)} $


4. Shade:

(i) $\dfrac{1}{2}$

of the circles in box

(ii) $\dfrac{2}{3}$

of the triangles in box

(iii) $\dfrac{3}{5}$

of the squares in box                                                 

(a)


$\dfrac{1}{2}$  of the circles in box


(b)


$\dfrac{2}{3}$  of the triangles in box


(c)



$\dfrac{3}{5}$  of the squares in box

Ans:

(i) Given: \[12\] circles in the box.

We need to shade $\dfrac{1}{2}$of the circles in the box.

As we know , there are \[12\] circles in the box.

$ \Rightarrow \dfrac{1}{2}$ of the \[12\] circles

$= \dfrac{1}{2} \times 12 $  

 $= 6\,\,circles\,\, $

Hence, we have to shade any \[6\]circles in the box.

(Image will be uploaded soon)


(ii) Given: \[9\] triangles in the box.

We need to shade $\dfrac{2}{3}\,$ of the triangles in the box.

As we know ,there are \[9\] triangles in the box.

$ \Rightarrow \dfrac{2}{3}\,\,of\,the\,\,9\,\,triangles   $

$ = \dfrac{2}{3} \times 9 $

$ = 6\,\,triangles   $

Hence, we have to shade any \[6\,\]triangles in the box.

(Image will be uploaded soon)


(iii) Given: \[15\] squares in the box.

We need to shade $\dfrac{3}{5}$ of the squares in the box.

As we know ,there are \[15\] squares in the box.

$ \Rightarrow \dfrac{3}{5}\,of\,the\,15\,\,squares   $

  $ = \dfrac{3}{5} \times 15   $ 

   $= \dfrac{3 \times 15}{5} $   

  $ = 3 \times 3   $

  $ = 9\,squares$

Hence, we have to shade any \[9\,\] squares in the box.

(Image will be uploaded soon)


5. Find:

(a) $\dfrac{1}{2}\,\,$of (i) \[24\] (ii) \[46\]

Ans:

 (i) \[24\]

We need to find $\dfrac{1}{2}\,$of  \[24\].

Multiplying $\dfrac{1}{2}\,$by \[24\],we get 

$= \dfrac{1}{2} \times 24   $

 $ = 12$

(ii) \[46\]

We need to find $\dfrac{1}{2}\,\,$ of  \[46\].

Multiplying $\dfrac{1}{2}\,$ by \[46\],we get 

$   = \dfrac{1}{2} \times 46   $

$   = 23 $


(b) $\dfrac{2}{3}$ of  (i) \[18\] (ii) \[27\]

Ans: (i) \[18\]

We need to find $\dfrac{2}{3}$ of  \[18\].

Multiplying  $\dfrac{2}{3}$by \[18\],we get 

$ = \dfrac{2}{3} \times 18  $ 

$ = 2 \times 6   $

  $ = 12 $


(ii) \[27\]

We need to find $\dfrac{2}{3}$of  \[27\].

Multiplying $\dfrac{2}{3}$ by \[18\],we get 

$  = \dfrac{2}{3} \times 27   $

$  = 2 \times 9   $

$   = 18 $


(c)  $\dfrac{3}{4}$ of (i) \[16\] (ii) \[36\]

Ans: 

(i) \[16\]

We need to find $\dfrac{3}{4}$ of  \[16\].

Multiplying $\dfrac{3}{4}$ by \[16\],we get 

$= \dfrac{3}{4} \times 16   $

$ = 3 \times 4 $ 

$  = 12  $ 


(ii) \[36\] We need to find  $\dfrac{3}{4}$ of  \[36\].

Multiplying $\dfrac{3}{4}$by \[36\],we get 

$= \dfrac{3}{4} \times 36 $  

$= 3 \times 9   $

$  = 27$


(d) $\dfrac{4}{5}$ of (i) \[20\] (ii) \[35\]

Ans: 

(i) \[20\]

We need to find  $\dfrac{4}{5}$ of  \[20\].

Multiplying $\dfrac{4}{5}$ by \[20\],we get 

$= \dfrac{4}{5} \times 20$   

 $= 4 \times 4   $

 $= 16 $


(ii) \[35\]

We need to find $\dfrac{4}{5}$ of  \[35\].

Multiplying $\dfrac{4}{5}$ by \[35\],we get 

$ = \dfrac{4}{5} \times 35 $

$ = 4 \times 7 $  

$= 28$


6. Multiply and express as a mixed fraction:

(a) \[3 \times 5\dfrac{1}{5}\]

Firstly we need to convert the given mixed fraction into improper fraction.

