Find three rational numbers between 4 and 5. - Vidyadip

Question

Find three rational numbers between 4 and 5.

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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 $\frac{17}{4},\frac{9}{2},\frac{19}{4}$

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