Feat: fraction d'une quantité

4e/08_Fractions_et_operations/3E_fractions_quantite.tex

@@ -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}

4e/08_Fractions_et_operations/exercises.tex

@@ -138,16 +138,32 @@
     \begin{multicols}{2}
         \begin{enumerate}
             \item $\dfrac{3}{4}$ de 8\euro.
-    
+                \begin{tikzpicture}[scale=0.8]
-                \includegraphics[scale=0.5]{./fig/8euros.pdf}
+                    \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 }]