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} $

Given:

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

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

To do:

We have to find which of the given pairs represent the same rational number.

Solution:

To find if the given pairs represent the same rational number, we have to simplify them.

(i) $\frac{-7}{21}=\frac{-7\times1}{3\times7}=\frac{-1}{3}$
 $\frac{3}{9}=\frac{3\times1}{3\times3}=\frac{1}{3}$

Clearly,

$\frac{-1}{3}≠\frac{1}{3}$

Therefore, \( \frac{-7}{21} \) and \( \frac{3}{9} \) do not represent the same rational number.

(ii)  $\frac{-16}{20}=\frac{-4\times4}{4\times5}=\frac{-4}{5}$

 $\frac{20}{-25}=\frac{4\times5}{-5\times5}=\frac{-4}{5}$

Clearly,

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

Therefore, \( \frac{-16}{20} \) and \( \frac{20}{-25} \) represent the same rational number.

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Updated on: 10-Oct-2022

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