Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\begin{aligned}&214\times \frac{\frac{15\times 32\times 45}{2}}{75}\\&\frac{15\times \frac{32}{2}\times 5}{75}\\&\frac{2480}{2}\times 5\end{aligned}\]
Simplify \(15\times 32\) to \(480\).
\[\begin{aligned}&214\times \frac{\frac{480\times 45}{2}}{75}\\&\frac{15\times \frac{32}{2}\times 5}{75}\\&\frac{2480}{2}\times 5\end{aligned}\]
Simplify \(480\times 45\) to \(21600\).
\[\begin{aligned}&214\times \frac{\frac{21600}{2}}{75}\\&\frac{15\times \frac{32}{2}\times 5}{75}\\&\frac{2480}{2}\times 5\end{aligned}\]
Simplify \(\frac{21600}{2}\) to \(10800\).
\[\begin{aligned}&214\times \frac{10800}{75}\\&\frac{15\times \frac{32}{2}\times 5}{75}\\&\frac{2480}{2}\times 5\end{aligned}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\begin{aligned}&214\times \frac{10800}{75}\\&\frac{\frac{15\times 32\times 5}{2}}{75}\\&\frac{2480}{2}\times 5\end{aligned}\]
Simplify \(15\times 32\) to \(480\).
\[\begin{aligned}&214\times \frac{10800}{75}\\&\frac{\frac{480\times 5}{2}}{75}\\&\frac{2480}{2}\times 5\end{aligned}\]
Simplify \(480\times 5\) to \(2400\).
\[\begin{aligned}&214\times \frac{10800}{75}\\&\frac{\frac{2400}{2}}{75}\\&\frac{2480}{2}\times 5\end{aligned}\]
Simplify \(\frac{2400}{2}\) to \(1200\).
\[\begin{aligned}&214\times \frac{10800}{75}\\&\frac{1200}{75}\\&\frac{2480}{2}\times 5\end{aligned}\]
214*10800/75;1200/75;2480/2*5
