Question

If we multiply a fraction by itself and divide the product by its reciprocal, the fraction thus obtained is $18\frac{26}{27}$. What is the original fraction?

• A. $2\frac{2}{3}$
• B. $2\frac{1}{3}$
• C. $1\frac{2}{3}$
• D. $3\frac{2}{3}$

Answer 1

The correct option is A $2\frac{2}{3}$

Let the fraction be $x$. Then,

$\frac{x\times x}{\frac{1}{x}}=18\frac{26}{27}$

$\Rightarrow x^3=\frac{512}{27}$

$\Rightarrow x=\sqrt[3]{3\frac{512}{27}}=\frac{8}{3}=2\frac{2}{3}$