Question 6: Find two rational numbers between \(4\) and \(5\).
Solution:
1st Rational Number: Average of \(4\) and \(5\)
\[\begin{align*}
&=\frac{4+5}{2}\\
&=\frac{9}{2}\\
\end{align*}\]
2nd Rational Number: Average of \(4\) and \(\frac{9}{2}\)
\[\begin{align*}
& =\left(4+\frac{9}{2}\right)\div 2\\
& =\left(\frac{8+9}{2}\right)\div 2\\
& =\frac{17}{2}\times \frac{1}{2}\\
& =\frac{17}{4}\\
\end{align*}\]
——-OR——-
Average of \(5\) and \(\frac{9}{2}\)
\[\begin{align*}
&=\left(5+\frac{9}{2}\right)\div 2\\
& =\left(\frac{10+9}{2}\right)\div 2\\
& =\frac{19}{2}\times \frac{1}{2} \\
& =\frac{19}{4} \\
\end{align*}\]