We take \[5\dfrac{1}{5}\] and multiply \[5\] by \[5\] and add \[1\],we get 

\[ = (5 \times 5) + 1 = 26\]

Using \[26\] as numerator ,we get 

\[5\dfrac{1}{5} = \dfrac{{26}}{5}\]

Now , \[3 \times 5\dfrac{1}{5}\]\[ = 3 \times \dfrac{{26}}{5}\]

$ = \dfrac{3 \times 26}{5}   $

$ = \dfrac{78}{5}   $ 

And  convert it into mixed fraction ,firstly  divide \[78\] by \[5\] and take remainder\[(3)\]as numerator and quotient\[(15)\] as whole number,we get

\[ = 15\dfrac{3}{5}\]


(b) \[5 \times 6\dfrac{3}{4}\]

Firstly we need to convert the given mixed fraction into improper fraction.

We take \[6\dfrac{3}{4}\] and multiply \[6\] by \[4\] and add \[3\],we get 

\[ = (6 \times 4) + 3 = 27\]

Using \[27\] as numerator ,we get 

\[6\dfrac{3}{4} = \dfrac{27}{4}\]

Now , \[5 \times 6\dfrac{3}{4} = 5 \times \dfrac{27}{4}\]

$= \dfrac{5 \times 27}{4} $  

$  = \dfrac{135}{4}$

And convert it into mixed fraction ,firstly  divide \[135\] by \[4\] and take remainder\[(3)\]as numerator and quotient \[(33)\] as whole number,we get

\[ = 33\dfrac{3}{4}\]


(c) \[7 \times 2\dfrac{1}{4}\]

Firstly we need to convert the given mixed fraction into improper fraction.

We take \[2\dfrac{1}{4}\] and multiply \[2\] by \[4\]and add \[1\],we get 

\[ = (2 \times 4) + 1 = 9\]

Using \[9\]as numerator ,we get 

\[2\dfrac{1}{4} = \dfrac{9}{4}\]

Now , \[7 \times 2\dfrac{1}{4} = 7 \times \dfrac{9}{4}\]

\[ = \dfrac{{63}}{4}\] 

And  convert it into mixed fraction ,firstly  divide \[63\] by \[4\] and take remainder\[(3)\]as numerator and quotient \[(15)\] as whole number,we get

\[ = 15\dfrac{3}{4}\]


(d) \[4 \times 6\dfrac{1}{3}\]

 Firstly we need to convert the given mixed fraction into improper fraction.

We take \[6\dfrac{1}{3}\] and multiply \[6\] by \[3\]and add \[1\],we get 

\[ = (6 \times 3) + 1 = 19\]

Using \[19\] as numerator ,we get 

\[6\dfrac{1}{3} = \dfrac{{19}}{3}\]

Now , \[4 \times 6\dfrac{1}{3} = 4 \times \dfrac{{19}}{3}\]

$ = \dfrac{4 \times 19}{3} $  

$= \dfrac{76}{3}    $

And  convert it into mixed fraction ,firstly  divide \[76\] by \[3\] and take remainder \[(1)\]as numerator and quotient \[(25)\] as whole number,we get

\[ = 25\dfrac{1}{3}\]


(e) \[3\dfrac{1}{4} \times 6\]

Firstly we need to convert the given mixed fraction into improper fraction.

We take \[3\dfrac{1}{4}\] and multiply \[3\] by \[4\]and add \[1\],we get 

\[ = (3 \times 4) + 1 = 13\]

Using \[13\] as numerator ,we get 

\[3\dfrac{1}{4} = \dfrac{{13}}{4}\]

Now , \[3\dfrac{1}{4} \times 6 = \dfrac{{13}}{4} \times 6\]

$ = \dfrac{13 \times 3}{2}   $

$ = \dfrac{39}{2} $  

And  convert it into mixed fraction ,firstly  divide \[39\] by \[2\] and take remainder \[(1)\]as numerator and quotient \[(19)\] as whole number,we get

\[ = 19\dfrac{1}{2}\]


(f) \[3\dfrac{2}{5} \times 8\]

Firstly we need to convert the given mixed fraction into improper fraction.

