NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals

Exercise 2.1: Multiplication of Fractions

• Multiplying Fractions by Whole Numbers: Understanding how to multiply fractions by whole numbers.

• Multiplying Two Fractions: Learning the method to multiply two fractions.

• Multiplying Mixed Numbers: Converting mixed numbers to improper fractions and then multiplying them.

Exercise 2.2: Division of Fractions

• Reciprocal of a Fraction: Introduction to the concept of reciprocals.

• Dividing Fractions by Whole Numbers: Method to divide fractions by whole numbers using reciprocals.

• Dividing a Fraction by Another Fraction: Understanding the steps to divide one fraction by another fraction.

• Word Problems: Applying division of fractions to solve real-life problems.

Exercise 2.3: Multiplication of Decimal Numbers

This section in Maths Class 7 Chapter 2 covers the rules and methods for multiplying decimal numbers. It includes step-by-step instructions for aligning the decimal points and performing multiplication, followed by placing the decimal point in the product correctly. Practical examples and problems help reinforce the concept and provide practice in multiplying decimals in various contexts.

Exercise 2.4: Division of Decimal Numbers

This section focuses on dividing decimal numbers, explaining how to handle the decimal point in both the dividend and the divisor. It includes methods for converting the divisor into a whole number by multiplying both the dividend and the divisor by a power of ten. The section in Class 7 Fractions and Decimals provides numerous examples and exercises to practice the division of decimals, ensuring a clear understanding of the process.

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

Exercise - 2.1

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

(i). $\text{2 }\times \frac{\text{1}}{\text{5}}$

(a) 

Ans: corresponds to $\text{(d)}$  

Because,  $2\times \frac{1}{5}=\frac{1}{5}+\frac{1}{5}$                                                                

(ii). $\text{2 }\times \frac{\text{1}}{\text{2}}$

(b)

Ans: corresponds to $\text{(b)}$

Because, $2\times \frac{1}{2}=\frac{1}{2}+\frac{1}{2}$

(iii). $\text{3 }\times \frac{\text{2}}{\text{3}}$

(c)

Ans:  corresponds to $\text{(a)}$   

Because, $3\times \frac{2}{3}=\frac{2}{3}+\frac{2}{3}+\frac{2}{3}$ 

(iv). $\text{3 }\times \frac{\text{1}}{\text{4}}$

(d)

Ans: Corresponds to $\text{(c)}$

Because, $3\times \frac{1}{4}=\frac{1}{4}+\frac{1}{4}+\frac{1}{4}$ 

2. Some pictures $\left(\text{a}\right)\text{to}\left(\text{c}\right)$ are given below. Tell which of them show: 

(i). $\text{3 }\times \frac{\text{1}}{\text{5}}\text{=}\frac{\text{3}}{\text{5}}$

(a)

Ans: Corresponds to $\text{(c)}$                    

Because, $3\times \frac{1}{5}=\frac{1}{5}+\frac{1}{5}+\frac{1}{5}$  

(ii). $\text{2 }\times \frac{\text{1}}{\text{3}}\text{=}\frac{\text{2}}{\text{3}}$ 

(b)

Ans: Corresponds to $\text{(a)}$                   

Because, $2\times \frac{1}{3}=\frac{1}{3}+\frac{1}{3}$ 

(iii). $\text{3 }\times \frac{\text{3}}{\text{4}}\text{=2}\frac{\text{1}}{\text{4}}$

(c)

Ans: Corresponds to $\text{(b)}$                  

Because, $3\times \frac{3}{4}=\frac{3}{4}+\frac{3}{4}+\frac{3}{4}$      

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

(i). $\text{7 }\times \frac{\text{3}}{\text{5}}$        

Ans: Multiplying and reducing to lowest form and converting into a mixed fraction,   

$7\times \frac{3}{5}=\frac{7\times 3}{5}=\frac{21}{5}=4\frac{1}{5}$

(ii). $\text{4 }\times \frac{\text{1}}{\text{3}}$ 

Ans: Multiplying and reducing to lowest form and converting into a mixed fraction,

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

(iii). $\text{2 }\times \frac{\text{6}}{\text{7}}$    

Ans: Multiplying and reducing to lowest form and converting into a mixed fraction,

$2\times \frac{6}{7}=\frac{2\times 6}{7}=\frac{12}{7}=1\frac{5}{7}$       

(iv). $\text{5 }\times \frac{\text{2}}{\text{9}}$ 

Ans: Multiplying and reducing to lowest form and converting into a mixed fraction,

$5\times \frac{2}{9}=\frac{5\times 2}{9}=\frac{10}{9}=1\frac{1}{9}$

(v). $\frac{\text{2}}{\text{3}}\times \text{ 4}$     

Ans: Multiplying and reducing to lowest form and converting into a mixed fraction,

$\frac{2}{3}\times 4=\frac{2\times 4}{3}=\frac{8}{3}=2\frac{2}{3}$   

(vi)  $\frac{\text{5}}{\text{2}}\times \text{ 6}$    

Ans: Multiplying and reducing to lowest form and converting into a mixed fraction,

$\frac{5}{2}\times 6=5\times 3=15$

(vii)   $\text{11 }\times \frac{\text{4}}{\text{7}}$    

Ans: Multiplying and reducing to lowest form and converting into a mixed fraction,

$11\times \frac{4}{7}=\frac{11\times 4}{7}=\frac{44}{7}=6\frac{2}{7}$ 

(viii)  $\text{20 }\times \frac{\text{4}}{\text{5}}$ 

Ans: Multiplying and reducing to lowest form and converting into a mixed fraction,

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

(ix)  $\text{13 }\times \frac{\text{1}}{\text{3}}$      

Ans: Multiplying and reducing to lowest form and converting into a mixed fraction,    

$13\times \frac{1}{3}=\frac{13\times 1}{3}=\frac{13}{3}=4\frac{1}{3}$ 

(x)  $\text{15 }\times \frac{\text{3}}{\text{5}}$ 

Ans: Multiplying and reducing to lowest form and converting into a mixed fraction,   

$15\times \frac{3}{5}=3\times 3=9$                

4. Shade: 

(i). $\frac{\text{1}}{\text{2}}$ of the circles in box

(ii).

