Question

Find a rational number between

$-\frac{3}{4}$ and $-\frac{2}{5}$.

Answer 1

If $x$ and $y$ are two rational numbers, where $x<y$.

Then, $\frac{x+y}{2}$ is a rational number, which lies between $x$ and $y$.

That is, $x<\frac{x+y}{2}<y$

Here, $x=-\frac{3}{4}$ and $y=-\frac{2}{5}$

Rational number between $-\frac{3}{4}$ and $-\frac{2}{5}$is given by:

$$\begin{gathered} \frac{x+y}{2} \\ =\frac{(-\frac{3}{4})+(-\frac{2}{5})}{2} \\ =\frac{(-\frac{3}{4}-\frac{2}{5})}{2}[TakeLeastCommonMutiple(L.C.M)innumerator] \\ =\frac{\frac{-15-8}{20}}{2} \\ =\frac{-\frac{23}{20}}{2} \\ =-\frac{23}{40} \end{gathered}$$

We have, $-\frac{3}{4}<-\frac{23}{40}<-\frac{2}{5}$.

Therefore, the rational number between $-\frac{3}{4}$ and $-\frac{2}{5}$ is $-\frac{23}{40}$.