NCERT Solutions for Class 7 Maths Chapter 2 - Fractions and Decimals Exercise 2.3

Exercise - 2.3

1. Find:

(i) $\text{12 }\!\!\div\!\!\text{ }\dfrac{\text{3}}{\text{4}}$ 

Ans: Calculating the value,

$12\div \dfrac{3}{4}=12\times \dfrac{4}{3}=16$

(ii) $\text{14 }\!\!\div\!\!\text{ }\dfrac{\text{5}}{\text{6}}$ 

Ans: Calculating the value,

$14\div \dfrac{5}{6}=14\times \dfrac{6}{5}=\dfrac{84}{5}=16\dfrac{4}{5}$

(iii) $\text{8 }\!\!\div\!\!\text{ }\dfrac{\text{7}}{\text{3}}$ 

Ans: Calculating the value,

$8\div \dfrac{7}{3}=8\times \dfrac{3}{7}=\dfrac{24}{7}=3\dfrac{3}{7}$

(iv) $\text{4 }\!\!\div\!\!\text{ }\dfrac{\text{8}}{\text{3}}$ 

Ans: Calculating the value,

$4\div \dfrac{8}{3}=4\times \dfrac{3}{8}=\dfrac{3}{2}=1\dfrac{1}{2}$           

(v) $\text{3 }\!\!\div\!\!\text{ 2}\dfrac{\text{1}}{\text{3}}$ 

Ans: Calculating the value,

$3\div 2\dfrac{1}{3}=3\div \dfrac{7}{3}=3\times \dfrac{3}{7}=\dfrac{9}{7}=1\dfrac{2}{7}$           

(vi) \[\text{5 }\!\!\div\!\!\text{ 3}\dfrac{\text{4}}{\text{7}}\] 

Ans: Calculating the value,

$5\div 3\dfrac{4}{7}=5\div \dfrac{25}{7}=5\times \dfrac{7}{25}=\dfrac{7}{5}=1\dfrac{2}{5}$

2. Find the reciprocal of each of the following fractions. Classify the reciprocals as a proper fraction, improper fractions and whole numbers.

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

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

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

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

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

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

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

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

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

(iv) $\dfrac{\text{6}}{\text{5}}$ 

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

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

(v) $\dfrac{\text{12}}{\text{7}}$ 

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

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

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

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

Reciprocal of $\dfrac{\text{1}}{\text{8}}\text{=8}\to \text{Whole number}$

(vii) $\dfrac{\text{1}}{\text{11}}$ 

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

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

3. Find:

(i) $\dfrac{\text{7}}{\text{3}}\text{ }\!\!\div\!\!\text{ 2}$ 

Ans: Calculating the value,

$\dfrac{7}{3}\div 2=\dfrac{7}{3}\times \dfrac{1}{2}=\dfrac{7\times 1}{3\times 2}=\dfrac{7}{6}=1\dfrac{1}{6}$

(ii) $\dfrac{\text{4}}{\text{9}}\text{ }\!\!\div\!\!\text{ 5}$

Ans: Calculating the value,

$\dfrac{4}{9}\div 5=\dfrac{4}{9}\times \dfrac{1}{5}=\dfrac{4\times 1}{9\times 5}=\dfrac{4}{45}$ 

(iii) $\dfrac{\text{6}}{\text{13}}\text{ }\!\!\div\!\!\text{ 7}$ 

Ans: Calculating the value,

$\dfrac{6}{13}\div 7=\dfrac{6}{13}\times \dfrac{1}{7}=\dfrac{6\times 1}{13\times 7}=\dfrac{6}{91}$ 

(iv) $\text{4}\dfrac{\text{1}}{\text{3}}\text{ }\!\!\div\!\!\text{ 3}$

Ans:  Calculating the value,

$4\dfrac{1}{3}\div 3=\dfrac{13}{3}\div 3=\dfrac{13}{3}\times \dfrac{1}{3}=\dfrac{13}{9}=1\dfrac{4}{9}$

(v) $\text{3}\dfrac{\text{1}}{\text{2}}\text{ }\!\!\div\!\!\text{ 4}$ 

Ans: Calculating the value,

$3\dfrac{1}{2}\div 4=\dfrac{7}{2}\div 4=\dfrac{7}{2}\times \dfrac{1}{4}=\dfrac{7}{8}$

