# exo59.tex

\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}