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) $4\dfrac{3}{7} \div 7$