(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.
