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Mathematics Question on Need For Rational Numbers

Which of the following pairs represent the same rational number?
(i) −721  and39\frac{-7}{21} \space and \frac{3}{9}

(ii) −1620  and  20−25\frac{-16}{20}\space and\space \frac{20}{-25}

(iii) −2−3  and  23\frac{-2}{-3}\space and \space \frac{2}{3}

(iv) −35  and  −1220\frac{-3}{5} \space and \space \frac{-12}{20}

(v) 8−5  and  −2415\frac{8}{-5}\space and \space \frac{-24}{15}

(vi) 13  and  −19\frac{1}{3}\space and\space \frac{-1}{9}

(vii) −5−9  and  5−9\frac{-5}{-9}\space and \space \frac{5}{-9}

Answer

(i)−721  and  39\frac{-7}{21} \space and\space \frac{3}{9}

=−721=−13=\frac{-7}{21} = \frac{-1}{3}

39=13\frac{3}{9}=\frac{1}{3}

As 13≠13\frac{1}{3}≠\frac{1}{3}

therefore, it does not represent same rational numbers.

(ii) −1620  and  20−25\frac{-16}{20}\space and \space \frac{20}{-25}

=−1620=−45=\frac{-16}{20} = \frac{-4}{5}

=20−25=−45=\frac{20}{-25}=\frac{-4}{5}

Therefore, it represents same rational numbers.

(iii)−2−3  and  23\frac{-2}{-3}\space and \space\frac{2}{3}

=−2−3=23=\frac{-2}{-3}=\frac{2}{3}
Therefore, it represents same rational numbers.

(iv)−35  and  −1220\frac{-3}{5}\space and\space\frac{-12}{20}

=−1220=−35=\frac{-12}{20}=\frac{-3}{5}
Therefore, it represents same rational numbers.

(v)8−5  and  −2415\frac{8}{-5}\space and\space\frac{-24}{15}

=−2415=−85=\frac{-24}{15}=\frac{-8}{5}

=8−5=−85=\frac{8}{-5}=\frac{-8}{5}
Therefore, it represents same rational numbers.

(vi)13  and  −19\frac{1}{3}\space and\space\frac{-1}{9}

As 13≠−19\frac{1}{3}≠\frac{-1}{9}

therefore, it does not represent same rational numbers.

(vii)−5−9  and  5−9\frac{-5}{-9}\space and\space\frac{5}{-9}

=−5−9=59=\frac{-5}{-9}=\frac{5}{9}

As 59≠−59\frac{5}{9}≠\frac{-5}{9}
therefore, it does not represent same rational numbers.