We take \[3\dfrac{2}{5}\] and multiply \[3\] by \[5\]and add \[2\],we get 

\[ = (3 \times 5) + 2 = 17\]

Using \[17\] as numerator ,we get 

\[3\dfrac{2}{5} = \dfrac{{17}}{5}\]

Now , \[3\dfrac{2}{5} \times 8 = \dfrac{{17}}{5} \times 8\]

$ = \dfrac{17 \times 8}{5}  $ 

 $= \dfrac{136}{5} $ 

And convert it into mixed fraction ,firstly  divide \[27\] by \[5\] and take remainder \[(1)\]as numerator and quotient \[(27)\] as whole number,we get

\[ = 27\dfrac{1}{5}\]


7. Find:

(a) $\dfrac{1}{2}$ of  (i) \[2\dfrac{3}{4}\] (ii) \[4\dfrac{2}{9}\]

Ans:

(i) \[2\dfrac{3}{4}\]

We need to find $\dfrac{1}{2}$ of  \[2\dfrac{3}{4}\].

Firstly we need to convert the given mixed fraction into improper fraction.

We take \[2\dfrac{3}{4}\] and multiply \[2\] by \[4\]and add \[3\],we get 

\[ = (2 \times 4) + 3 = 11\]

Using \[11\] as numerator ,we get 

\[2\dfrac{3}{4} = \dfrac{{11}}{4}\]

Now, $\dfrac{1}{2} \times 2\dfrac{3}{4} = \dfrac{1}{2} \times \dfrac{{11}}{4}$

Using Multiplication of Fraction rule ,which  is given by

Product of fraction \[ = \](product of numerator)/(product of denominator) ,we get 

\[ = \dfrac{{11}}{8}\] 

And convert it into mixed fraction ,firstly  divide \[11\] by \[8\] and take remainder \[(3)\] as numerator and quotient \[(1)\] as whole number,we get

\[ = 1\dfrac{3}{8}\]


(ii) \[4\dfrac{2}{9}\]

We need to find $\dfrac{1}{2}$ of  \[4\dfrac{2}{9}\].

Firstly we need to convert the given mixed fraction into improper fraction.

We take \[4\dfrac{2}{9}\] and multiply \[4\] by \[9\] and add \[2\],we get 

\[ = (4 \times 9) + 2 = 38\]

Using \[38\] as numerator ,we get 

\[4\dfrac{2}{9} = \dfrac{{38}}{9}\]

Now, $\dfrac{1}{2} \times 4\dfrac{2}{9} = \dfrac{1}{2} \times \dfrac{38}{9}$

Using Multiplication of Fraction rule which  is given by

Product of fraction \[ = \](product of numerator)/(product of denominator),we get 

\[ = \dfrac{{19}}{9}\] 

And convert it into mixed fraction ,firstly  divide \[19\] by \[9\] and take remainder \[(1)\] as numerator and quotient \[(2)\] as whole number,we get

\[ = 2\dfrac{1}{9}\]


(b) $\dfrac{5}{8}$ of (i) \[3\dfrac{5}{6}\]  (ii) \[9\dfrac{2}{3}\]

Ans:

(i) \[3\dfrac{5}{6}\]

We need to find $\dfrac{5}{8}$ of  \[3\dfrac{5}{6}\].

Firstly we need to convert the given mixed fraction into improper fraction.

We take \[3\dfrac{5}{6}\] and multiply \[3\] by \[6\] and add \[5\],we get 

\[ = (3 \times 6) + 5 = 23\]

Using \[23\] as numerator ,we get 

\[3\dfrac{5}{6} = \dfrac{{23}}{6}\]

Now, $\dfrac{5}{8} \times 3\dfrac{5}{6} = \dfrac{5}{8} \times \dfrac{{23}}{6}$

Using Multiplication of Fraction rule which  is given by

Product of fraction \[ = \](product of numerator)/(product of denominator),we get 

\[ = \dfrac{{115}}{{48}}\] 

And convert it into mixed fraction ,firstly  divide \[115\] by \[48\] and take remainder \[(19)\] as numerator and quotient \[(2)\] as whole number,we get

\[ = 2\dfrac{{19}}{{48}}\]


(ii) \[9\dfrac{2}{3}\]

We need to find $\dfrac{5}{8}$ of  \[9\dfrac{2}{3}\].

Firstly we need to convert the given mixed fraction into improper fraction.

