Question 6: \((ii)\) \(3\) and \(4\)
Solution:
1st Rational Number: Average of \(3\) and \(4\)
\[\begin{align*}
&=\frac{3+4}{2}\\
&=\frac{7}{2}\\
\end{align*}\]
2nd Rational Number: Average of \(3\) and \(\frac{7}{2}\)
\[\begin{align*}
& =\left(3+\frac{7}{2}\right)\div 2\\
& =\left(\frac{6+7}{2}\right)\div 2\\
& =\frac{13}{2}\times \frac{1}{2}\\
& =\frac{13}{4}\\
\end{align*}\]
——-OR——-
Average of \(4\) and \(\frac{7}{2}\)
\[\begin{align*}
&=\left(4+\frac{7}{2}\right)\div 2\\
& =\left(\frac{8+7}{2}\right)\div 2\\
& =\frac{15}{2}\times \frac{1}{2} \\
& =\frac{15}{4} \\
\end{align*}\]