To find a rational number x between two rational numbers \(\frac{a}{b}\) and \(\frac{c}{d},\) we use

\(\text{x}=\frac{1}{2}(\frac{a}{b}+\frac{c}{d})\)

Therefore, 

to find rational number x (let) between 4 and 5

\(\text{x}=\frac{1}{2}(4+5)\)

\(\Rightarrow\) \(\text{x}=\frac{1}{2}\times9\)

\(\Rightarrow\) \(\text{x}=\frac{9}{2}\)

Now if we find a rational number between 4 and \(\frac{9}{2}\) it will also be between 4 and 5 since \(\frac{9}{2}\) lies between 4 and 5 

Therefore, 

to find rational number y (let) between 4 and \(\frac{9}{2}\)

\(\text{y}=\frac{1}{2}(4+\frac{9}{2})\)

\(\Rightarrow\) \(\text{y}=\frac{1}{2}(\frac{8+9}{2})\) 

\(\Rightarrow\) \(\text{y}=\frac{1}{2}\times\frac{17}{2}\) 

\(\Rightarrow\) \(\text{y}=\frac{17}{4}\) 

Now if we find a rational number between \(\frac{9}{2}\) and 5 it will also be between 4 and 5 since \(\frac{9}{2}\) lies between 4 and 5 

Therefore, 

to find rational number z (let) between \(\frac{9}{2}\)and 5

\(\text{z} =\frac{1}{2}(\frac{9}{2}+5)\)

\(\Rightarrow\) \(\text{z}= \frac{1}{2}(\frac{9+10}{2})\)

\(\Rightarrow\) \(\text{z}=\frac{1}{2}\times\frac{19}{2}\)

\(\Rightarrow\) \(\text{z}=\frac{19}{4}\)