Feat: début du chapitre sur les fractions pour les 4e
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4e/08_Fractions_et_operations/1E_representation.pdf
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4e/08_Fractions_et_operations/1E_representation.pdf
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4e/08_Fractions_et_operations/1E_representation.tex
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4e/08_Fractions_et_operations/1E_representation.tex
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\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\author{Benjamin Bertrand}
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\title{Fractions et opérations - Exercices}
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\date{2021-11-14}
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4e/08_Fractions_et_operations/2E_add_soust_frac.pdf
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4e/08_Fractions_et_operations/2E_add_soust_frac.pdf
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4e/08_Fractions_et_operations/2E_add_soust_frac.tex
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4e/08_Fractions_et_operations/2E_add_soust_frac.tex
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\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\author{Benjamin Bertrand}
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\title{Fractions et opérations - Exercices}
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\date{2021-11-14}
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4e/08_Fractions_et_operations/3E_fractions_quantite.pdf
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4e/08_Fractions_et_operations/3E_fractions_quantite.pdf
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4e/08_Fractions_et_operations/3E_fractions_quantite.tex
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4e/08_Fractions_et_operations/3E_fractions_quantite.tex
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\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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|
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\author{Benjamin Bertrand}
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\title{Fractions et opérations - Exercices}
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\date{2021-11-14}
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4e/08_Fractions_et_operations/exercises.tex
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4e/08_Fractions_et_operations/exercises.tex
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\begin{exercise}[subtitle={Représenter des fractions}, step={1}, origin={Les maths ensemble et pour chacun 5e}, topics={ Fractions et opérations }, tags={ Fraction }]
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Pour chacune des figures, trouve une fraction qui correspond à la partie grisée.
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\begin{minipage}{0.55\linewidth}
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\includegraphics[scale=0.7]{./fig/surface_partagee}
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\end{minipage}
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\begin{minipage}{0.4\linewidth}
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\begin{enumerate}[label={Figure \arabic*}: ]
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\item \dotfill
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~\vspace{0.5cm}
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\item \dotfill
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~\vspace{0.5cm}
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\item \dotfill
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~\vspace{0.5cm}
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\item \dotfill
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~\vspace{0.5cm}
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\item \dotfill
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~\vspace{0.5cm}
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\item \dotfill
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~\vspace{0.5cm}
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\item \dotfill
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\end{enumerate}
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\end{minipage}
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\textbf{Mode avancé}: trouve une deuxième fraction pour chaque figure avec un dénominateur différent.
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\textbf{Mode expert}: pour chaque figure, trouve la fraction avec le plus petit dénominateur possible.
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\end{exercise}
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\begin{solution}
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\begin{minipage}{0.55\linewidth}
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\includegraphics[scale=0.7]{./fig/surface_partagee}
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\end{minipage}
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\begin{minipage}{0.4\linewidth}
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\begin{enumerate}[label={Figure \arabic*}: ]
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\item $\frac{4}{12}= \frac{1}{3}$
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~\vspace{0.5cm}
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\item $\frac{4}{10} = \frac{2}{5}$
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~\vspace{0.5cm}
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\item $\frac{6}{16} = \frac{3}{8}$
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~\vspace{0.5cm}
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\item $\frac{8}{20} = \frac{2}{5}$
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~\vspace{0.5cm}
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\item $\frac{6}{16} = \frac{3}{8}$
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~\vspace{0.5cm}
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\item $\frac{8}{24} = \frac{1}{3}$
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~\vspace{0.5cm}
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\item $\frac{10}{20} = \frac{1}{2}$
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\end{enumerate}
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\end{minipage}
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\end{solution}
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\begin{exercise}[subtitle={Partage de l'agneau \Rep \Rai}, step={2}, origin={Les maths ensemble et pour chacun 4e}, topics={ Fractions et opérations }, tags={ Fraction }]
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\begin{quote}
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Nous allons partager cet agneau, dit le lion en s'adressant au singe et au renard.
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Puisque nous sommes trois, j'en prends d'abord le tiers: c'est juste.
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Ensuite, comme roi des animaux, il m'en revient, en plus, la moitié.
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Enfin, je m'attribue encore le sixième parce que tel est mon bon plaisir.
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Après cela, partagez-vous le reste.
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\flushright{La Fontaine}
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\end{quote}
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Que penses-tu de cette histoire?
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\end{exercise}
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\begin{solution}
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\begin{multicols}{2}
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\begin{itemize}
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\item Méthode graphique
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\begin{tikzpicture}
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\draw (3, 1.5) node{L'agneau};
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\draw [black,fill=red](0, 0) rectangle ++(1, 1);
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\draw [black,fill=red](1, 0) rectangle ++(1, 1);
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\draw (1, -0.5) node{$\dfrac{1}{3}$};
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\draw [black,fill=green](2, 0) rectangle ++(1, 1);
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\draw [black,fill=green](3, 0) rectangle ++(1, 1);
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\draw [black,fill=green](4, 0) rectangle ++(1, 1);
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\draw (3.5, -0.5) node{$\dfrac{1}{2}$};
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\draw (5, 0) rectangle ++(1, 1);
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\draw (5.5, -0.5) node{$\dfrac{1}{6}$};
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\end{tikzpicture}
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\item Méthode calculatoire
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\begin{itemize}
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\item Le tiers: $\frac{1}{3}=\frac{2}{6}$
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\item La moitié $\frac{1}{2}=\frac{3}{6}$
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\item Le sixième $\frac{1}{6}$
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\end{itemize}
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Au final, le lion aura mangé:
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\[
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\frac{1}{3} + \frac{1}{2} + \frac{1}{6} = \frac{6}{6}
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\]
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\end{itemize}
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\end{multicols}
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Donc tout l'agneau. Il ne reste rien pour les autres animaux.
