Example 1.2.19

With our examples from the beginning of this subsection:

  1. \(\begin{aligned}[t] 3\div\frac{2}{7}\amp=3\multiplyright{\frac{7}{2}}\\ \amp=\divideunder{3}{1}\cdot\frac{7}{2}\\ \amp=\frac{21}{2}\\ \ \end{aligned}\)

  2. \(\begin{aligned}[t] \frac{18}{19}\div5\amp=\frac{18}{19}\div\divideunder{5}{1}\\ \amp=\frac{18}{19}\multiplyright{\frac{1}{5}}\\ \amp=\frac{18}{95}\\ \ \end{aligned}\)

  3. \(\begin{aligned}[t] \frac{14}{3}\div\frac{8}{9}\amp=\frac{14}{3}\multiplyright{\frac{9}{8}}\\ \amp=\frac{14}{\highlight{1}}\cdot\frac{\highlight{3}}{8}\\ \amp=\frac{\highlight{7}}{1}\cdot\frac{3}{\highlight{4}}\\ \amp=\frac{21}{4} \end{aligned}\)

  4. \(\begin{aligned}[t] \frac{\ \frac{2}{5}\ }{\frac{5}{2}}\amp=\frac{2}{5}\highlight{{}\div{}}\frac{5}{2}\\ \amp=\frac{2}{5}\multiplyright{\frac{2}{5}}\\ \amp=\frac{4}{25}\\ \ \end{aligned}\)

in-context