Ans: Half of the circles in the box are,

$\frac{\text{1}}{\text{2}}\text{of}\text{12}\text{circles=}\frac{\text{1}}{\text{2}}\times \text{ 12=6}\text{circles}$

(iii). $\frac{\text{2}}{\text{3}}$ of the triangles in box 

(b)

Ans: Two-third of the triangles in the box are,$\frac{\text{2}}{\text{3}}\text{of}\text{9}\text{triangles=}\frac{\text{2}}{\text{3}}\times \text{ 9=2 }\times \text{ 3=6}\text{triangles}$

(iv). $\frac{\text{3}}{\text{5}}$ of the squares inbox

(v). (c)

Ans: Three-fifth of the squares in the box are,

$\frac{\text{3}}{\text{5}}\text{of}\text{15}\text{squares=}\frac{\text{3}}{\text{5}}\times \text{ 15=3 }\times \text{ 3=9}\text{squares}$

5. Find

(a).$\frac{\text{1}}{\text{2}}\text{of}\text{(i)}\text{24}\text{(ii)}\text{46}$

Ans:

(i) Calculating the value,

$\frac{\text{1}}{\text{2}}\text{of}\text{24=12}$

(ii) Calculating the value,

$\frac{\text{1}}{\text{2}}\text{of}\text{46=23}$ 

(b). $\frac{\text{2}}{\text{3}}\text{of}\text{(i)}\text{18}\text{(ii)}\text{27}$ 

Ans:

(i) Calculating the value, $\frac{\text{2}}{\text{3}}\text{of}\text{18=}\frac{\text{2}}{\text{3}}\times \text{ 18=2 }\times \text{ 6=12}$

(ii) Calculating the value, $\frac{\text{2}}{\text{3}}\text{of}\text{27=}\frac{\text{2}}{\text{3}}\times \text{ 27=2 }\times \text{ 9=18}$ 

(c)  $\frac{\text{3}}{\text{4}}\text{of}\text{(i)}\text{16}\text{(ii)}\text{36}$          

Ans:

(i) Calculating the value,

$\frac{\text{3}}{\text{4}}\text{of}\text{16=}\frac{\text{3}}{\text{4}}\times \text{ 16=3 }\times \text{ 4=12}$

(ii) Calculating the value,

$\frac{\text{3}}{\text{4}}\text{of}36\text{=}\frac{\text{3}}{\text{4}}\times \text{ 36=3 }\times \text{ 9=27}$  

(d)  $\frac{\text{4}}{\text{5}}\text{of}\text{(i)}\text{20}\text{(ii)}\text{35}$ 

Ans:

(i) Calculating the value,

$\frac{\text{4}}{\text{5}}\text{of}20\text{=}\frac{\text{4}}{\text{5}}\times \text{ 20=4 }\times \text{ 4=16}$

(ii) Calculating the value,

$\frac{\text{4}}{\text{5}}\text{of}35\text{=}\frac{\text{4}}{\text{5}}\times \text{ 35=4 }\times \text{ 7=28}$ 

6.   Multiply and express as a mixed fraction:

(a)  $\text{3 }\times \text{ 5}\frac{\text{1}}{\text{5}}$       

Ans: Multiplying and expressing the term as mixed fraction,

$3\times 5\frac{1}{5}=3\times \frac{26}{5}=\frac{3\times 26}{5}=\frac{78}{5}=15\frac{3}{5}$

(b) $\text{5 }\times \text{ 6}\frac{\text{3}}{\text{4}}$          

Ans: Multiplying and expressing the term as mixed fraction,

$5\times 6\frac{3}{4}=5\times \frac{27}{4}=\frac{5\times 27}{4}=\frac{135}{4}=33\frac{3}{4}$ 

(c) $\text{7 }\times \text{ 2}\frac{\text{1}}{\text{4}}$

Ans: Multiplying and expressing the term as mixed fraction,

$7\times 2\frac{1}{4}=7\times \frac{9}{4}=\frac{7\times 9}{4}=\frac{63}{4}=15\frac{3}{4}$        

(d)  $\text{4 }\times \text{ 6}\frac{\text{1}}{\text{3}}$ 

Ans: Multiplying and expressing the term as mixed fraction,

$4\times 6\frac{1}{3}=4\times \frac{19}{3}=\frac{4\times 19}{3}=\frac{76}{3}=25\frac{1}{3}$ 

(e)  $\text{3}\frac{\text{1}}{\text{4}}\times \text{ 6}$ 

Ans: Multiplying and expressing the term as mixed fraction,

$3\frac{1}{4}\times 6=\frac{13}{4}\times 6=\frac{13\times 3}{2}=\frac{39}{2}=19\frac{1}{2}$  

(f)  $\text{3}\frac{\text{2}}{\text{5}}\times \text{ 8}$ 

Ans: Multiplying and expressing the term as mixed fraction,

$3\frac{2}{5}\times 8=\frac{17}{5}\times 8=\frac{17\times 8}{5}=\frac{136}{5}=27\frac{1}{5}$

