(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. 

\(\frac{-5}{12}\) is a negative number.

All negative numbers are less than 0 and therefore, lie to the left of 0 on the number line.

Hence,\(\frac{-5}{12}\) lies to the left of 0 on the number line. 

Therefore, the rational numbers, \(\frac{1}{3}\)and \(\frac{-5}{12}\)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.