Find three rational numbers between $\frac{2}{3}$ and $\frac{3}{4}$.
Rational number between $\frac{2}{3}$ and $\frac{3}{4}$ :
$\frac{1}{2}\left(\frac{2}{3}+\frac{3}{4}\right)$
$=\frac{1}{2}\left(\frac{8+9}{12}\right)$
$=\frac{17}{24}$
We know,
$\frac{2}{3}<\frac{17}{24}<\frac{3}{4}$
Rational number between $\frac{2}{3}$ and $\frac{17}{24}$ :
$\frac{1}{2}\left(\frac{2}{3}+\frac{17}{24}\right)$
$=\frac{1}{2}\left(\frac{16+17}{24}\right)$
$=\frac{1}{2}\left(\frac{33}{24}\right)$
$=\frac{33}{48}=\frac{33 \div 3}{48 \div 3}=\frac{11}{16}$
Rational number between $\frac{17}{24}$ and $\frac{3}{4}$ :
$\frac{1}{2}\left(\frac{17}{24}+\frac{3}{4}\right)$
$=\frac{1}{2}\left(\frac{17+18}{24}\right)$
$=\frac{1}{2}\left(\frac{35}{24}\right)$
$=\frac{35}{48}$
We know,
$\frac{2}{3}<\frac{11}{16}<\frac{17}{24}<\frac{35}{48}<\frac{3}{4}$
Thus, the three rational numbers are $\frac{11}{16}, \frac{17}{24}$ and $\frac{35}{48}$.
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