7. Find:

(a)  $\frac{\text{1}}{\text{2}}\text{of}\text{(i)}\text{2}\frac{\text{3}}{\text{4}}\text{(ii)}\text{4}\frac{\text{2}}{\text{9}}$             

Ans:

(i) Calculating the value, $$\frac{\text{1}}{\text{2}}\text{of}\text{2}\frac{\text{3}}{\text{4}}\text{=}\frac{\text{1}}{\text{2}}\times \text{ 2}\frac{\text{3}}{\text{4}}\text{=}\frac{\text{1}}{\text{2}}\times \frac{\text{11}}{\text{4}}\text{=}\frac{\text{11}}{\text{8}}\text{=1}\frac{\text{3}}{\text{8}}$$ 

(ii) Calculating the value, $$\frac{\text{1}}{\text{2}}\text{of}\text{4}\frac{\text{2}}{\text{9}}\text{=}\frac{\text{1}}{\text{2}}\times \text{ 4}\frac{\text{2}}{\text{9}}\text{=}\frac{\text{1}}{\text{2}}\times \frac{\text{38}}{\text{9}}\text{=}\frac{\text{19}}{\text{9}}\text{=2}\frac{\text{1}}{\text{9}}$$ 

(b)  $\frac{\text{5}}{\text{8}}\text{of}\text{(i)}\text{3}\frac{\text{5}}{\text{6}}\text{(ii)}\text{9}\frac{\text{2}}{\text{3}}$ 

Ans:

(i) Calculating the value, $$\frac{\text{5}}{\text{8}}\text{of}\text{3}\frac{\text{5}}{\text{6}}\text{=}\frac{\text{5}}{\text{8}}\times \text{ 3}\frac{\text{5}}{\text{6}}\text{=}\frac{\text{5}}{\text{8}}\times \frac{\text{23}}{\text{6}}\text{=}\frac{\text{115}}{\text{48}}\text{=2}\frac{\text{19}}{\text{48}}$$ 

(ii) Calculating the value, $$\frac{\text{5}}{\text{8}}\text{of}\text{9}\frac{\text{2}}{\text{3}}\text{=}\frac{\text{5}}{\text{8}}\times \text{ 9}\frac{\text{2}}{\text{3}}\text{=}\frac{\text{5}}{\text{8}}\times \frac{\text{29}}{\text{3}}\text{=}\frac{\text{145}}{\text{24}}\text{=6}\frac{\text{1}}{\text{24}}$$ 

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

(i). How much water did Vidya drink?

Ans:   Water consumed by Vidya is,$\text{=}\frac{\text{2}}{\text{5}}\text{of}\text{5}\text{litres=}\frac{\text{2}}{\text{5}}\times \text{ 5=2}\text{litres}$ 

Hence, Vidya drank $2$ litres of water from the bottle.

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

Ans: Water consumed by Pratap $$\text{= }\left(\text{1-}\frac{\text{2}}{\text{5}}\right)$$part of bottle

Pratap consumed $\frac{\text{3}}{\text{5}}\text{of}\text{5}\text{litres}\text{water=}\frac{\text{3}}{\text{5}}\times \text{ 5=3}\text{lites}$ 

Hence, Pratap drank $\frac{3}{5}$ part of the total quantity of water present in the bottle.

Exercise - 2.2

1. Find:

(i) $\frac{\text{1}}{\text{4}}\text{of}$ (a) $\frac{\text{1}}{\text{4}}$ (b) $\frac{\text{3}}{\text{5}}$ (c) $\frac{\text{4}}{\text{3}}$ 

Ans:

(a) Calculating the value,

$\frac{\text{1}}{\text{4}}\text{of}\frac{\text{1}}{\text{4}}\text{=}\frac{\text{1}}{\text{4}}\times \frac{\text{1}}{\text{4}}\text{=}\frac{\text{1 }\times \text{ 1}}{\text{4 }\times \text{ 4}}\text{=}\frac{\text{1}}{\text{16}}$ 

(b) Calculating the value,

$\frac{\text{1}}{\text{4}}\text{of}\frac{\text{3}}{\text{5}}\text{=}\frac{\text{1}}{\text{4}}\times \frac{\text{3}}{\text{4}}\text{=}\frac{\text{1 }\times \text{ 3}}{\text{4 }\times \text{ 4}}\text{=}\frac{\text{3}}{\text{16}}$ 

(c) Calculating the value,

$\frac{\text{1}}{\text{4}}\text{of}\frac{\text{4}}{\text{3}}\text{=}\frac{\text{1}}{\text{4}}\times \frac{\text{4}}{\text{3}}\text{=}\frac{\text{1 }\times \text{ 4}}{\text{4 }\times \text{ 3}}\text{=}\frac{\text{1}}{\text{3}}$ 

(ii) $$\frac{\text{1}}{\text{7}}\text{of}$$ (a) $$\frac{\text{2}}{\text{9}}$$ (b) $$\frac{\text{6}}{\text{5}}$$ (c) $\frac{\text{3}}{\text{10}}$ 

Ans:

(a) Calculating the value,

$\frac{\text{1}}{\text{7}}\text{of}\frac{\text{2}}{\text{9}}\text{=}\frac{\text{1}}{\text{7}}\times \frac{\text{2}}{\text{9}}\text{=}\frac{\text{1 }\times \text{ 2}}{\text{7 }\times \text{ 9}}\text{=}\frac{\text{2}}{\text{63}}$ 

