4.  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}\div 1\frac{1}{2}               (vii)\;3\frac{1}{5}\div 1\frac{2}{3}             (viii)\;2\frac{1}{5}\div 1\frac{1}{5}

Answers (1)

As we know, The division of a number by a / b is equivalent to multiplication of that number with b / a which is also called the reciprocal of a / b. So,

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

\Rightarrow \; \frac{2}{5}\div \frac{1}{2}=\frac{2}{5}\times\frac{2}{1}=\frac{4}{5}

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

\Rightarrow \; \frac{4}{9}\div \frac{2}{3}=\frac{4}{9}\times\frac{3}{2}=\frac{12}{18}=\frac{2}{3}

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

\Rightarrow \; \frac{3}{7}\div \frac{8}{7}=\frac{3}{7}\times\frac{7}{8}=\frac{3}{8}

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

\Rightarrow \;2 \frac{1}{3}\div \frac{3}{5}=\frac{7}{3}\div\frac{3}{5}=\frac{7}{3}\times\frac{5}{3}=\frac{35}{9}=3\frac{8}{9}

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

\;3 \frac{1}{2}\div \frac{8}{3}=\frac{7}{2}\div\frac{8}{3}=\frac{7}{2}\times\frac{3}{8}=\frac{21}{16}=1\frac{5}{16}

 

(vi)\;\frac{2}{5}\div 1\frac{1}{2}

\Rightarrow \;\frac{2}{5}\div 1\frac{1}{2}=\frac{2}{5}\div\frac{3}{2}=\frac{2}{5}\times\frac{2}{3}=\frac{4}{15}

(vii)\;3\frac{1}{5}\div 1\frac{2}{3}

\Rightarrow \;3\frac{1}{5}\div 1\frac{2}{3}=\frac{16}{5}\div\frac{5}{3}=\frac{16}{5}\times\frac{3}{5}=\frac{48}{25}=1\frac{23}{25}

(viii)\;2\frac{1}{5}\div 1\frac{1}{5}

\Rightarrow \;2\frac{1}{5}\div 1\frac{1}{5}=\frac{11}{5}\div\frac{6}{5}=\frac{11}{5}\times\frac{5}{6}=\frac{11}{6}=1\frac{5}{6}

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