Exercice 115 :
↓ Enoncé :
Calculer :
- \(\dfrac{16}{24} \times \dfrac{9}{8} \times \dfrac{5}{6}\)
- \(3 \times \dfrac{5}{12} \times \dfrac{18}{25}\)
- \(\dfrac{7}{10} \times \dfrac{20}{14} \times \dfrac{21}{6}\)
- \(\dfrac{4}{9} \times 27 \times \dfrac{3}{8}\)
↓ Solution :
\[
\begin{align*}
\dfrac{16}{24} \times \dfrac{9}{8} \times \dfrac{5}{6} &= \dfrac{16\times 9\times 5}{24\times 8\times 6} \\
&= \dfrac{720}{1152} \\
&= \dfrac{5}{8}
\end{align*}
\]
\[
\begin{align*}
3 \times \dfrac{5}{12} \times \dfrac{18}{25} &= \dfrac{3\times 5\times 18}{1\times 12\times 25} \\
&= \dfrac{270}{300} \\
&= \dfrac{9}{10}
\end{align*}
\]
\[
\begin{align*}
\dfrac{7}{10} \times \dfrac{20}{14} \times \dfrac{21}{6} &= \dfrac{7\times 20\times 21}{10\times 14\times 6} \\
&= \dfrac{2940}{840} \\
&= \dfrac{7}{2}
\end{align*}
\]
\[
\begin{align*}
\dfrac{4}{9} \times 27 \times \dfrac{3}{8} &= \dfrac{4\times 27\times 3}{9\times 1\times 8} \\
&= \dfrac{324}{72} \\
&= \dfrac{9}{2}
\end{align*}
\]