(b) Calculating the value,

$\frac{\text{1}}{\text{7}}\text{of}\frac{\text{2}}{\text{9}}\text{=}\frac{\text{1}}{\text{7}}\times \frac{\text{6}}{\text{5}}\text{=}\frac{\text{1 }\times \text{ 6}}{\text{7 }\times \text{ 5}}\text{=}\frac{\text{6}}{\text{35}}$ 

(c) Calculating the value,

$\frac{\text{1}}{\text{7}}\text{of}\frac{\text{2}}{\text{9}}\text{=}\frac{\text{1}}{\text{7}}\times \frac{\text{3}}{\text{10}}\text{=}\frac{\text{1 }\times \text{ 3}}{\text{7 }\times \text{ 10}}\text{=}\frac{3}{70}$ 

2. Multiply and reduce to lowest form (if possible):

(i) $\frac{\text{2}}{\text{3}}\times \text{ 2}\frac{\text{2}}{\text{3}}$ 

Ans: Multiplying and reducing to lowest form,  

$\frac{2}{3}\times 2\frac{2}{3}=\frac{2}{3}\times \frac{8}{3}=\frac{2\times 8}{3\times 3}=\frac{16}{9}=1\frac{7}{9}$ 

(ii) $\frac{\text{2}}{\text{7}}\times \frac{\text{7}}{\text{9}}$

Ans: Multiplying and reducing to lowest form,  

$\frac{2}{7}\times \frac{7}{9}=\frac{2\times 7}{7\times 9}=\frac{2}{9}$

(iii) $\frac{\text{3}}{\text{8}}\times \frac{\text{6}}{\text{4}}$ 

Ans: Multiplying and reducing to lowest form, 

$\frac{3}{8}\times \frac{6}{4}=\frac{3\times 6}{8\times 4}=\frac{3\times 3}{8\times 2}=\frac{9}{16}$

(iv) $\frac{\text{9}}{\text{5}}\times \frac{\text{3}}{\text{5}}$ 

Ans: Multiplying and reducing to lowest form, 

$\frac{9}{5}\times \frac{3}{5}=\frac{9\times 3}{5\times 5}=\frac{27}{25}=1\frac{2}{25}$

(v) $\frac{\text{1}}{\text{3}}\times \frac{\text{15}}{\text{8}}$ 

Ans: Multiplying and reducing to lowest form,

$\frac{1}{3}\times \frac{15}{8}=\frac{1\times 15}{3\times 8}=\frac{1\times 5}{1\times 8}=\frac{5}{8}$

(vi) $\frac{\text{11}}{\text{2}}\times \frac{\text{3}}{\text{10}}$ 

Ans: Multiplying and reducing to lowest form,  

$\frac{11}{2}\times \frac{3}{10}=\frac{11\times 3}{2\times 10}=\frac{33}{20}=1\frac{3}{20}$ 

(vii) $\frac{\text{4}}{\text{5}}\times \frac{\text{12}}{\text{7}}$ 

Ans: Multiplying and reducing to lowest form,  

$\frac{4}{5}\times \frac{12}{7}=\frac{4\times 12}{5\times 7}=\frac{48}{35}=1\frac{13}{35}$

3. Multiply the following fractions:

(i) $\frac{\text{2}}{\text{5}}\times \text{ 5}\frac{\text{1}}{\text{4}}$

Ans: Performing multiplication,

$\frac{2}{5}\times 5\frac{1}{4}=\frac{2}{5}\times \frac{21}{4}=\frac{2\times 21}{5\times 4}=\frac{1\times 21}{5\times 2}=\frac{21}{10}=2\frac{1}{10}$ 

(ii) $\text{6}\frac{\text{2}}{\text{5}}\times \frac{\text{7}}{\text{9}}$ 

Ans: Performing multiplication,

$6\frac{2}{5}\times \frac{7}{9}=\frac{32}{5}\times \frac{7}{9}=\frac{32\times 7}{5\times 9}=\frac{224}{45}=4\frac{44}{45}$

(iii) $\frac{\text{3}}{\text{2}}\times \text{ 5}\frac{\text{1}}{\text{3}}$ 

Ans: Performing multiplication,

$\frac{3}{2}\times 5\frac{1}{3}=\frac{3}{2}\times \frac{16}{3}=\frac{48}{6}=8$ 

(iv) $\frac{\text{5}}{\text{6}}\times \text{ 2}\frac{\text{3}}{\text{7}}$ 

Ans: Performing multiplication,

$\frac{5}{6}\times 2\frac{3}{7}=\frac{5}{6}\times \frac{17}{7}=\frac{85}{42}=2\frac{1}{42}$ 

(v) $\text{3}\frac{\text{2}}{\text{5}}\times \frac{\text{4}}{\text{7}}$

Ans: Performing multiplication,

$3\frac{2}{5}\times \frac{4}{7}=\frac{17}{7}\times \frac{4}{7}=\frac{68}{35}=1\frac{33}{35}$

(vi) $\text{2}\frac{\text{3}}{\text{5}}\times \text{ 3}$ 

Ans: Performing multiplication,

$2\frac{3}{5}\times 3=\frac{13}{5}\times \frac{3}{1}=\frac{13\times 3}{5\times 1}=\frac{39}{5}=7\frac{4}{5}$

(vii) $\text{3}\frac{\text{4}}{\text{7}}\times \frac{\text{3}}{\text{5}}$ 

Ans: Performing multiplication,

$3\frac{4}{7}\times \frac{3}{5}=\frac{25}{7}\times \frac{3}{5}=\frac{5\times 3}{7\times 1}=\frac{15}{7}=2\frac{1}{7}$

