%%% % Application : pourcentage %%% \setKVdefault[ClesPourcentage]{Appliquer,Calculer=false,Augmenter=false,Reduire=false,Fractionnaire=false,Decimal,Formule=false,Concret=false,GrandeurA=Grandeur A,GrandeurB=Total,Largeur=1cm,MotReduction=diminution,AideTableau=false,ColorFill=white,CouleurTab=gray!15} \defKV[ClesPourcentage]{Unite=\setKV[ClesPourcentage]{Concret}} \newcommand\Pourcentage[3][]{% \useKVdefault[ClesPourcentage]% \setKV[ClesPourcentage]{#1}% \ifboolKV[ClesPourcentage]{Reduire}{% \ifboolKV[ClesPourcentage]{Formule}{% R\'eduire une quantit\'e de \num{#2}~\%, cela revient \`a multiplier cette quantit\'e par $1-\dfrac{\num{#2}}{100}$. Par cons\'equent, si on r\'eduit \num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{} de \num{#2}~\%, cela donne : \[\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\times\left(1-\frac{\num{#2}}{100}\right)=\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\times(1-\num{\fpeval{#2/100}})=\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\times\num{\fpeval{(1-#2/100)}}=\num{\fpeval{#3*(1-#2/100)}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\] }{% Calculons ce que repr\'esente la \useKV[ClesPourcentage]{MotReduction} de \num{#2}~\%. \ifboolKV[ClesPourcentage]{AideTableau}{% \xdef\NomA{\useKV[ClesPourcentage]{GrandeurA}}% \xdef\NomB{\useKV[ClesPourcentage]{GrandeurB}}% \xdef\NomCouleurTab{\useKV[ClesPourcentage]{CouleurTab}}% \xdef\NomLargeurTab{\useKV[ClesPourcentage]{Largeur}}% \begin{center} \Propor[Math,GrandeurA=\NomA,GrandeurB=\NomB,CouleurTab=\NomCouleurTab,Largeur=\NomLargeurTab]{/\num{#3},\num{#2}/100} \end{center} \FlecheCoefInv{\tiny$\times\num{\fpeval{#2/100}}$}% On obtient une \useKV[ClesPourcentage]{MotReduction} de $\num{\fpeval{#2/100}}\times\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}=\num{\fpeval{#3*#2/100}}$\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{}. Donc un total de $\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}-\num{\fpeval{#3*#2/100}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}=\num{\fpeval{#3*(1-#2/100)}}$\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{}.% }{Pour calculer \num{#2}~\% de \num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{}, on effectue le calcul : \[\ifboolKV[ClesPourcentage]{Fractionnaire}{\frac{\num{#2}}{100}}{\num{\fpeval{#2/100}}}\times\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}=\ifboolKV[ClesPourcentage]{Fractionnaire}{\frac{\num{\fpeval{#2*#3}}}{100}}{\num{\fpeval{#2*#3/100}}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\ifboolKV[ClesPourcentage]{Fractionnaire}{=\num{\fpeval{#2*#3/100}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}}{}\]% On obtient une \useKV[ClesPourcentage]{MotReduction} de $\num{\fpeval{#3*#2/100}}$\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{}.\\Donc un total de $\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}-\num{\fpeval{#3*#2/100}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}=\num{\fpeval{#3*(1-#2/100)}}$\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{}.} } }{% \ifboolKV[ClesPourcentage]{Augmenter}{% \ifboolKV[ClesPourcentage]{Formule}{% Augmenter de \num{#2}~\% une quantit\'e, cela revient \`a multiplier cette quantit\'e par $1+\dfrac{\num{#2}}{100}$. Par cons\'equent, si on augmente \num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{} de \num{#2}~\%, cela donne : \[\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\times\left(1+\frac{\num{#2}}{100}\right)=\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\times(1+\num{\fpeval{#2/100}})=\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\times\num{\fpeval{(1+#2/100)}}=\num{\fpeval{#3*(1+#2/100)}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\] }{% Calculons ce que repr\'esente l'augmentation de \num{#2}~\%. % \ifboolKV[ClesPourcentage]{AideTableau}{% \xdef\NomA{\useKV[ClesPourcentage]{GrandeurA}}% \xdef\NomB{\useKV[ClesPourcentage]{GrandeurB}}% \xdef\NomCouleurTab{\useKV[ClesPourcentage]{CouleurTab}}% \xdef\NomLargeurTab{\useKV[ClesPourcentage]{Largeur}}% \begin{center}% \Propor[Math,GrandeurA=\NomA,GrandeurB=\NomB,CouleurTab=\NomCouleurTab,Largeur=\NomLargeurTab]{/\num{#3},\num{#2}/100}% \end{center}% \FlecheCoefInv{\tiny$\times\num{\fpeval{#2/100}}$}% On obtient une augmentation de $\num{\fpeval{#2/100}}\times\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}=\num{\fpeval{#3*#2/100}}$\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{}.\\Donc un total de $\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}+\num{\fpeval{#3*#2/100}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}=\num{\fpeval{#3*(1+#2/100)}}$\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{}.% }{Pour calculer \num{#2}~\% de \num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{}, on effectue le calcul : \[\ifboolKV[ClesPourcentage]{Fractionnaire}{\frac{\num{#2}}{100}}{\num{\fpeval{#2/100}}}\times\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}=\ifboolKV[ClesPourcentage]{Fractionnaire}{\frac{\num{\fpeval{#2*#3}}}{100}}{\num{\fpeval{#2*#3/100}}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\ifboolKV[ClesPourcentage]{Fractionnaire}{=\num{\fpeval{#2*#3/100}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}}{}\]% On obtient une augmentation de $\num{\fpeval{#3*#2/100}}$\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{}.\\Donc un total de $\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}+\num{\fpeval{#3*#2/100}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}=\num{\fpeval{#3*(1+#2/100)}}$\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{}.} } }{% \ifboolKV[ClesPourcentage]{Calculer}{% \xdef\NomA{\useKV[ClesPourcentage]{GrandeurA}}% \xdef\NomB{\useKV[ClesPourcentage]{GrandeurB}}% \xdef\NomCouleurTab{\useKV[ClesPourcentage]{CouleurTab}}% \xdef\NomLargeurTab{\useKV[ClesPourcentage]{Largeur}}% \Propor[Math,GrandeurA=\NomA,GrandeurB=\NomB,CouleurTab=\NomCouleurTab,Largeur=\NomLargeurTab]{\num{#2}/\num{#3},/100}% \xdef\colorfill{\useKV[ClesPourcentage]{ColorFill}}% \FlechesPB{2}{1}{\scriptsize$\times\num{\fpeval{#3/100}}$}% \FlechesPH{1}{2}{\scriptsize$\div\num{\fpeval{#3/100}}$}% \xdef\ResultatPourcentage{\fpeval{#2*100/#3}}% }{% Pour calculer \num{#2}~\% de \num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\useKV[ClesPourcentage]{Unite}}{}, on effectue le calcul :% \[\ifboolKV[ClesPourcentage]{Fractionnaire}{\frac{\num{#2}}{100}}{\num{\fpeval{#2/100}}}\times\num{#3}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}=\ifboolKV[ClesPourcentage]{Fractionnaire}{\frac{\num{\fpeval{#2*#3}}}{100}}{\num{\fpeval{#2*#3/100}}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}\ifboolKV[ClesPourcentage]{Fractionnaire}{=\num{\fpeval{#2*#3/100}}\ifboolKV[ClesPourcentage]{Concret}{~\text{\useKV[ClesPourcentage]{Unite}}}{}}{}\]% }% }% }% }%