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Feat: fraction d'une quantité
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Bertrand Benjamin 2021-11-14 19:55:34 +01:00
parent f86b240d4b
commit f1f826c1f5
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4e/08_Fractions_et_operations/1E_representation.pdf
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4e/08_Fractions_et_operations/2E_add_soust_frac.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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@ -1,6 +1,8 @@
\documentclass[a4paper,10pt]{article}
\usepackage{myXsim}
\usetikzlibrary{shapes.geometric}
\author{Benjamin Bertrand}
\title{Fractions et opérations - Exercices}
\date{2021-11-14}

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4e/08_Fractions_et_operations/exercises.tex
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@ -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 }]