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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?

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Let the fraction be x. Then,

\(\frac{x\times{x}}{\frac1x} = 18\frac{26}{27} ⇒ x^3 = \frac{512}{27}⇒x = \sqrt[3]{\frac{512}{27}}=\frac83=2\frac23.\)

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