EX-02-S07

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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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code : 719