Question 6: \((i)\) \(\frac{1}{3}\) and \(\frac{1}{4}\)
Solution:
1st Rational Number: Average of \(\frac{1}{3}\) and \(\frac{1}{4}\)
\[\begin{align*}
&=\left(\frac{1}{3}+\frac{1}{4}\right)\div 2 \\
&=\left(\frac{4+3}{12}\right) \div 2 \\
&=\frac{7}{12}\times \frac{1}{2}\\
&=\frac{7}{24}\end{align*}\]
2nd Rational Number: Average of \(\frac{1}{3}\) and \(\frac{7}{24}\)
\[\begin{align*}
& =\left(\frac{1}{3}+\frac{7}{24}\right)div 2 \\
&=\left(\frac{8+7}{24}\right)\div 2 \\
& =\frac{15}{24}\times \frac{1}{2} \\
& =\frac{15}{48} \end{align*}\]
——-OR——-
Average of \(\frac{1}{4}\) and \(\frac{7}{24}\)
\[\begin{align*}
&=\left(\frac{1}{4}+\frac{7}{24}\right)\div 2\\
& =\left(\frac{1}{4}+\frac{7}{24}\right)\div 2\\
& =\frac{13}{24}\times \frac{1}{2} \\
&=\frac{13}{48}\\
\end{align*}\]