4. Which is greater:

(i) $\frac{\text{2}}{\text{7}}\text{of}\frac{\text{3}}{\text{4}}\text{or}\frac{\text{3}}{\text{5}}\text{of}\frac{\text{5}}{\text{8}}$

Ans: Calculating the greater term,

$\frac{\text{2}}{\text{7}}\text{of}\frac{\text{3}}{\text{4}}\text{or}\frac{\text{3}}{\text{5}}\text{of}\frac{\text{5}}{\text{8}}$                

$\Rightarrow \frac{\text{2}}{\text{7}}\times \frac{\text{3}}{\text{4}}\text{or}\frac{\text{3}}{\text{5}}\times \frac{\text{5}}{\text{8}}$ 

$\Rightarrow \frac{\text{3}}{\text{14}}\text{or}\frac{\text{3}}{\text{8}}$

$\Rightarrow \frac{3}{14}<\frac{3}{8}$ 

Hence, $\frac{\text{3}}{\text{5}}\text{of}\frac{\text{5}}{\text{8}}$ is greater.

(ii) $\frac{\text{1}}{\text{2}}\text{of}\frac{\text{6}}{\text{7}}\text{or}\frac{\text{2}}{\text{3}}\text{of}\frac{\text{3}}{\text{7}}$ 

Ans:

Calculating the greater term,

$\frac{\text{1}}{\text{2}}\text{of}\frac{\text{6}}{\text{7}}\text{or}\frac{\text{2}}{\text{3}}\text{of}\frac{\text{3}}{\text{7}}$                

$\Rightarrow \frac{\text{1}}{\text{2}}\times \frac{\text{6}}{\text{7}}\text{or}\frac{\text{2}}{\text{3}}\times \frac{\text{3}}{\text{7}}$ 

$\Rightarrow \frac{\text{6}}{\text{14}}\text{or}\frac{\text{2}}{\text{7}}$ $\Rightarrow \frac{\text{6}}{\text{14}}>\frac{\text{2}}{\text{7}}$ 

Hence, $\frac{\text{1}}{\text{2}}\text{of}\frac{\text{6}}{\text{7}}$ is greater.

5. Saili plants $$\text{4}$$ saplings in a row in her garden. The distance between

two adjacent saplings is $$\frac{\text{3}}{\text{4}}$$ m. Find the 

distance between the first and the last sapling. 

Ans: Given: Saili plants $$4$$ saplings in a row where the distance between two 

adjacent saplings $=\frac{3}{4}$m.

The number of gaps in saplings $$=3$$ 

Hence, 

The distance between the first and the last saplings$\text{=3 }\times \frac{\text{3}}{\text{4}}\text{=}\frac{\text{9}}{\text{4}}\text{m=2}\frac{\text{1}}{\text{4}}\text{m}$

Therefore, the distance between the first and the last saplings is $\text{2}\frac{\text{1}}{\text{4}}\text{m}$

6. Lipika reads a book for $\text{1}\frac{\text{3}}{\text{4}}$ hours every day. 

She reads the entire book in $$\text{6}$$ days. How many hours in all were 

required by her to read the book?

Ans: Given: Time taken for reading a book by Lipika $=1\frac{3}{4}$ hours.

Lipika reads the entire book in $6$ days

Calculating the Total hours taken by Lipika to read the entire book,

$=1\frac{3}{4}\times 6=\frac{7}{4}\times 6=\frac{21}{2}=10\frac{1}{2}$ hours.

Hence, it would take $10$ hours to read the book.

7. A car runs $\text{16}$ km using $$\text{1}$$ litre of petrol. How much 

distance will it cover using   $\text{2}\frac{\text{3}}{\text{4}}$ litres of 

petrol?

Ans: Given: A car covers the distance$\text{=16}\text{km}$ in $1$ litre of 

petrol.

Calculating the distance covered by car in $2\frac{3}{4}$ litres of petrol,

Distance$\text{=2}\frac{\text{3}}{\text{4}}\text{of}\text{16}\text{km=}\frac{\text{11}}{\text{4}}\times \text{ 16=44}\text{km}$

Therefore, car will cover a distance of $44$ km in $2\frac{3}{4}$ litres of petrol.

8. (a)

(i) Provide the number in the box , such that 

$\frac{\text{2}}{\text{3}}\times \text{=}\frac{\text{10}}{\text{30}}$ 

Ans: The number inside the box should be $\frac{2}{3}\times =\frac{10}{30}$ 

(ii) The simplest form of the number obtained in $$ is _____.

Ans: The simplest form of the number obtained in 

$\frac{\text{5}}{\text{10}}\text{is}\frac{\text{1}}{\text{2}}$

(b) 

(i) Provide the number in the box $$ , such that $\frac{3}{5}\times =\frac{24}{75}$.

Ans: The number inside the box should be $\frac{3}{5}\times =\frac{24}{75}$ 

(ii) The simplest form of the number obtained in is______.

