Find three rational numbers between 4 and 5.
Question:

Find three rational numbers between 4 and 5.

Solution:

Rational number between 4 and 5 :

$\frac{1}{2}(4+5)$

$=\frac{9}{2}$

Rational number between 4 and $\frac{9}{2}$ :

$\frac{1}{2}\left(4+\frac{9}{2}\right)$

$=\frac{1}{2}\left(\frac{8+9}{2}\right)$

$=\frac{1}{2}\left(\frac{17}{2}\right)$

$=\frac{17}{4}$

Rational number between $\frac{9}{2}$ and 5 :

$\frac{1}{2}\left(\frac{9}{2}+5\right)$

$=\frac{1}{2}\left(\frac{9+10}{2}\right)$

$=\frac{19}{4}$

We know,

$4<\frac{17}{4}<\frac{9}{2}<\frac{19}{4}<5$

Thus, the three rational numbers are $\frac{17}{4}, \frac{9}{2}$ and $\frac{19}{4}$.

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