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What is the positive difference between 516\frac{5}{16}165​​ and its reciprocal?
Question

What is the positive difference between 516\frac{5}{16}​ and its reciprocal?

A.

27380\frac{73}{80}​​

B.

26180\frac{61}{80}

C.

27180\frac{71}{80}

D.

26980\frac{69}{80}

Correct option is C

Given:

Number =516= \frac{5}{16}​​

Solution:

Reciprocal of 516=165 \frac{5}{16} = \frac{16}{5}

165516=(16×165×5)80=2562580=23180=27180\left| \frac{16}{5} - \frac{5}{16} \right| = \left| \frac{(16 \times 16 - 5 \times 5)}{80} \right| = \left| \frac{256 - 25}{80} \right| = \frac{231}{80} = 2\frac{71}{80}​​

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