Which of the following pairs represent the same rational number?
(i) $\frac{- 7}{21} a n d \frac{3}{9}$ (ii) $\frac{- 16}{20} a n d \frac{20}{- 25}$ (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) $\frac{- 5}{- 9} and \frac{5}{- 9}$

Solution

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

$\frac{- 7}{21} = \frac{- 1}{3} \frac{3}{9} = \frac{1}{3}$

As $\frac{- 1}{3} \neq \frac{1}{3}$ , therefore, it does not represent same rational numbers.

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

$\frac{- 16}{20} = \frac{- 4}{5}$

$\frac{- 20}{25} = \frac{- 4}{5}$

Therefore, it represents same rational numbers.

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

$\frac{- 2}{- 3} = \frac{2}{3}$

Therefore, it represents same rational numbers.

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

$\frac{- 12}{20} = \frac{- 3}{5}$

Therefore, it represents same rational numbers.

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

$\frac{- 24}{15} = \frac{- 8}{5} \frac{8}{- 5} = \frac{- 8}{5}$

Therefore, it represents same rational numbers.

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

As $\frac{1}{3} \neq \frac{- 1}{9}$ , therefore, it does not represent same rational numbers.

(vii) $\frac{- 5}{- 9} a n d \frac{5}{- 9}$

$\frac{- 5}{- 9} = \frac{5}{9} As \frac{5}{9} \neq \frac{- 5}{9}, therefore, it does not represent same rational numbers .$

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