The difference of $${\text{1}}\frac{3}{{16}}$$ and its reciprocal is equal to

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Question

The difference of $${\text{1}}\frac{3}{{16}}$$ and its reciprocal is equal to = ?

Options:

A . $$1\frac{1}{8}$$

B . $$\frac{4}{3}$$

C . $$\frac{{15}}{{16}}$$

D . None of these

Answer: Option D
$$\eqalign{
& {\text{Required differnce}} \cr
& {\text{ = }}\frac{{19}}{{16}} - \frac{{16}}{{19}} = \frac{{{{19}^2} - {{16}^2}}}{{304}} \cr
& = \frac{{\left( {19 + 16} \right)\left( {19 - 16} \right)}}{{304}} \cr
& = \frac{{35 \times 3}}{{304}} \cr
& = \frac{{105}}{{304}} \cr} $$

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