Question

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

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

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

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

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

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

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

Answer 1

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

\(=\frac{-7}{21} = \frac{-1}{3}\)

\(\frac{3}{9}=\frac{1}{3}\)

As \(\frac{1}{3}≠\frac{1}{3}\)

therefore, it does not represent same rational numbers.

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

\(=\frac{-16}{20} = \frac{-4}{5}\)

\(=\frac{20}{-25}=\frac{-4}{5}\)

Therefore, it represents same rational numbers.

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

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

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

\(=\frac{-12}{20}=\frac{-3}{5}\)
Therefore, it represents same rational numbers.

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

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

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

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

As \(\frac{1}{3}≠\frac{-1}{9}\)

therefore, it does not represent same rational numbers.

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

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

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