retour
Donner les résultats sous la forme d'un entier ou d'une fraction irréductible
\[A= \frac 1 2 - \frac 1 3 + \frac 1 4\;;\]
Corrigé
\[\begin{aligned}
A &= \frac 1 2 - \frac 1 3 + \frac 1 4&\\
&=\frac 6 {12} - \frac 4 {12} + \frac 3 {12}&\\
&=\frac{6-4+3}{12}&\\
&=\frac 5 {12}.&
\end{aligned}\]
\[B = 2 - \frac{13} 7 + \left(1 + \frac 5 2\right)\;;\]
Corrigé
\[\begin{aligned}
B &= 2 - \frac{13} 7 + \left(1+\frac 5 2\right)&\\
&=2 - \frac{13}7 + \left(\frac 2 2 + \frac 5 2\right)&\\
&=2 - \frac{13} 7 + \frac 7 2&\\
&=\frac{28}{14} - \frac{26}{14}+\frac{49}{14}&\\
&=\frac{51}{14}.&
\end{aligned}\]
\[C = \left(\frac 2 3 - \frac 3 4\right) + 3\times \left(\frac 4 5 - \frac 5 6\right)\;;\]
Corrigé
\[\begin{aligned}
C &= \left(\frac 2 3 - \frac 3 4\right) + 3\times\left(\frac 4 5 - \frac 5 6\right)&\\
&=\frac{8-9}{12} + 3\times \frac{24-25}{30}&\\
&=-\frac 1 {12} + 3\times \left(-\frac 1 {30}\right)&\\
&=-\frac 1 {12} - \frac 3 {30}&\\
&=-\frac 1 {12} - \frac 1 {10}&\\
&=\frac{-5-6}{60}&\\
&= -\frac{11}{60}.&
\end{aligned}\]
\[D = \frac{3 : \dfrac 3 4}{\dfrac 7 5 : 7}\;;\]
Corrigé
\[\begin{aligned}
D &= \frac{3:\dfrac 3 4}{\dfrac 7 5 : 7}&\\
&= \frac{3\times \dfrac 4 3}{\dfrac 7 5 \times \dfrac 1 7}&\\
&=\frac{4}{\dfrac 1 5}&\\
&=4 \times 5&\\
&=20.&
\end{aligned}\]
\[E = \dfrac{\dfrac 1 3 + \dfrac 1 2 - \dfrac 3 7}{\dfrac 2 3 - \dfrac 4 7 + \dfrac 1 6}\;;\]
Corrigé
\[\begin{aligned}
E &= \dfrac{\dfrac 1 3 + \dfrac 1 2 - \dfrac 3 7}{\dfrac 2 3 - \dfrac 4 7 + \dfrac 1 6}&\\
&= \dfrac{\dfrac{14+28-18}{42}}{\dfrac{28-24+21}{42}}&\\
&=\dfrac{\dfrac{24}{42}}{\dfrac{25}{42}}&\\
&=\dfrac{24}{42} \times \dfrac{42}{25}&\\
&=\dfrac{24}{25}.&
\end{aligned}\]
\[F=\left(\dfrac 1 2 + \dfrac 5 3\right) \times \dfrac{3+ \dfrac 7 4}{\dfrac 1 2 - \dfrac 5 6}.\]
Corrigé
\[\begin{aligned}
F &= \left(\frac 1 2 + \frac 5 3\right) \times \frac{3+\dfrac 7 4}{\dfrac 1 2 - \dfrac 5 6}&\\
&= \dfrac{3+10}{6}\times \dfrac{\dfrac{12+7}{4}}{\dfrac{3-5}6}&\\
&=\dfrac{\dfrac{19}4}{-\dfrac 2 6}&\\
&=\dfrac{\dfrac{19}4}{-\dfrac 1 3}&\\
&=\dfrac{19} 4 \times (-3)&\\
&=-\dfrac{57} 4.&
\end{aligned}\]
retour