Question
Find three rational numbers between $4$ and $5.$
✓
Answer
First rational number between $4$ and $5 =\frac{1}{2}[4+5]$
$=\frac{1}{2}\times9$
$=\frac{9}{2}$
$\therefore4<\frac{9}{2}<5$Second rational number between $4$ and $\frac{9}{2}$
$=\frac{1}{2}\Big[4+\frac{9}{2}\Big]$
$=\frac{1}{2}\Big[\frac{8+9}{2}\Big]$
$=\frac{1}{2}\times\frac{17}{2}$
$=\frac{17}{4}$and third rational number between $\frac{9}{2}$ and $5$
$=\frac{1}{2}\Big[\frac{9}{2}+5\Big]$
$=\frac{1}{2}\Big[\frac{9+10}{2}\Big]$
$=\frac{1}{2}\times\frac{19}{2}$
$=\frac{19}{4}$
$\therefore4<\frac{17}{4}<\frac{9}{2}<\frac{19}{4}<5$
$\therefore$ Required three rational numbers and $\frac{17}{4},\frac{9}{2},\frac{19}{4}$
$=\frac{1}{2}\times9$
$=\frac{9}{2}$
$\therefore4<\frac{9}{2}<5$Second rational number between $4$ and $\frac{9}{2}$
$=\frac{1}{2}\Big[4+\frac{9}{2}\Big]$
$=\frac{1}{2}\Big[\frac{8+9}{2}\Big]$
$=\frac{1}{2}\times\frac{17}{2}$
$=\frac{17}{4}$and third rational number between $\frac{9}{2}$ and $5$
$=\frac{1}{2}\Big[\frac{9}{2}+5\Big]$
$=\frac{1}{2}\Big[\frac{9+10}{2}\Big]$
$=\frac{1}{2}\times\frac{19}{2}$
$=\frac{19}{4}$
$\therefore4<\frac{17}{4}<\frac{9}{2}<\frac{19}{4}<5$
$\therefore$ Required three rational numbers and $\frac{17}{4},\frac{9}{2},\frac{19}{4}$
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