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Calculer chaque expression et donner le résultat sous la forme d'une
fraction irréductible.
\[A=\left(\frac 4 5 - \frac 1 {15}\right)\times\left(\frac 1 6 + \frac 1 4\right)\;;\]
Corrigé
\[\begin{aligned}
A &= \left(\frac 4 5 - \frac 1 {15}\right) \times \left(\frac 1 6 + \frac 1 4\right)&\\
&=\left(\frac{12}{15}-\frac 1{15}\right)\left(\frac 2 {12} + \frac 3 {12}\right)&\\
&=\frac{12 - 1}{15} \times \frac{2+3}{12}&\\
&=\frac{11}{15} \times \frac 5 {12}&\\
&=\frac{11\times 5}{15\times 12}&\\
&=\frac{11}{3\times 12}&\\
&=\frac{11}{36}.&
\end{aligned}\]
\[B=\frac 4 3 \times \left(\frac 1 8 - 1\right)\;;\]
Corrigé
\[\begin{aligned}
B &= \frac 4 3 \times \left(\frac 1 8 - 1\right)&\\
&= \frac 4 3 \times \left(\frac 1 8 - \frac 8 8\right)&\\
&= \frac 4 3 \times \left(-\frac 7 8\right)&\\
&= -\frac{4\times 7}{3\times 8}&\\
&=-\frac 7 {3\times 2}&\\
&=-\frac 7 6.&
\end{aligned}\]
\[C=\dfrac{\dfrac{-9} 4 \times \dfrac 5 9}{1-\dfrac 7 {12}}.\]
Corrigé
\[\begin{aligned}
C&=\dfrac{\dfrac{-9} 4 \times \dfrac 5 9}{1-\dfrac 7 {12}}&\\
&= \dfrac{-\dfrac{5}{4}}{\dfrac{12}{12}-\dfrac 7 {12}}&\\
&=\dfrac{-\dfrac 5 4}{\dfrac 5 {12}}&\\
&=-\dfrac 5 4 \times \dfrac {12} 5&\\
&= -3.&
\end{aligned}\]
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