Correction exercice 3

Correction

Fiche 2-rev3-2

Exercice 3

Calculer les fractions suivantes. Simplifier au maximum le résultat.

$$D = \dfrac{3}{5}-\dfrac{2}{5}\times \dfrac{7}{6} \qquad E=\dfrac{-\dfrac{3}{4} + \dfrac{5}{7}}{\dfrac{2}{3} + \dfrac{3}{4}}  \qquad F=\dfrac{\dfrac{4}{5} – \dfrac{2}{3}}{\dfrac{2}{5} – \dfrac{4}{3}}$$

Correction

$\begin{align} D &= \dfrac{3}{5}-\dfrac{2}{5}\times \dfrac{7}{6} \\\\
&= \dfrac{3}{5} – \dfrac{7}{15} \\\\
&=\dfrac{9}{15} – \dfrac{7}{15} \\\\
&=\dfrac{2}{15}
\end{align}$

$\quad$

$\begin{align} E&=\dfrac{-\dfrac{3}{4} + \dfrac{5}{7}}{\dfrac{2}{3} + \dfrac{3}{4}} \\\\
&= \dfrac{-\dfrac{21}{28}+\dfrac{20}{28}}{\dfrac{8}{12}+\dfrac{9}{12}} \\\\
&=\dfrac{-\dfrac{1}{28}}{\dfrac{17}{12}}\\\\
&=-\dfrac{1}{28} \times \dfrac{12}{17} \\\\
&=-\dfrac{3}{119}
\end{align}$

$\quad$

$\begin{align} F&=\dfrac{\dfrac{4}{5} – \dfrac{2}{3}}{\dfrac{2}{5} – \dfrac{4}{3}} \\\\
&=\dfrac{\dfrac{12}{15}-\dfrac{10}{15}}{\dfrac{6}{15}-\dfrac{20}{15}} \\\\
&=\dfrac{\dfrac{2}{15}}{-\dfrac{14}{15}}\\\\
&=-\dfrac{2}{15} \times \dfrac{15}{14}\\\\
&=-\dfrac{1}{7}
\end{align}$