\psshadowbox{ \begin{minipage}{1.0\linewidth-5\fboxsep} Pour additionner ou soustraire deux fractions, il faut qu'elles soient écrites avec le même dénominateur. \end{minipage} } \begin{description} \item[Exemple \no1] $\dfrac35+\dfrac76$\par \begin{center} \small \begin{tabular}{|c|*{10}{c|}} \hline $\times$&1&2&3&4&5&6&7&8&9&10\\ \hline 5&\ldots&\ldots&\ldots&\ldots&\ldots&\fbox{30}&\ldots&\ldots&\ldots&\ldots\\ \hline 6&\ldots&\ldots&\ldots&\ldots&\fbox{30}&\ldots&\ldots&\ldots&\ldots&\ldots\\ \hline \end{tabular} \end{center} \vspace{7.5mm}\par $\dfrac{\rnode{A}{3}}{\rnode{C}{5}}\,=\,\dfrac{\rnode{B}{\phantom{18}}}{\rnode{D}{30}}$ \kern2cm$\dfrac{\rnode{E}{7}}{\rnode{G}{6}}\,=\,\dfrac{\rnode{F}{\phantom{35}}}{\rnode{H}{30}}$\kern2cm $\dfrac35+\dfrac76=\dfrac{}{30}+\dfrac{}{30}=\dfrac{}{30}$ \nccurve[angleA=30,angleB=120,offsetA=2mm]{->}{A}{B}\naput{\small$\times\ldots$}\nccurve[angleA=-30,angleB=-120,offsetA=-2mm,offsetB=-1mm]{->}{C}{D}\nbput{\small$\times\ldots$} \nccurve[angleA=30,angleB=120,offsetA=2mm]{->}{E}{F}\naput{\small$\times\ldots$}\nccurve[angleA=-30,angleB=-120,offsetA=-2mm,offsetB=-1mm]{->}{G}{H}\nbput{\small$\times\ldots$} \par\vspace{7.5mm}\par \item[Exemple \no2] $\dfrac79-\dfrac56$ \begin{center} \small \begin{tabular}{|c|*{10}{c|}} \hline $\times$&1&2&3&4&5&6&7&8&9&10\\ \hline 6&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots\\ \hline 9&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots\\ \hline \end{tabular} \end{center} \vspace{7.5mm}\par $\dfrac{\rnode{A}{7}}{\rnode{C}{9}}\,=\,\dfrac{\rnode{B}{\phantom{18}}}{\rnode{D}{\phantom{30}}}$ \kern2cm$\dfrac{\rnode{E}{5}}{\rnode{G}{6}}\,=\,\dfrac{\rnode{F}{\phantom{35}}}{\rnode{H}{\phantom{30}}}$\kern2cm$\dfrac79-\dfrac56=\dfrac{}{\ldots}-\dfrac{}{\ldots}=\dfrac{}{\ldots}$ \nccurve[angleA=30,angleB=120,offsetA=2mm]{->}{A}{B}\naput{\small$\times\ldots$}\nccurve[angleA=-30,angleB=-120,offsetA=-2mm,offsetB=-1mm]{->}{C}{D}\nbput{\small$\times\ldots$} \nccurve[angleA=30,angleB=120,offsetA=2mm]{->}{E}{F}\naput{\small$\times\ldots$}\nccurve[angleA=-30,angleB=-120,offsetA=-2mm,offsetB=-1mm]{->}{G}{H}\nbput{\small$\times\ldots$} \par\vspace{7.5mm}\par \item[Exemple \no3] $\dfrac47-\dfrac43$ \begin{center} \small \begin{tabular}{|c|*{10}{c|}} \hline $\times$&1&2&3&4&5&6&7&8&9&10\\ \hline \ldots&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots\\ \hline \ldots&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots&\ldots\\ \hline \end{tabular} \end{center} \vspace{7.5mm}\par $\dfrac{\rnode{A}{4}}{\rnode{C}{7}}\,=\,\dfrac{\rnode{B}{\phantom{18}}}{\rnode{D}{\phantom{30}}}$ \kern2cm$\dfrac{\rnode{E}{4}}{\rnode{G}{3}}\,=\,\dfrac{\rnode{F}{\phantom{35}}}{\rnode{H}{\phantom{30}}}$\kern2cm$\dfrac47-\dfrac43=\dfrac{}{\ldots}-\dfrac{}{\ldots}=\dfrac{}{\ldots}$ \nccurve[angleA=30,angleB=120,offsetA=2mm]{->}{A}{B}\naput{\small$\times\ldots$}\nccurve[angleA=-30,angleB=-120,offsetA=-2mm,offsetB=-1mm]{->}{C}{D}\nbput{\small$\times\ldots$} \nccurve[angleA=30,angleB=120,offsetA=2mm]{->}{E}{F}\naput{\small$\times\ldots$}\nccurve[angleA=-30,angleB=-120,offsetA=-2mm,offsetB=-1mm]{->}{G}{H}\nbput{\small$\times\ldots$} \end{description} \par\vspace{7.5mm}\par\dotfill\par \ding{46} Effectue les calculs suivants : \[A=\frac35+\frac27\kern0.1\linewidth B=\frac14-\frac56\kern0.1\linewidth C=\frac59-\frac7{12}\] \begin{Solution} \[A=\frac{31}{\ldots}\kern0.1\linewidth B=\frac{-7}{\ldots}\kern0.1\linewidth C=\frac{-1}{\ldots}\] \end{Solution}