Find:
(i) $\frac{2}{5}\div\frac{1}{2}$
(ii) $\frac{4}{9}\div\frac{2}{3}$
(iii) $\frac{3}{7}\div\frac{8}{7}$
(iv) $2\frac{1}{3}\div\frac{3}{5}$
(v) $3\frac{1}{2}\div\frac{8}{3}$
(vi) $\frac{2}{5}\div1\frac{1}{2}$
(vii) $3\frac{1}{5}\div1\frac{2}{3}$
(viii) $2\frac{1}{5}\div1\frac{1}{5}$

To do:

We have to find

(i) $\frac{2}{5}\div\frac{1}{2}$

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

(iii) $\frac{3}{7}\div\frac{8}{7}$

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

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

(vi) $\frac{2}{5}\div1\frac{1}{2}$

(vii) $3\frac{1}{5}\div1\frac{2}{3}$

(viii) $2\frac{1}{5}\div1\frac{1}{5}$

Solution:

We know that,

$\frac{a}{b} \div \frac{c}{d}=\frac{a}{b}\times \frac{c}{d}$

Therefore,

(i) $\frac{2}{5}\div\frac{1}{2}$

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

$=\frac{2\times2}{5\times1}$

$=\frac{4}{5}$

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

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

$=\frac{4\times3}{9\times2}$

$=\frac{12}{18}$

$=\frac{2}{3}$

(iii) $\frac{3}{7}\div\frac{8}{7}$

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

$=\frac{3\times7}{7\times8}$

$=\frac{3}{8}$

(iv) $2\frac{1}{3}\div\frac{3}{5}=\frac{2\times3+1}{3}\times\frac{5}{3}$

$=\frac{6+1}{3}\times\frac{5}{3}$

$=\frac{7}{3}\times\frac{5}{3}$

$=\frac{7\times5}{3\times3}$

$=\frac{35}{9}$

(v) $3\frac{1}{2}\div\frac{8}{3}=\frac{3\times2+1}{2}\times\frac{3}{8}$

$=\frac{6+1}{2}\times\frac{3}{8}$

$=\frac{7}{2}\times\frac{3}{8}$

$=\frac{7\times3}{2\times8}$

$=\frac{21}{16}$

(vi) $\frac{2}{5}\div1\frac{1}{2}=\frac{2}{5}\div\frac{1\times2+1}{2}$

$=\frac{2}{5}\div\frac{3}{2}$

$=\frac{2}{5}\times\frac{2}{3}$  

$=\frac{2\times2}{5\times3}$

$=\frac{4}{15}$

(vii) $3\frac{1}{5}\div1\frac{2}{3}=\frac{3\times5+1}{5}\div\frac{1\times3+2}{3}$

$=\frac{15+1}{5}\div\frac{5}{3}$

$=\frac{16}{5}\times\frac{3}{5}$

$=\frac{16\times3}{5\times5}$

$=\frac{48}{25}$

(viii) $2\frac{1}{5}\div1\frac{1}{5}=\frac{2\times5+1}{5}\div\frac{1\times5+1}{5}$

$=\frac{11}{5}\div\frac{6}{5}$

$=\frac{11}{5}\times\frac{5}{6}$

$=\frac{11\times5}{5\times6}$

$=\frac{11}{6}$