Ans: The simplest form of the number obtained in 

$\frac{\text{8}}{\text{15}}\text{is}\frac{\text{8}}{\text{15}}$

Exercise - 2.3

1. Find:

(i) $\text{12 }÷\frac{\text{3}}{\text{4}}$ 

Ans: Calculating the value,

$12÷\frac{3}{4}=12\times \frac{4}{3}=16$

(ii) $\text{14 }÷\frac{\text{5}}{\text{6}}$ 

Ans: Calculating the value,

$14÷\frac{5}{6}=14\times \frac{6}{5}=\frac{84}{5}=16\frac{4}{5}$ 

(iii) $\text{8 }÷\frac{\text{7}}{\text{3}}$ 

Ans:  Calculating the value,

$8÷\frac{7}{3}=8\times \frac{3}{7}=\frac{24}{7}=3\frac{3}{7}$

(iv) $\text{4 }÷\frac{\text{8}}{\text{3}}$ 

Ans: Calculating the value,

$4÷\frac{8}{3}=4\times \frac{3}{8}=\frac{3}{2}=1\frac{1}{2}$

(v) $\text{3 }÷\text{ 2}\frac{\text{1}}{\text{3}}$ 

Ans: Calculating the value,

$3÷2\frac{1}{3}=3÷\frac{7}{3}=3\times \frac{3}{7}=\frac{9}{7}=1\frac{2}{7}$           

(vi) $$\text{5 }÷\text{ 3}\frac{\text{4}}{\text{7}}$$ 

Ans: Calculating the value,

$5÷3\frac{4}{7}=5÷\frac{25}{7}=5\times \frac{7}{25}=\frac{7}{5}=1\frac{2}{5}$

2. Find the reciprocal of each of the following fractions. Classify the 

reciprocals as proper fraction, improper fractions and whole numbers.

(i) $\frac{\text{3}}{\text{7}}$

Ans: Calculating the reciprocal and stating the type of the fraction,

Reciprocal of $\frac{\text{3}}{\text{7}}\text{=}\frac{\text{7}}{\text{3}}\to \text{Improper}\text{fraction}$  

(ii) $\frac{\text{5}}{\text{8}}$

Ans: Calculating the reciprocal and stating the type of the fraction,

Reciprocal of$\frac{\text{5}}{\text{8}}\text{=}\frac{\text{8}}{\text{5}}\to \text{Improper}\text{fraction}$

(iii) $\frac{\text{9}}{\text{7}}$

Ans: Calculating the reciprocal and stating the type of the fraction,

Reciprocal of $\frac{\text{9}}{\text{7}}\text{=}\frac{\text{7}}{\text{9}}\to \text{Proper}\text{fraction}$

(iv) $\frac{\text{6}}{\text{5}}$ 

Ans: Calculating the reciprocal and stating the type of the fraction,

Reciprocal of $\frac{\text{6}}{\text{5}}\text{=}\frac{\text{5}}{\text{6}}\to \text{Proper}\text{fraction}$

(v) $\frac{\text{12}}{\text{7}}$ 

Ans: Calculating the reciprocal and stating the type of the fraction,

Reciprocal of $\frac{\text{12}}{\text{7}}\text{=}\frac{\text{7}}{\text{12}}\to \text{Proper}\text{fraction}$  

(vi) $\frac{\text{1}}{\text{8}}$

Ans: Calculating the reciprocal and stating the type of the fraction,

Reciprocal of $\frac{\text{9}}{\text{7}}\text{=8}\to \text{Whole number}$

(vii) $\frac{\text{1}}{\text{11}}$ 

Ans: Calculating the reciprocal and stating the type of the fraction,

Reciprocal of $\frac{\text{1}}{\text{11}}\text{=11}\to \text{Whole number}$

3. Find:

(i) $\frac{\text{7}}{\text{3}}÷\text{ 2}$ 

Ans: Calculating the value,

$\frac{7}{3}÷2=\frac{7}{3}\times \frac{1}{2}=\frac{7\times 1}{3\times 2}=\frac{7}{6}=1\frac{1}{6}$

(ii) $\frac{\text{4}}{\text{9}}÷\text{ 5}$

Ans: Calculating the value,

$\frac{4}{9}÷5=\frac{4}{9}\times \frac{1}{5}=\frac{4\times 1}{9\times 5}=\frac{4}{45}$ 

(iii) $\frac{\text{6}}{\text{13}}÷\text{ 7}$ 

Ans: Calculating the value,

$\frac{6}{13}÷7=\frac{6}{13}\times \frac{1}{7}=\frac{6\times 1}{13\times 7}=\frac{6}{91}$ 

(iv) $\text{4}\frac{\text{1}}{\text{3}}÷\text{ 3}$

Ans:  Calculating the value,

$4\frac{1}{3}÷3=\frac{13}{3}÷3=\frac{13}{3}\times \frac{1}{3}=\frac{13}{9}=1\frac{4}{9}$

(v) $\text{3}\frac{\text{1}}{\text{2}}÷\text{ 4}$ 

Ans: Calculating the value,

$3\frac{1}{2}÷4=\frac{7}{2}÷4=\frac{7}{2}\times \frac{1}{4}=\frac{7}{8}$

(vi) $\text{4}\frac{\text{3}}{\text{7}}÷\text{ 7}$ 

Ans: Calculating the value,

$4\frac{3}{7}÷7=\frac{31}{7}÷7=\frac{31}{7}\times \frac{1}{7}=\frac{31}{49}$

4. Find:

(i) $\frac{\text{2}}{\text{5}}÷\frac{\text{1}}{\text{2}}$

Ans:  Calculating the value,

$\frac{2}{5}÷\frac{1}{2}=\frac{2}{5}\times \frac{2}{1}=\frac{2\times 2}{5\times 1}=\frac{4}{5}$ 

(ii) $\frac{\text{4}}{\text{9}}÷\frac{\text{2}}{\text{3}}$ 

Ans: Calculating the value,

$\frac{4}{9}÷\frac{2}{3}=\frac{4}{9}\times \frac{3}{2}=\frac{2}{3}$

(iii) $\frac{\text{3}}{\text{7}}÷\frac{\text{8}}{\text{7}}$

Ans:  Calculating the value,

$\frac{3}{7}÷\frac{8}{7}=\frac{3}{7}\times \frac{7}{8}=\frac{3}{8}$

(iv) $\text{2}\frac{\text{1}}{\text{3}}÷\frac{\text{3}}{\text{5}}$ 

Ans: Calculating the value,

$2\frac{1}{3}÷\frac{3}{5}=\frac{7}{3}÷\frac{3}{5}=\frac{7}{3}\times \frac{5}{3}=\frac{35}{9}=3\frac{8}{9}$

