Q

# Find: 2 / 5 divided by 1 / 2

4.  Find:

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

Views

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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