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\end{solution}
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\begin{exercise}[subtitle={Additions et Soustraction \Cal}, step={2}, origin={Les maths ensemble et pour chacun 4e}, topics={ Fractions et opérations }, tags={ Fraction }]
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Calculer en détaillant les étapes (vous pouvez vous aider d'un dessin pour guider vos calculs)
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\begin{multicols}{3}
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\begin{enumerate}[label={\Alph*=}]
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\item $\dfrac{5}{6} + \dfrac{2}{3}$
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\item $\dfrac{5}{2} + \dfrac{1}{6}$
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\item $1 + \dfrac{2}{3}$
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\item $2 + \dfrac{5}{6}$
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\item $\dfrac{5}{2} - \dfrac{3}{4}$
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\item $2 - \dfrac{1}{4}$
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\end{enumerate}
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\end{multicols}
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\end{exercise}
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\begin{solution}
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\begin{multicols}{3}
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\begin{enumerate}[label={\Alph*=}]
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\item $\dfrac{5}{6} + \dfrac{2}{3} = \dfrac{5}{6} = \dfrac{4}{6} = \dfrac{9}{6} = \dfrac{3}{2}$
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\item $\dfrac{5}{2} + \dfrac{1}{6} = \dfrac{15}{6} = \dfrac{1}{6} = \dfrac{16}{6} = \dfrac{8}{3}$
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\item $1 + \dfrac{2}{3} = \dfrac{3}{3} + \dfrac{2}{3} = \dfrac{5}{3}$
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\item $2 + \dfrac{5}{6} = \dfrac{12}{6} + \dfrac{5}{6} = \dfrac{17}{6}$
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\item $\dfrac{5}{2} - \dfrac{3}{4} = \dfrac{10}{4} - \dfrac{3}{4} \dfrac{7}{4}$
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\item $2 - \dfrac{1}{4} = \dfrac{8}{4} - \frac{1}{4} = \dfrac{7}{4}$
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\end{enumerate}
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\end{multicols}
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\end{solution}
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\begin{exercise}[subtitle={Fractions de quantités \Rep}, step={3}, origin={}, topics={ Fractions et opérations }, tags={ Fraction }]
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Calcule les quantités suivantes
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\begin{multicols}{2}
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\begin{enumerate}
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\item $\dfrac{3}{4}$ de 8\euro.
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\includegraphics[scale=0.5]{./fig/8euros.pdf}
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\item $\dfrac{1}{2}$ de 10 étoiles.
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\includegraphics[scale=0.5]{./fig/10etoiles.pdf}
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\item $\dfrac{5}{3}$ de 12m.
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\includegraphics[scale=0.6]{./fig/12m.pdf}
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\item $\dfrac{4}{5}$ de 20 élèves.
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\item $\dfrac{25}{100}$ de 40\euro.
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\item $\dfrac{3}{5}$ de 100L.
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\item $\dfrac{3}{2}$ de 6m.
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\item $50\%$ de 10kg.
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\end{enumerate}
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\end{multicols}
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\textbf{Expert en français} par quelle opération se traduit le mot "de"?
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\end{exercise}
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\begin{solution}
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\end{solution}
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\begin{exercise}[subtitle={Au travail! }, step={3}, origin={Les maths ensemble et pour chacun 4e}, topics={ Fractions et opérations }, tags={ Fraction }]
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Abdou a 48 minutes d'étude pour travailler. Il passe $\frac{1}{4}$ du temps à s'installer, $\dfrac{1}{3}$ du temps à sortir ses affaires, $\dfrac{1}{6}$ du temps à parler et le reste du temps il travaille.
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Combien de temps a-t-il travaillé?
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\end{exercise}
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\begin{solution}
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\begin{itemize}
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\item Temps à s'installer: $\dfrac{1}{4} \times 48 = 12$
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\item Temps à sortir ses affaires: $\dfrac{1}{3} \times 48 = 16$
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\item Temps à parler: $\dfrac{1}{6} \times 48 = 8$
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\end{itemize}
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Il a donc travaillé $48 - 12 - 16 - 8 = 12$ minutes.
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\end{solution}
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28
4e/08_Fractions_et_operations/index.rst
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Fractions et opérations
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#######################
|
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:date: 2021-11-14
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:modified: 2021-11-14
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:authors: Benjamin Bertrand
|
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:tags: Fraction
|
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:category: 4e
|
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:summary: Addition, soustraction et multiplication des fractions
|
||||
|
||||
Reprise de la progression et des exercices proposés dans le livre Les maths ensemble et pour chacun.
|
||||
|
||||
Étape 1: Représentation des fractions
|
||||
=====================================
|
||||
|
||||
Étape 2: Sens de l'addition et de la soustraction quand les dénominateurs sont multiples
|
||||
========================================================================================
|
||||
|
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Étape 3: Lien entre fraction et multiplication
|
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==============================================
|
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|
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Étape 4: Addition et soustraction quand les dénominateurs ne sont pas multiples
|
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===============================================================================
|
||||
|
||||
Étape 5: Problèmes utilisant la multiplication de fractions
|
||||
===========================================================
|
||||
|
||||
|
||||
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