We take \[9\dfrac{2}{3}\] and multiply \[9\] by \[3\] and add \[2\],we get 

\[ = (9 \times 3) + 2 = 29\]

Using \[29\] as numerator ,we get 

\[9\dfrac{2}{3} = \dfrac{{29}}{3}\]

Now, $\dfrac{5}{8} \times 9\dfrac{2}{3} = \dfrac{5}{8} \times \dfrac{{29}}{3}$

Using Multiplication of Fraction rule which  is given by

Product of fraction \[ = \](product of numerator)/(product of denominator),we get 

\[ = \dfrac{{145}}{{24}}\] 

And convert it into mixed fraction ,firstly  divide \[145\] by \[24\] and take remainder \[(1)\] as numerator and quotient \[(6)\] as whole number,we get

\[ = 6\dfrac{1}{{24}}\]


8.  Vidya and Pratap went for a picnic. Their mother gave them a water bottle that contained 5 litres of water. Vidya consumed $\dfrac{2}{5}$of the water. Pratap consumed the remaining water.

(i) How much water did Vidya drink?

(ii) What fraction of the total quantity of water did Pratap drink?

Ans:

Given: Total quantity of water in bottle = \[5\] litres

(i) We know, Vidya consumed =  $\dfrac{2}{5}$ of  \[5\] litres

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

  $ = 2   $ 

Therefore, Vidya drank 2 litres of water from the bottle.

(ii) We know , Pratap consumed the remaining fraction of water .

So, Pratap consumed \[ = (1 - \dfrac{2}{5})\] part of bottle

                                      \[ = \dfrac{{5 - 2}}{3}\]

                                      \[ = \dfrac{3}{5}\] part of bottle

Pratap consumed $\dfrac{3}{5}$ of \[5\] litres water \[ = \dfrac{3}{5} \times 5\]                                           

                                                            \[ = 3\] litres

Therefore, Pratap drank $\dfrac{3}{5}$ part of the total quantity of water.


Chapter 2 - Fractions and Decimals

An essential Chapter to create a strong foundation for mathematics and something wholly new and different for the students till now. Fractions and decimals have the necessary implications in our lives. From our daily activities such as buying groceries to doing the business of any commodity. NCERT Solutions for Class 7 Maths Chapter 2 covers the following topic:

  1. Introduction

  2. How well you have learned about fractions

  3. Multiplication of fractions

  4. Multiplication of a fraction by a whole number

  5. Exercise 2.2 Questions and Answers

  6. Multiplication of a Fraction by a Fraction

  7. Value of the Products

 

Introduction

You cannot have advance learning of mathematics if you do not understand the concepts of decimals and fractions. Many important concepts and calculations in mathematics are based on the concepts of decimals and fractions. It can be safely said that the entire modern mathematics would not have been possible without the notions of fractions and decimals. This chapter touches upon what you have learned previously about them, such as proper and improper fractions, how you formed mixed fractions. Then it touches upon how you were in previous lessons when you were taught to add such a combination of fractions or subtract them.

 

Then, the Chapter reminds you of the lessons about the types of fractions, such as equivalent fractions and comparison of it with fractions and its representation on a number line.

 

It takes you on a further journey to this concept. This chapter will teach you how to multiply a given set of fractions and decimals. Also, it will show you how to divide them.

 

How Well You Have Learned About Fractions

The teachers understand that the concept of the fraction is crucial for understanding mathematics, and not only that, it is also very essential to do everyday functions of life. The teachers do not want you not to be clear about them. So, this segment of the Chapter first defines ta proper fraction and tests students on their understanding through questions regarding numerator and denominator.

 

The segment moves on to define what is an improper fraction. After making the students understand what an improper fraction is, the section uses all these concepts to make the student understand mixed fractions. To further explain these, the Chapter gives innumerable examples involving various situations.

 

Then the Chapter moves to the section of the first exercise. The questions in this exercise have been created to test the student on his holistic understanding of the concepts taught until now. This exercise is essential for this makes sure you are ready for further concepts.

 

Once the students learn more about proper fractions, improper fractions, and mixed fractions, they will be required to solve many questions that are mentioned in the examples and exercises. This will help them to assess their understanding level when it comes to this section, and implement the right formulas wherever it is required. Therefore, it becomes important for the students to go through this section carefully and understand every aspect of the section thoroughly. 

 

Multiplication of Fractions

This part of the Chapter makes the student understand and help them do multiplication of fractions. Getting to know how to multiply fractions is essential and it is essential to understand more advanced mathematics you get promoted each year. From cooking to sports, from sewing to carpentry, it is impossible to escape fractions in daily life. This part teaches the Chapter teaches the student how to multiply the fractions utilize them to, for example, calculating areas of triangles.

 

The students will be asked to find out the area of a rectangle or a triangle. They will have to apply the right formula to get the right answer for the given question. For example, the students will be given a question that includes a rectangle that has length and breadth of 7cm and 4cm each respectively. The students have to find the area of the rectangle with the given numbers. To do this, you can refer to the examples that are given in the NCERT books and learn them properly. For calculating the area of the rectangle, you need to know the multiplication of fractions thoroughly. Once you know how to multiply fractions, it will be a piece of cake for you to find out the area of the given objects.

