NCERT Solution class 7 chapter 2 exercise 2.4

Exercise 2.4

Question 1

Find :

(i) 12 \div \dfrac{3}{4}

Sol : 

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


 

(ii) 4\div \dfrac{5}{6}

Sol :

14 \div\dfrac{5}{6} 14\times \dfrac{6}{5} =\dfrac{84}{5}


 

(iii) 8\div \dfrac{7}{3}

Sol :

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


 

(iv) 4\div \dfrac{8}{3}

Sol :

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


(v) 3\div 2\dfrac{1}{3}

Sol :

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


(vi) 5\div 3\dfrac{4}{7}

Sol :

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


 

Question 2

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

(i) \dfrac{3}{7}  (ii) \dfrac{5}{8}  (iii) \dfrac{9}{7}

(iv) \dfrac{6}{5}  (v) \dfrac{12}{7}  (vi) \dfrac{1}{8}

(vii) \dfrac{1}{11}

Sol :

Note : A proper fraction is the fraction which has its denominator greater than its numerator while improper fraction is the fraction which has its numerator greater than its denominator. Whole numbers are a collection of all positive integers including 0.

(i) \dfrac{3}{7} 

Reciprocal =\dfrac{7}{3}

Therefore, it is an improper fraction.


(ii) \dfrac{5}{8} 

Reciprocal =\dfrac{8}{5}

Therefore, it is an improper fraction.


(iii) \dfrac{9}{7}

Reciprocal =\dfrac{7}{9}

Therefore, it is an proper fraction.


(iv) \dfrac{6}{5} 

Reciprocal =\dfrac{5}{6}

Therefore, it is an proper fraction.


(v) \dfrac{12}{7} 

Reciprocal =\dfrac{7}{12}

Therefore, it is an proper fraction.


(vi) \dfrac{1}{8}

Reciprocal =\dfrac{8}{1}

Therefore, it is a whole number.


(vii) \dfrac{1}{11}

Reciprocal =\dfrac{11}{1}

Therefore, it is a whole number.


 

Question 3

Find :

(i) \dfrac{7}{3} \div 2 (ii) \dfrac{4}{9} \div 5 (iii) \dfrac{6}{13} \div 7 (iv) 4\dfrac{1}{3} \div 3 (v)  3\dfrac{1}{2} \div 4 (vi) 4\dfrac{3}{7} \div 7

Sol :

(i) \dfrac{7}{3} \div 2 =\dfrac{7}{3} \times \dfrac{1}{2} =\dfrac{7}{6}


(ii) \dfrac{4}{9} \div 5 =\dfrac{4}{9} \times \dfrac{1}{5} =\dfrac{4}{45}


(iii) \dfrac{6}{13} \div 7 =\dfrac{6}{13} \times \dfrac{1}{7} =\dfrac{6}{91}


(iv) 4\dfrac{1}{3} \div 3  =\dfrac{13}{3} \div \dfrac{3}{1} =\dfrac{13}{3} \times \dfrac{1}{3} =\dfrac{13}{9}


(v)  3\dfrac{1}{2} \div 4 =\dfrac{7}{2} \div \dfrac{4}{1}  =\dfrac{7}{2} \times \dfrac{1}{4} =\dfrac{7}{8}


(vi) 4\dfrac{3}{7} \div 7 =\dfrac{31}{7} \div \dfrac{1}{7}  =\dfrac{31}{7} \times \dfrac{1}{7} =\dfrac{31}{49}


 

Question 4

Find :

(i) \dfrac{2}{5} \div \dfrac{1}{2} (ii) \dfrac{4}{9} \div \dfrac{2}{3}

(iii) \dfrac{3}{7} \div \dfrac{8}{7} (iv) 2\dfrac{1}{3} \div \dfrac{3}{5}

(v) 3\dfrac{1}{2} \div \dfrac{8}{3} (vi) \dfrac{2}{5} \div 1\dfrac{1}{2}

(vii) 3\dfrac{1}{5} \div 1\dfrac{2}{3} (viii) 2\dfrac{1}{5} \div 1\dfrac{1}{5}

Sol :

 

(i) \dfrac{2}{5} \div \dfrac{1}{2} =\dfrac{2}{5} \times \dfrac{2}{1} =\dfrac{4}{5}


(ii) \dfrac{4}{9} \div \dfrac{2}{3} =\dfrac{4}{9} \times \dfrac{3}{2} =\dfrac{2}{3}


(iii) \dfrac{3}{7} \div \dfrac{8}{7} =\dfrac{3}{7} \times \dfrac{7}{8} =\dfrac{3}{8}


(iv) 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}


(v) 3\dfrac{1}{2} \div \dfrac{8}{3} =\dfrac{7}{2} \div \dfrac{8}{3} =\dfrac{7}{2} \times \dfrac{3}{8} =\dfrac{21}{16}


(vi) \dfrac{2}{5} \div 1\dfrac{1}{2} =\dfrac{2}{5} \div \dfrac{3}{2} =\dfrac{2}{5} \times \dfrac{2}{3} =\dfrac{4}{15}


(vii) 3\dfrac{1}{5} \div 1\dfrac{2}{3} =\dfrac{16}{5} \div \dfrac{5}{3} =\dfrac{16}{5} \times \dfrac{3}{5} =\dfrac{48}{25}


(viii) 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}

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