\(\begin{array}{l}
4\frac{2}{3}:3\frac{2}{7} = \frac{{14}}{3}:\frac{{23}}{7} = \frac{{14}}{3} \times \frac{7}{{23}} = \frac{{98}}{{69}} = 1\frac{{29}}{{69}} \\
4\frac{2}{3}:3\frac{2}{7} = \frac{{14}}{3}:\frac{{23}}{7} = \frac{{98}}{{21}}:\frac{{69}}{{21}} = \frac{{98}}{{69}} = 1\frac{{29}}{{69}} \\
4\frac{2}{3}:3\frac{2}{7} = 14:9\frac{6}{7} = 98:69 = 1\frac{{29}}{{69}} \\
\end{array}\)
Just for fun!
