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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) $2\frac{1}{5}\div1\frac{1}{5}=\frac{2\times5+1}{5}\div\frac{1\times5+1}{5}$
$=\frac{11}{5}\div\frac{6}{5}$
$=\frac{11}{5}\times\frac{5}{6}$
$=\frac{11\times5}{5\times6}$
$=\frac{11}{6}$
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