 

Multiplication of a Fraction by a Whole Number

This section of the Chapter from NCERT Class 7 Maths Chapter 2 exercise 2.2, teaches the student a new concept. The teachers realize that a fraction may not always multiply with another fraction. A fraction can also multiply with a whole number. So, this section focuses on teaching students to multiply fractions with numbers that are whole. The section uses multiple diagrams and presents numerous scenarios using this to make you completely understand how it works. 

 

Using the same process used above to teach the students how to multiply a fraction by another fraction; otherwise, the knowledge would remain incomplete. Once the student understands the concepts of multiplication, it would become more comfortable for the students to understand the concepts involving the division of fractions in different scenarios, such as division of a fraction by another fraction and division of a fraction by a whole number.

 

The use of decimals can also represent fractions. Decimals numbers are utilized to describe what is smaller than 1 unit. Section of the Chapter moves on to make the students learn the concepts of the decimal point. Decimal points are very much used by us all, in all areas of life. This section makes the student understand how to calculate numbers that have decimal points. The students are then tested on their skill of understanding and problem solving by given a set of questions to solve in the exercise regarding theirs. 

 

After teaching the student about the multiplication of decimal numbers, this Chapter, regarding fractions and decimals exercise 2.2, moves on to explain the student the technicalities about the multiplication of decimal points with numbers. The Chapter focuses on what happens if a decimal number is multiplied by whole numbers such as 10, 100, or 1000. In this Chapter, the student learns to depend on where the decimal point is placed in a given number; it can be converted to a fraction with a denominator of 10, 100, and so on. 

 

The Chapter shows to students through many examples of the shift of the decimal point when multiplied by numbers such as 10,100 or 1000. Then using these examples, the Chapter defines what is a decimal number so that it is crystal clear to the student. The Chapter then moves on to a small exercise to measure what the student has understood until now.

 

Once the Chapter makes the student understand the concept regarding the multiplication of decimal numbers, the Chapter moves on to the next important part. That is the division of the decimal number. The concepts regarding the fraction numbers would remain incomplete without the knowledge of how to convert them in decimals to help in the division of those numbers. 

 

Exercise 2.2 Questions and Answers

The part of the Chapter from exercise 2.2 Class 7 that comes after understanding the concept of division is the division of them by numbers of 10 and its multiple. This part teaches the students about how does the decimal point react when divided by such numbers. In this part, you can explore how the decimal point shifts towards the left, depending upon the value of the number it is getting divided from.

 

Once it is clear to the student of the nature of the decimal point and how it reacts in different situations such as when the number is multiplied or divided. This Chapter of Class 7 Maths Chapter 2 exercise 2.2 moves on to the segment where it teaches the student about the division of the decimal number by a whole number. The students will have to answer the questions mentioned in exercise 2.2 on the basis of their understanding and knowledge that they have gained.

 

Multiplication of a Fraction by a Fraction

This section will focus on making you learn how you can multiply a fraction with another fraction to find a solution for a given question. To find out the answers, the student needs to learn about specific products that will help them in understanding the concept behind this. They will learn about equal parts in a given fraction, how to differentiate it, how to divide the fractional numbers, and how you can find the shaded part in a given fraction. 

 

The students have to go through this section carefully and understand it thoroughly as it might be tricky for them when it comes to multiplying a fractional number with another fractional number. You can also try to solve the “Try These” questions that are mentioned in the NCERT books and also go through the examples correctly to understand the concept clearly. 

 

Value of the Products

This section will teach you how the product of adding or multiplying two whole numbers becomes a bigger number. It will show you to determine the value of the products when you are multiplying two fractions at the same time. To understand this, you must go through the section and guess what happens two proper fractions are multiplied with each other. You will also learn how multiplying two proper fractions can produce a product that is lesser than the fractions that you have multiplied. It will also teach you how to multiply two improper and proper fractions to get the value of the product. 

 

The section also helps you in differentiating the product that you have obtained by multiplying two improper fractions, two proper fractions, and one improper with appropriate fractions. In the examinations, the students will be asked to prove that how the value of the product is less when two proper fractions are multiplied. Similarly, they might be asked to determine that the value of the product is more when two improper fractions are multiplied with each other. Therefore, it becomes essential for the students to learn the multiplication process correctly and implement it correctly in a given question.

 

About Vedantu 

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