Question
Insert three rational number between:$6$ and $7$
✓
Answer
A rational number lying between $6$ and $7$
$=\frac{6+7}{2} $
$=\frac{13^2}{2}$
A rational number lying between $6$ and $\frac{13}{2}$
$=\frac{6+\frac{13}{2}}{2} $
$=\frac{\frac{25}{2}}{2} $
$=\frac{25}{4}$
A rational number lying between $\frac{13}{2}$ and $7$
$=\frac{\frac{13}{2}+7}{2} $
$=\frac{\frac{27}{2}}{2} $
$=\frac{27}{4} $
$6<\frac{25}{4}<\frac{13}{2}<\frac{27}{4}<7$
Hence, three rational numbers between $6$ and $7$ are $\frac{25}{4}, \frac{13}{2}$ and $\frac{27}{4}$
$=\frac{6+7}{2} $
$=\frac{13^2}{2}$
A rational number lying between $6$ and $\frac{13}{2}$
$=\frac{6+\frac{13}{2}}{2} $
$=\frac{\frac{25}{2}}{2} $
$=\frac{25}{4}$
A rational number lying between $\frac{13}{2}$ and $7$
$=\frac{\frac{13}{2}+7}{2} $
$=\frac{\frac{27}{2}}{2} $
$=\frac{27}{4} $
$6<\frac{25}{4}<\frac{13}{2}<\frac{27}{4}<7$
Hence, three rational numbers between $6$ and $7$ are $\frac{25}{4}, \frac{13}{2}$ and $\frac{27}{4}$
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