Question

Find five rational number between $1$ and $2$.

Answer 1

Step 1: Find a common difference:

To find $n$ rational no in between any integer say $a$ and $b$, the common difference must be less than $\frac{b-a}{n}$

In this case the common difference must be less than $\frac{1}{5}$

Assume the common difference is $\frac{1}{10}$

Step 2: Find the rational number

The rational number between $1$ and $2$ is

$$\begin{gathered} 1+\frac{1}{10},1+\frac{2}{10},1+\frac{3}{10},1+\frac{4}{10},1+\frac{5}{10} \\ =\frac{11}{10},\frac{12}{10},\frac{13}{10},\frac{14}{10},\frac{15}{10} \\ =\frac{11}{10},\frac{6}{5},\frac{13}{10},\frac{7}{5},\frac{3}{2} \end{gathered}$$

Hence, five rational number between $1$ and $2$ is $\frac{11}{10},\frac{6}{5},\frac{13}{10},\frac{7}{5},\frac{3}{2}$