If a fraction is multiplied by itself and then divided by the reciprocal of the same fraction the result is $18\frac{26}{27}$, then the fraction is

Given:

A fraction is multiplied by itself and then divided by the reciprocal of the same fraction.

The result is $18\frac{26}{27}$.
To do:

We have to find the fraction.

Solution:

Let the fraction be $\frac{x}{y}$

The fraction is multiplied by itself.

This implies,

$\frac{x}{y}\times\frac{x}{y}=\frac{x^2}{y^2}$

The resultant value is divided by the reciprocal of the same fraction. The result is $18\frac{26}{27}$.

Reciprocal of $\frac{x}{y}$ is $\frac{y}{x}$.

Therefore,

$\frac{x^2}{y^2}\times\frac{y}{x}=18\frac{26}{27}$

$\frac{x}{y}=18\frac{26}{27}$

$=\frac{18\times27+26}{27}$
 $=\frac{486+26}{27}$

$=\frac{512}{27}$

The required fraction is $\frac{512}{27}$.

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Updated on: 10-Oct-2022

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