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Q.6 Which of the following pairs represent the same rational number?
(i) \(\frac{-7}{21} \) and \(\frac{3}{9} \)
(ii) \(\frac{-16}{20} \) and \(\frac{20}{-25} \)
(iii)\(\frac{-2}{-3} \) and \(\frac{2}{3} \)
(iv) \(\frac{-3}{5} \) and \(\frac{-12}{20} \)
(v) \(\frac{8}{-5} \) and \(\frac{-24}{15} \)
(vi) \(\frac{1}{3} \) and \(\frac{-1}{9} \)
(vii) \(\frac{-5}{-9} \) and \(\frac{5}{-9} \)
Answer :

(i) \(\frac{-7}{21} \) and \(\frac{3}{9} \)
Or, \(\frac{-7×3}{21×3} \) and \(\frac{3×7}{9×7} \)
Or, \(\frac{-21}{63} \) and \(\frac{21}{63} \)
Since -21\(\neq \) 21 so \(\frac{-7}{21} \) and \(\frac{3}{9} \)do not represent the same rational number
(ii) \(\frac{-16}{20} \) and \(\frac{20}{-25} \)
Or, \(\frac{-16×5}{20×5} \) and \(\frac{20×4}{25×4} \)
Or, \(\frac{-80}{100} \) and \(\frac{80}{100} \)
Since -80\(\neq \) 80 so \(\frac{-16}{20} \) and \(\frac{20}{-25} \)do not represent the same rational number
(iii) \(\frac{-2}{-3} \) and \(\frac{2}{3} \)
Or, \(\frac{2}{3} \) and \(\frac{2}{3} \)
so\(\frac{2}{3} \) and \(\frac{2}{3} \) represent the same rational number
(iv) \(\frac{-3}{5} \) and \(\frac{-12}{20} \)
Or, \(\frac{-3×4}{5×4} \) and \(\frac{-12×1}{20×1} \)
Or, \(\frac{-12}{20} \) and \(\frac{-12}{20} \)
Since \(\frac{-12}{20} \) = \(\frac{-12}{20} \)
so \(\frac{-3}{5} \) and \(\frac{-12}{20} \) represent the same rational number