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

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

(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