Question:
Which of the following statements are true and which are false?
(i) $\frac{-3}{5}$ lies to the left of 0 on the number line.
(ii) $\frac{-12}{7}$ lies to the right of 0 on the number line.
(iii) The rational numbers $\frac{1}{3}$ and $\frac{-5}{2}$ are on opposite sides of 0 on the number line.
(iv) The rational number $\frac{-18}{-13}$ lies to the left of 0 on the number line.
Solution:
(i) True
A negative number always lies to the left of 0 on the number line.
(ii) False
A negative number always lies to the left of 0 on the number line.
(iii) True
Negative and positive numbers always lie on the opposite sides of 0 on the number line.
(iv) False
The negative sign cancels off and the number becomes $\frac{18}{13}$; it lies to the right of 0 on the number line.