(vi) $\text{4}\dfrac{\text{3}}{\text{7}}\text{ }\!\!\div\!\!\text{ 7}$ 

Ans: Calculating the value,

$4\dfrac{3}{7}\div 7=\dfrac{31}{7}\div 7=\dfrac{31}{7}\times \dfrac{1}{7}=\dfrac{31}{49}$

4. Find:

(i) $\dfrac{\text{2}}{\text{5}}\text{ }\!\!\div\!\!\text{ }\dfrac{\text{1}}{\text{2}}$

Ans:  Calculating the value,

$\dfrac{2}{5}\div \dfrac{1}{2}=\dfrac{2}{5}\times \dfrac{2}{1}=\dfrac{2\times 2}{5\times 1}=\dfrac{4}{5}$ 

(ii) $\dfrac{\text{4}}{\text{9}}\text{ }\!\!\div\!\!\text{ }\dfrac{\text{2}}{\text{3}}$ 

Ans: Calculating the value,

$\dfrac{4}{9}\div \dfrac{2}{3}=\dfrac{4}{9}\times \dfrac{3}{2}=\dfrac{2}{3}$

(iii) $\dfrac{\text{3}}{\text{7}}\text{ }\!\!\div\!\!\text{ }\dfrac{\text{8}}{\text{7}}$

Ans:  Calculating the value,

$\dfrac{3}{7}\div \dfrac{8}{7}=\dfrac{3}{7}\times \dfrac{7}{8}=\dfrac{3}{8}$

(iv) $\text{2}\dfrac{\text{1}}{\text{3}}\text{ }\!\!\div\!\!\text{ }\dfrac{\text{3}}{\text{5}}$ 

Ans: Calculating the value,

$2\dfrac{1}{3}\div \dfrac{3}{5}=\dfrac{7}{3}\div \dfrac{3}{5}=\dfrac{7}{3}\times \dfrac{5}{3}=\dfrac{35}{9}=3\dfrac{8}{9}$

(v) $\text{3}\dfrac{\text{1}}{\text{2}}\text{ }\!\!\div\!\!\text{ }\dfrac{\text{8}}{\text{3}}$ 

Ans: Calculating the value,

$3\dfrac{1}{2}\div \dfrac{8}{3}=\dfrac{7}{2}\div \dfrac{3}{8}=\dfrac{7}{2}\times \dfrac{3}{8}=\dfrac{7\times 3}{2\times 8}=\dfrac{21}{16}=1\dfrac{5}{16}$

(vi) $\dfrac{\text{2}}{\text{5}}\text{ }\!\!\div\!\!\text{ 1}\dfrac{\text{1}}{\text{2}}$

Ans:  Calculating the value,

$2\dfrac{1}{3}\div \dfrac{3}{5}=\dfrac{2}{5}\div 1\dfrac{1}{2}=\dfrac{2}{5}\div \dfrac{3}{2}=\dfrac{2}{5}\times \dfrac{2}{3}=\dfrac{2\times 2}{5\times 3}=\dfrac{4}{15}$

(vii) $\text{3}\dfrac{\text{1}}{\text{5}}\text{ }\!\!\div\!\!\text{ 1}\dfrac{\text{2}}{\text{3}}$

Ans:  Calculating the value,

$3\dfrac{1}{5}\div 1\dfrac{2}{3}=\dfrac{16}{5}\div \dfrac{5}{3}=\dfrac{16}{5}\times \dfrac{3}{5}=\dfrac{16\times 3}{5\times 5}=\dfrac{48}{25}=1\dfrac{23}{25}$

(viii) $\text{2}\dfrac{\text{1}}{\text{5}}\text{ }\!\!\div\!\!\text{ 1}\dfrac{\text{1}}{\text{5}}$ 

Ans: Calculating the value,

$2\dfrac{1}{5}\div 1\dfrac{1}{5}=\dfrac{11}{5}\div \dfrac{6}{5}=\dfrac{11}{5}\times \dfrac{5}{6}=\dfrac{11}{6}=1\dfrac{5}{6}$

Conclusion

Class 7 Maths Chapter 2.3, "Fractions and Decimals," emphasizes the importance of careful alignment of decimal points to ensure accurate calculations. By practising these skills, students will be better equipped to tackle more complex mathematical problems in higher classes. Ex 2.3 Class 7 focuses on the concept of Multiplication of Fractions, which is essential for understanding how to deal with parts of a whole in various mathematical and real-life contexts. The comprehensive approach ensures that students gain confidence and proficiency in handling fractional operations, preparing them for future academic success.

NCERT Solution Class 7 Maths Chapter 2 - Fractions and Decimals Other Exercises

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