Question

if we multiply a fraction by itself and divide the product by the reciprocal, the fraction bcomes 1826/27. what is the original fraction.

Answer 1

Here let the original fraction be $\frac{x}{y}$.
Now, according to the given question,
$$\begin{gathered} \frac{\left({\displaystyle \frac{x}{y}}\right)\left({\displaystyle \frac{x}{y}}\right)}{\left({\displaystyle \frac{y}{x}}\right)}=\frac{1826}{27} \\ \frac{\left({\displaystyle \frac{x^2}{y^2}}\right)}{\left({\displaystyle \frac{y}{x}}\right)}=\frac{1826}{27} \\ \left({\displaystyle \frac{x^2}{y^2}}\right)\left(\frac{x}{y}\right)=\frac{1826}{27} \\ \frac{x^3}{y^3}=\frac{1826}{27} \\ \frac{x}{y}=\frac{\sqrt[3]{1826}}{\sqrt[3]{27}} \\ \frac{x}{y}=\frac{12.22}{3} \\ \frac{x}{y}=\frac{1222}{300} \\ \frac{x}{y}=\frac{611}{150} \end{gathered}$$

Therefore, the original fraction is $\frac{\mathbf{611}}{\mathbf{150}}$