Question

Which of the following statement is true about a rational number $\frac{-2}{3}$ ?

• A. It lies to the left side of ${}^{\prime }{0}^{\prime }$ on the number line.
• B. It lies to the right side of ${}^{\prime }{0}^{\prime }$ on the number line.
• C. It is not possible to represent on the number line.
• D. It cannot be determined on which side the number lies.

Answer 1

The correct option is A It lies to the left side of ${}^{\prime }{0}^{\prime }$ on the number line.

We know that every positive number occupies space right to the origin while the negative numbers are present on the left side of the origin. Let us learn to represent a rational number on a number line with few steps.

(i) Draw a line and locate the point having the coordinate as $0$. This point is known as the origin.

If the given number is positive, locate it on the right side of the origin. If it is a negative number, locate it on the left side of zero.

Divide each unit into the values which are equal to the denominator of the fraction. For example: for representing $\frac{4}{5}$ on the number line you need to divide each unit into $5$ subunits.

Similarly,

$\frac{-2}{3}$ is a negative rational number and it is known that $\frac{-2}{3}$ is greater than $-1$ and less than $0$. Therefore, $\frac{-2}{3}$ lies between $0$ and $-1$ and on the left side of '0' on the number line.

Hence, $\frac{-2}{3}$ lies to the left side of '0' on the number line.