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

Answer: (A)

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.