Question

The rational number lying between the numbers $\frac{1}{3}$ and $\frac{3}{4}$ are

• A. $\frac{97}{300}$,$\frac{299}{500}$
• B. $\frac{99}{300}$,$\frac{301}{400}$
• C. $\frac{95}{300}$,$\frac{301}{400}$
• D. $\frac{117}{300}$,$\frac{287}{400}$

Answer 1

The correct option is D $\frac{117}{300}$,$\frac{287}{400}$

To insert rational numbers between $2$ numbers, we will arrange the options and check if they are in ascending order.
$\frac{1}{3}?\frac{117}{300}⟹300<351\frac{3}{4}?\frac{287}{400}⟹1200>1148$
They are in ascending order, i.e., $\frac{1}{3},\frac{117}{300},\frac{287}{400},\frac{3}{4}$
From the given options only option $D$ satisfies this condition. Hence, $D$ is the answer.