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in Number System by (65.3k points)

Which of the following pairs represent the same rational number ?

(i) \(\frac{8}{-5}\) and \(\frac{-24}{15}\)

(ii) \(\frac{1}{3}\) and \(\frac{-1}{9}\)

(iii) \(\frac{-5}{-9}\) and \(\frac{5}{-9}\)

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 (i) \(\frac{8}{-5}\) and \(\frac{-24}{15}\)

\(\frac{8}{-5}\times\frac{-3}{-3} = \frac{-24}{15}\)

∴ The above pair of numbers represent the same rational number.

(ii) \(\frac{1}{3}\) and \(\frac{-1}{9}\)

\(\frac{1}{3}\) is a positive rational number and \(\frac{-1}{9}\) is a negative Rational Number.

Therefore this pair does not represent the same rational number.

(iii) \(\frac{-5}{-9}\) and \(\frac{5}{-9}\)

\(\frac{-5}{-9}\times\frac{-1}{-1} = \frac{5}{9}\)  is a positive rational number and \(\frac{5}{-9}\) is a negative rational number.

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