Question

A rational number between two rational number $a$ and $b$is _______.

Answer 1

Explanation:

Let, $a\mathrm{and}\mathrm{b}$are any two unequal rational numbers.

So, we can assume that $a<b....................\left(A\right)$

Adding $a$ both sides, we get

$a+a<a+b$

Dividing both sides by 2, we get

$$\begin{gathered} \frac{2a}{2}<\frac{a+b}{2} \\ =a<\frac{a+b}{2}..............\left(1\right) \end{gathered}$$

Adding $b$both sides to the equation $A$, we get

$a+b<b+b$

Dividing both sides by 2, we get

$$\begin{gathered} \frac{a+b}{2}<\frac{2b}{2} \\ =\frac{a+b}{2}<b..................\left(2\right) \end{gathered}$$

From the equation$\left(1\right)\mathrm{and}\left(2\right)$, we get

$a<\frac{a+b}{2}<b$

Hence, we can say that a rational number between two rational numbers $a\mathrm{and}b$ is$\frac{a+b}{2}$.