Question

Mark the correct alternative in each of the following:

Which of the following pairs of rational numbers are on the opposite side of the zero on the number line?

(a) $\frac{3}{7}$ and $\frac{5}{12}$ (b) $-\frac{3}{7}$ and $\frac{-5}{12}$ (c) $\frac{3}{7}$ and $\frac{-5}{12}$ (d) None of these

Answer 1

The rational numbers $\frac{3}{7}$ and $\frac{5}{12}$ are positive rational numbers. We know that every positive rational number is greater than 0, so both the rational numbers $\frac{3}{7}$ and $\frac{5}{12}$ are represented by points on the right of the zero on the number line.

The rational numbers $-\frac{3}{7}$ and $\frac{-5}{12}$ are negative rational numbers. We know that every negative rational number is less than 0, so both the rational numbers $\frac{3}{7}$ and $\frac{5}{12}$ are represented by points on the left of the zero on the number line.

The rational numbers $\frac{3}{7}$ is a positive rational number whereas the rational number $\frac{-5}{12}$ is a negative rational numbers. We know that every negative rational number is less than 0 and every positive rational number is greater than 0, so the rational number $\frac{3}{7}$ is represented by point on the right of the zero and $\frac{-5}{12}$ is represented by point on the left of the zero on the number line.
Thus, the rational numbers $\frac{3}{7}$ and $\frac{-5}{12}$ are on the opposite side of the zero on the number line.

Hence, the correct answer is option (c).