(v) $\text{3}\frac{\text{1}}{\text{2}}÷\frac{\text{8}}{\text{3}}$ 

Ans: Calculating the value,

$3\frac{1}{2}÷\frac{8}{3}=\frac{7}{2}÷\frac{3}{8}=\frac{7}{2}\times \frac{3}{8}=\frac{7\times 3}{2\times 8}=\frac{21}{16}=1\frac{5}{16}$

(vi) $\frac{\text{2}}{\text{5}}÷\text{ 1}\frac{\text{1}}{\text{2}}$

Ans: Calculating the value,

$2\frac{1}{3}÷\frac{3}{5}=\frac{2}{5}÷1\frac{1}{2}=\frac{2}{5}÷\frac{3}{2}=\frac{2}{5}\times \frac{2}{3}=\frac{2\times 2}{5\times 3}=\frac{4}{15}$

(vii) $\text{3}\frac{\text{1}}{\text{5}}÷\text{ 1}\frac{\text{2}}{\text{3}}$

Ans:  Calculating the value,

$3\frac{1}{5}÷1\frac{2}{3}=\frac{16}{5}÷\frac{5}{3}=\frac{16}{5}\times \frac{3}{5}=\frac{16\times 3}{5\times 5}=\frac{48}{25}=1\frac{23}{25}$

(viii) $\text{2}\frac{\text{1}}{\text{5}}÷\text{ 1}\frac{\text{1}}{\text{5}}$ 

Ans: Calculating the value,

$2\frac{1}{5}÷1\frac{1}{5}=\frac{11}{5}÷\frac{6}{5}=\frac{11}{5}\times \frac{5}{6}=\frac{11}{6}=1\frac{5}{6}$

Exercise 2.4

1. Find:

(i) $\text{0}\text{.2 }\times \text{ 6}$ 

Ans: Calculating the value,

$$0.2\times 6=1.2$$

(ii) $\text{8 }\times \text{ 4}\text{.6}$

Ans:  Calculating the value,

$$8\times 4.6=36.8$$

(iii) $\text{2}\text{.71 }\times \text{ 5}$ 

Ans: Calculating the value,

$$2.71\times 5=13.55$$

(iv) $\text{20}\text{.1 }\times \text{ 4}$ 

Ans: Calculating the value,

$$20.1\times 4=80.4$$

(v) $\text{0}\text{.05 }\times \text{ 7}$ 

Ans: Calculating the value,

$$0.05\times 7=0.35$$

(vi) $\text{211}\text{.02 }\times \text{ 4}$ 

Ans: Calculating the value,

$$211.02\times 4=844.08$$

(vii) $\text{2 }\times \text{ 0}\text{.86}$ 

Ans: Calculating the value,

$$2\times 0.86=1.72$$

2. Find the area of rectangle whose length is $$\text{5}\text{.7 cm}$$ and 

breadth is $$\text{3 cm}\text{.}$$

Ans: Given: The \[\text{Length of rectangle = 5}\text{.7 cm and Breadth of 

rectangle = 3 cm}\] 

Applying the area of rectangle formula,

$$\text{Area of rectangle = Length x Breadth}$$ 

$$\text{= 5}\text{.7 x 3 = 17}\text{.1 c}{\text{m}}^2$$  

Hence, the area of rectangle is $\text{17}\text{.1}\text{c}{\text{m}}^{\text{2}}$.

3. Find:

(i) $$\text{1}\text{.3 }\times \text{ 10}$$ 

Ans: Calculating the value,

$1.3\times 10=13.0$

(ii) $$\text{36}\text{.8 }\times \text{ 10}$$ 

Ans: Calculating the value,

$36.8\times 10=368.0$

(iii) $$\text{153}\text{.7 }\times \text{ 10}$$ 

Ans: Calculating the value,

$153.7\times 10=1537.0$

(iv) $$\text{168}\text{.07 }\times \text{ 10}$$

Ans: Calculating the value,

$168.07\times 10=1680.7$

(v) $$\text{31}\text{.1 }\times \text{ 100}$$ 

Ans: Calculating the value,

$31.1\times 100=3110.0$

(vi) $$\text{156}\text{.1 }\times \text{ 100}$$ 

Ans: Calculating the value,

$156.1\times 100=15610.0$

(vii) $$\text{3}\text{.62 }\times \text{ 100}$$ 

Ans: Calculating the value,

$3.62\times 100=362.0$

(viii) $$\text{43}\text{.07 }\times \text{ 100}$$ 

Ans: Calculating the value,

$43.07\times 100=4307.0$

(ix) $$\text{0}\text{.5 }\times \text{ 10}$$ 

Ans: Calculating the value,

$0.5\times 10=5.0$ 

(x) $$\text{0}\text{.08 }\times \text{ 10}$$ 

Ans: Calculating the value,

$0.08\times 10=0.80$ 

(xi) $$\text{0}\text{.9 }\times \text{ 100}$$

Ans: Calculating the value,

$0.9\times 100=90.0$

(xii) $$\text{0}\text{.03 }\times \text{ 1000}$$ 

Ans: Calculating the value,

$0.03\times 1000=30.0$ 

4. A two-wheeler covers a distance of\[\text{ }\!\!~\!\!\text{ 55}\text{.3 

km}\] 

in one litre of petrol. How much distance will it cover in $$\text{10 litres}$$ of 

petrol?

