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+\usetikzlibrary{shapes.geometric} + \author{Benjamin Bertrand} \title{Fractions et opérations - Exercices} \date{2021-11-14} diff --git a/4e/08_Fractions_et_operations/exercises.tex b/4e/08_Fractions_et_operations/exercises.tex index f47543d..1f51b17 100644 --- a/4e/08_Fractions_et_operations/exercises.tex +++ b/4e/08_Fractions_et_operations/exercises.tex @@ -138,16 +138,32 @@ \begin{multicols}{2} \begin{enumerate} \item $\dfrac{3}{4}$ de 8\euro. - - \includegraphics[scale=0.5]{./fig/8euros.pdf} + \begin{tikzpicture}[scale=0.8] + \foreach \k in {0,1,...,7} + {\draw (\k, 0) node {1\euro} circle (0.4);} + \end{tikzpicture} \item $\dfrac{1}{2}$ de 10 étoiles. - \includegraphics[scale=0.5]{./fig/10etoiles.pdf} + %\includegraphics[scale=0.5]{./fig/10etoiles.pdf} + \begin{tikzpicture}[scale=0.8] + \tikzstyle{scorestars}=[star, star points=5, star point ratio=2.25, draw, inner sep=3pt, anchor=outer point 3]% + \foreach \k in {0,1,...,9} + {\draw (\k, 0) node node[name=star\i, scorestars] {};} + \end{tikzpicture} \item $\dfrac{5}{3}$ de 12m. - \includegraphics[scale=0.6]{./fig/12m.pdf} + \begin{tikzpicture}[scale=0.7] + \draw [very thick](0, 0) -- (12, 0); + \draw [very thick](0, -1) -- (12, -1); + \foreach \k in {0,1,...,12} + {% + \draw [very thick](\k, -0.2) --++ (0, 0.2); + \draw [very thick](\k, -1.2) --++ (0, 0.2); + } + \end{tikzpicture} + \item $\dfrac{4}{5}$ de 20 élèves. \item $\dfrac{25}{100}$ de 40\euro. @@ -161,6 +177,68 @@ \begin{solution} + \begin{multicols}{2} + \begin{enumerate} + \item $\dfrac{3}{4}$ de 8\euro. + \begin{tikzpicture}[scale=0.8] + \foreach \k in {0,1,...,5} + {\draw [black, fill=black!20] (\k, 0) node {1\euro} circle (0.4);} + \foreach \k in {5,6,...,7} + {\draw (\k, 0) node {1\euro} circle (0.4);} + \end{tikzpicture} + Donc 6\euro. + + \item $\dfrac{1}{2}$ de 10 étoiles. + + %\includegraphics[scale=0.5]{./fig/10etoiles.pdf} + \begin{tikzpicture}[scale=0.8] + \tikzstyle{scorestars}=[star, star points=5, star point ratio=2.25, draw, inner sep=3pt, anchor=outer point 3]% + \foreach \k in {0,1,...,4} + {\draw (\k, 0) node node[name=star\i, scorestars, fill=black!20] {};} + \foreach \k in {0,1,...,4} + {\draw (5+\k, 0) node node[name=star\i, scorestars] {};} + \end{tikzpicture} + Donc 5 étoiles + + \item $\dfrac{5}{3}$ de 12m. + + \begin{tikzpicture}[scale=0.7] + \draw [very thick](0, 0) -- (12, 0); + \draw [very thick](0, -1) -- (12, -1); + \foreach \k in {0,1,...,12} + {% + \draw [very thick](\k, -0.2) --++ (0, 0.2); + \draw [very thick](\k, -1.2) --++ (0, 0.2); + } + \draw [red, very thick](0, 0) -- (12, 0); + \draw [red, very thick](0, -1) -- (8, -1); + \end{tikzpicture} + Donc 20m. + + + \item $\dfrac{4}{5}$ de 20 élèves. + \[ + \frac{4}{5} \times 20 = 16 \mbox{élèves} + \] + \item $\dfrac{25}{100}$ de 40\euro. + \[ + \frac{25}{100} \times 40 = 10 \mbox{\euro} + \] + \item $\dfrac{3}{5}$ de 100L. + \[ + \frac{3}{5} \times 100 = 60L + \] + \item $\dfrac{3}{2}$ de 6m. + \[ + \frac{3}{2} \times 6 = 9m + \] + \item $50\%$ de 10kg. + \[ + \frac{50}{100} \times 10 = 5kg + \] + \end{enumerate} + \end{multicols} + Le mot "de" est traduit pas $\times$ en mathématiques. \end{solution} \begin{exercise}[subtitle={Au travail! }, step={3}, origin={Les maths ensemble et pour chacun 4e}, topics={ Fractions et opérations }, tags={ Fraction }]