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Calculer
\[A = \left(1 + \frac 2 7\right) : \left(1 - \frac 2 7\right)\;;\]
Corrigé
\[\begin{aligned}
A &= \left(1 + \frac 2 7\right) : \left(1 - \frac 2 7\right)&\\
&= \frac{7+2} 7 : \frac{7-2} 7&\\
&=\frac 9 7 : \frac 5 7&\\
&=\frac 9 {\underset{1}{\cancel 7}} \times \frac {\overset{1}{\cancel 7}} 5&\\
&=\frac 9 5.&
\end{aligned}\]
\[B =-\frac 5 6 + 3\times \frac{11-1}{11+1}\;;\]
Corrigé
\[\begin{aligned}
B &= -\frac 5 6 + 3\times \frac{11-1}{11+1}&\\
&=-\frac 5 6 + 3\times \frac{10}{12}&\\
&=-\frac 5 6 + \frac{30}{12}&\\
&=\frac{-10+30}{12}&\\
&=\frac{20}{12}&\\
&=\frac 5 3.&
\end{aligned}\]
\[C = -\frac 3 {11} \times \left(1 - \frac 1 {14} - \frac 1 7\right)\;;\]
Corrigé
\[\begin{aligned}
C &= -\frac 3 {11} \times \left(1 - \frac 1 {14} - \frac 1 7\right)&\\
&= -\frac 3 {11} \times \frac{14-1-2}{14}&\\
&= -\frac 3 {\underset{1}{\cancel{11}}} \times \frac{\overset{1}{\cancel{11}}}{14}&\\
&=-\frac 3 {4}.&
\end{aligned}\]
\[D = 1 - \frac 1 3 : \frac 5 3 - \frac{28}{35}.\]
Corrigé
\[\begin{aligned}
D &= 1 - \frac 1 3 : \frac 5 3 - \frac{28}{35}&\\
&= 1 - \frac 1 {\underset{1}{\cancel{3}}} \times \frac{\overset{1}{\cancel{3}}} 5 - \frac{\overset{4}{\cancel{28}}}{\underset{5}{\cancel{35}}}&\\
&=1 - \frac 1 5 - \frac 4 5&\\
&=\frac{5 - 1 - 4}5&\\
&=0.&
\end{aligned}\]
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