Ans: Given: In one litre a two-wheeler covers a distance\[\text{ = 55}\text{.3 

km}\]

Since distance covered in one litre by a two-wheeler$$\text{ = 55}\text{.3 km}$$

$$\therefore \text{In 10 litrs, a two- wheeler covers a distance = 55}\text{.3 x 10 = 553}\text{.0 km}$$ 

Hence, $553$ km distance will be covered by two-wheeler in $10$ litres of petrol.

5.  Find:

(i) $\text{2}\text{.5 }\times \text{ 0}\text{.3}$

Ans:  Calculating the value,

$$\text{2}\text{.5 x 0}\text{.3 = 0}\text{.75}$$ 

(ii) $\text{0}\text{.1 }\times \text{ 51}\text{.7}$ 

Ans:  Calculating the value,

$$\text{0}\text{.1 x 51}\text{.7 = 5}\text{.17}$$

(iii) $\text{0}\text{.2 }\times \text{ 316}\text{.8}$ 

Ans: Calculating the value,

$$\text{0}\text{.2 x 316}\text{.8 = 63}\text{.36}$$

(iv) $\text{1}\text{.3 }\times \text{ 1}\text{.3}$ 

Ans: Calculating the value,

$$\text{1}\text{.3 x 3}\text{.1 = 4}\text{.03}$$

(v) $\text{0}\text{.5 }\times \text{ 0}\text{.05}$ 

Ans: Calculating the value,

$$\text{0}\text{.5 x 0}\text{.05 = 0}\text{.025}$$

(vi) $\text{11}\text{.2 }\times \text{ 0}\text{.15}$ 

Ans: Calculating the value,

$$\text{11}\text{.2 x 0}\text{.15 = 1}\text{.680 }$$

(vii) $\text{1}\text{.07 }\times \text{ 0}\text{.02}$ 

Ans: Calculating the value,

$$\text{1}\text{.07 x 0}\text{.02 = 0}\text{.0214}$$

(viii) $\text{10}\text{.05 }\times \text{ 1}\text{.05}$

Ans: Calculating the value,

$$\text{10}\text{.05 x 1}\text{.05 = 10}\text{.5525}$$

(ix) $\text{101}\text{.01 }\times \text{ 0}\text{.01}$ 

Ans: Calculating the value,

$$\text{101}\text{.01 x 0}\text{.01 = 1}\text{.0101}$$

(x) $\text{100}\text{.01 }\times \text{ 1}\text{.1}$

Ans: Calculating the value,

$$\text{100}\text{.01 x 1}\text{.1 = 110}\text{.11 }$$

Exercise 2.5

1. Find:

(i) $$\text{0}\text{.4 }÷\text{ 2}$$ 

Ans: Calculating the value,

$$0.4÷2=\frac{4}{10}\times \frac{1}{2}=\frac{2}{10}=0.2$$

(ii) $$\text{0}\text{.35 }÷\text{ 5}$$ 

Ans: Calculating the value,

$$0.35÷5=\frac{35}{100}\times \frac{1}{5}=\frac{7}{100}=0.07$$

(iii) $$\text{2}\text{.48 }÷\text{ 4}$$ 

Ans: Calculating the value,

$$2.48÷4=\frac{248}{100}\times \frac{1}{4}=\frac{62}{100}=0.62$$

(iv) $$\text{65}\text{.4 }÷\text{ 6}$$ 

Ans: Calculating the value,

$$65.4÷6=\frac{654}{10}\times \frac{1}{6}=\frac{109}{10}=10.9$$

(v) $$\text{651}\text{.2 }÷\text{ 4}$$ 

Ans: Calculating the value,

$$651.2÷4=\frac{6512}{10}\times \frac{1}{4}=\frac{1628}{10}=162.8$$

(vi) $$\text{14}\text{.49 }÷\text{ 7 }$$ 

Ans: Calculating the value,

$$14.49÷7=\frac{1449}{100}\times \frac{1}{7}=\frac{207}{100}=2.07$$

(vii) $$\text{3}\text{.96 }÷\text{ 4}$$

Ans: Calculating the value,

$$3.96÷4=\frac{396}{100}\times \frac{1}{4}=\frac{99}{100}=0.99$$

(viii) $$\text{0}\text{.80 }÷\text{ 5}$$ 

Ans: Calculating the value,

$$0.80÷5=\frac{80}{100}\times \frac{1}{5}=\frac{16}{100}=0.16$$

2. Find:

(i) $$\text{4}\text{.8 }÷\text{ 10}$$ 

Ans: Performing the given calculation,

$4.8÷10=\frac{4.8}{10}=0.48$

(ii) $$\text{52}\text{.5 }÷\text{ 10}$$ 

Ans: Performing the given calculation,

$52.5÷10=\frac{52.5}{10}=5.25$

(iii) $$\text{0}\text{.7 }÷\text{ 10}$$ 

Ans: Performing the given calculation,

$0.7÷10=\frac{0.7}{10}=0.07$

(iv) $$\text{33}\text{.1 }÷\text{ 10}$$

Ans: Performing the given calculation,

$33.1÷10=\frac{33.1}{10}=3.31$

(v) $$\text{272}\text{.23 }÷\text{ 10}$$ 

Ans: Performing the given calculation,

$272.23÷10=\frac{272.23}{10}=27.223$

(vi) $$\text{0}\text{.56 }÷\text{ 10 }$$