Question

Points P and Q represent $\frac{-1}{2}$ and $\frac{3}{4}$ on a number line respectively. Which of the given figures show the correct representation ?

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Draw a number line as shown :

Point X is the origin which is 0.
XA, AB, BC, XA' and A'B' are of length 1 unit each.

In a rational number, the denominator tells the number of equal parts into which the each unit has been divided. The numerator, tells ‘how many’ of these parts are considered.

Since the denominators of the given numbers are not same, we have to find their LCM.
The LCM of 2 and 4 is 4.
So, we have to divide each marking of 1 unit into 4 equal parts.

Now, $\frac{3}{4}$ means three out of four equal parts on the right of 0. So, it will be the 3rd part from the right of 0.

0 > $\frac{-1}{2}$ > -1 , So it will lie between 0 and -1.
The first marking from the left of 0 will be $\frac{-1}{4}$.
The second marking from the left of 0 will be $\frac{-2}{4}$, which is nothing but $\frac{-1}{2}$.

Hence, the above figure is the correct representation of P = $\frac{-1}{2}$ and Q = $\frac{3}{4}$ on the number line.