Question

Find two rational number between $-3$ and $-2$.

Answer 1

Let us consider the rational number as $x$

So to find the rational number between $-3$ and $-2$

By using the formula $x=\frac{1}{2}(a+c)$

$x=\frac{1}{2}(-3+(-2\left)\right)$

$=\frac{1}{2}(-3-2)$

$=\frac{1}{2}(-5)=\frac{-5}{2}$

Now we find the rational number between $-5/2$ and $-2$. Since $-5/2$ also lies between $-3$ and $-2$.

Let us consider another rational number as $y$

So let us use the formula again

$y=\frac{1}{2}(-5/2+(-2\left)\right)$

$=\frac{1}{2}\left(\right(-5/2)-2)$

$=\frac{1}{2}\left(\right(-5-4\left)/2\right)$

$=\frac{1}{2}\left(\frac{-9}{2}\right)$

$=\frac{1}{2}\times \frac{-9}{2}$

$=\frac{-9}{4}$

$\therefore$ Two rational number between $-3$ and $2$ is $\frac{-5}{2}$ and $\frac{-9}{4}$.