(i) True

\(\frac{-3}{5}\)is a negative number.

All negative numbers are less than 0 and therefore, 

lie to the left of 0 on the number line.

Hence, \(\frac{-3}{5}\)lies to the left of 0 on the number line.

(ii) False

 \(\frac{-12}{7}\) is a negative number.

All negative numbers are less than 0 and therefore, 

lie to the left of 0 on the number line.

Hence, \(\frac{-12}{7}\)lies to the left of 0 on the number line.

(iii) True

\(\frac{1}{3}\)is a positive number

All positive numbers are greater than 0 and therefore, 

lie to the right of 0 on the number line.

Hence,\(\frac{1}{3}\)lies to the right of 0 on the number line.

\(\frac{-5}{2}\)is a negative number.

All negative numbers are less than 0 and therefore, 

lie to the left of 0 on the number line.

Hence, \(\frac{-5}{2}\)lies to the left of 0 on the number line.

Therefore, 

the rational numbers, \(\frac{1}{3}\) and \(\frac{-5}{2}\) are on opposite sides of 0 on the number line.

(iv) False

\(\frac{-18}{-13} = \frac{-18\times-1}{-13\times-1} = \frac{18}{13}\)

\(\frac{18}{13}\)is a positive number.

All positive numbers are greater than 0 and therefore, 

lie to the right of 0 on the number line.

Hence, \(\frac{18}{13}\)lies to the right of 0 on the number line.