Example1.2.17

With our examples from the beginning of this subsection:

\begin{align*} 3\div\frac{2}{7}\amp=3\multiplyright{\frac{7}{2}}\amp\frac{18}{19}\div5\amp=\frac{18}{19}\div\divideunder{5}{1}\\ \amp=\divideunder{3}{1}\cdot\frac{7}{2}\amp\amp=\frac{18}{19}\multiplyright{\frac{1}{5}}\\ \amp=\frac{21}{2}\amp\amp=\frac{18}{95}\\ \\ \frac{14}{3}\div\frac{8}{9}\amp=\frac{14}{3}\multiplyright{\frac{9}{8}}\amp\frac{\ \frac{2}{5}\ }{\frac{5}{2}}\amp=\frac{2}{5}\highlight{{}\div{}}\frac{5}{2}\\ \amp=\frac{14}{\highlight{1}}\cdot\frac{\highlight{3}}{8}\amp\amp=\frac{2}{5}\multiplyright{\frac{2}{5}}\\ \amp=\frac{\highlight{7}}{1}\cdot\frac{3}{\highlight{4}}\amp\amp=\frac{4}{25}\\ \amp=\frac{21}{4} \end{align*}
in-context