For a fraction, \(\frac{a}{b}\)

\(\frac{a}{b} = \) \(\frac{a\times{n}}{b\times{n}}\)

Where, n ≠ 0

(i) We have to express \(\frac{-3}{5}\) as a rational number with denominator 20.

In order to make the denominator 20, multiply 5 by 4.

Therefore,

\(\frac{-3}{5}\) = \(\frac{-3\times4}{5\times4}\)

\(\Rightarrow\) \(\frac{-3}{5}\) = \(\frac{-12}{20}\)

(ii) We have to express \(\frac{-3}{5}\) as a rational number with denominator -30.

In order to make the denominator -30, multiply 5 by -6.

\(\frac{-3}{5}\) = \(\frac{-3\times4}{5\times-6}\)

\(\Rightarrow\) \(\frac{-3}{5}\) = \(\frac{18}{-30}\)

(iii) We have to express \(\frac{-3}{5}\) as a rational number with denominator 35.

In order to make the denominator 35, multiply 5 by 7. 

Therefore,

\(\frac{-3}{5}\) = \(\frac{-3\times7}{5\times7}\)

\(\Rightarrow\) \(\frac{-3}{5}\) = \(\frac{-21}{35}\)

(iv) We have to express \(\frac{-3}{5}\) as a rational number with denominator -40.

In order to make the denominator 20, multiply 5 by -8.

Therefore,

\(\frac{-3}{5}\) = \(\frac{-3\times8}{5\times-8}\)

\(\Rightarrow\) \(\frac{-3}{5}\) = \(\frac{24}{-40}\)