index.tex

\documentclass[a4paper]{article}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[greek,frenchb]{babel}
\usepackage{array,multicol,multirow,enumerate}
\usepackage{graphicx}
\usepackage{pstricks,pst-eucl}
\usepackage{lscape}
\usepackage{fancyhdr}
\usepackage{amsmath,amsfonts,amsthm,geometry}
\usepackage{frcursive}
\usepackage{geometry}
\geometry{ hmargin=1.5cm, vmargin=1.5cm }
\setlength{\parindent}{0mm}
 
% A virer ?
\def\d{$\diamond \,$}
% le symbole de multiplication
\def\*{\times}
% le symbole Euro
\def\Euro{\textgreek{\euro}\ }
% La fameuse \trou de Olivier K qui remplace un mot par un trou de la meme taille
\def\m@th{\mathsurround=0pt}
\def\trou#1{
    \setbox0=\hbox{\textbf{#1}} \dp0=0pt \m@th
    \underline{\hbox{\hskip\wd0}}
}
% Elle ne set pas souvent mais j'en ai bavé ;o)
\newcommand{\machine}[4]{
        \begin{pspicture}
        \rput(0,0){\rnode{A}{#1}}
        \rput(3,0.11){\rnode{B}{#2}}
        \psset{nodesep=5pt}
        \ncarc[arcangleA=25,arcangleB=25]{->}{A}{B}\mput*{\ovalnode{m}{#3}}
        \ncarc[arcangleA=25,arcangleB=25]{->}{B}{A}\mput*{\ovalnode{d}{#4}}
        \end{pspicture}
        \hskip 3.1cm}
 
 
% La fameuse \qcm de Nicolas Poulain qui permet de faire des qcm
\newcommand{\QCM}[4]{
    \begin{tabular}[t]{p{13cm}c}
    #1 & \psset{xunit=1 cm}
    \begin{pspicture}(-0.3,0)(1.5,0.5)
    \pspolygon(0,0)(1.5,0)(1.5,-.5)(0,-.5)
    \psline(.5,0)(.5,-.5) \psline(1,0)(1,-.5)
    \uput[90](0.25,0){A}  \uput[90](0.75,0){B} \uput[90](1.25,0){C}
    \end{pspicture} \\
    A: #2 \qquad B: #3 \qquad C: #4 & \\
    \end{tabular}}
% Ca peut toujours servir un petit carré ! (Merci Ahmed Kadi)
\newcommand{\smallbox}{
    \begin{pspicture}(.5,.5)
    \pspolygon(0,0)(.25,0)(.25,.25)(0,.25)
    \end{pspicture}}
% Vec (Merci Ahmed Kadi)
\renewcommand{\vec}[1]
{\mathord{\setbox0\hbox{$#1$} \mathop{\smash{#1}\setbox1\copy0\ht1
0.8\ht0 \vphantom{\copy1}\mskip0.8\thinmuskip} \limits^{\hbox
to\wd0{$\mskip0.8\thinmuskip$\rightarrowfill}}\mskip-0.8\thinmuskip}}
 
% Exo
\newcounter{nexo}
\setcounter{nexo}{0}
\newcommand{\exo}{
    \stepcounter{nexo}
    {\textbf{$\triangleright$ Exercice \arabic{nexo} :}}
}
% Questions
\newenvironment{questions}{\begin{enumerate}[1 $\, \diamond$]}{\end{enumerate}}
 
     \lhead{\textsf{Collège Chateau Forbin} - \textit{Mathématiques}}
    \chead{}
    \rhead{\textit{Année} 2005/2006}
    \pagestyle{fancy}
  \renewcommand{\headrulewidth}{0.5pt}
\begin{document}
{\noindent \textbf{NOM :} \hfill \textbf{Classe : \ldots}}
 
\vskip 0.3cm
 
{\noindent \textbf{Prénom :} \hfill \textit{lundi $21$ novembre
$2005$}}
%{\noindent \textbf{Prénom :} \psfig{figure=blason.eps,width=1.3cm}}%, height=10cm,width=6cm,width=18cm
\begin{center}
    {\large\textbf{Atelier 5\ieme~ : \og Les nombres en écriture fractionnaire \fg}}\\
    \small{\textit{À compléter sur ces feuilles}}\\
\end{center}
 
\vskip 0.3cm \hrule\vspace{\baselineskip}
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DEBUT DES EXERCICES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\exo \'Ecris les nombres suivants sous la forme d'une fraction de
nombres entiers : $0,2$ ; $55,55$ ; $10,01$ ; $0,875$ ; $2,5$ et
$5,89$.
\begin{multicols}{2}
\begin{questions}
    \item $0,2 =\frac{\ldots\ldots\ldots}{\ldots\ldots\ldots}$
    \vskip 0.4cm
    \item $55,55 =\frac{\ldots\ldots\ldots}{\ldots\ldots\ldots}$
    \vskip 0.4cm
    \item $10,01 =\frac{\ldots\ldots\ldots}{\ldots\ldots\ldots}$
    \vskip 0.4cm
    \item $0,875 =\frac{\ldots\ldots\ldots}{\ldots\ldots\ldots}$
    \vskip 0.4cm
    \item $2,5 =\frac{\ldots\ldots\ldots}{\ldots\ldots\ldots}$
    \vskip 0.4cm
    \item $5,89 =\frac{\ldots\ldots\ldots}{\ldots\ldots\ldots}$
    \vskip 0.4cm
\end{questions}
\end{multicols}
 
\vskip 0.5cm
 
\exo Les deux rectangles suivants ont les mêmes dimensions.
\begin{multicols}{2}
\psset{unit=0.5cm}
\pspicture(-3,0)(6,4)
\psframe(0,0)(6,4)
\multido{\i=1+1}{3} { \psline(0,\i)(6,\i)}
\multido{\i=1+1}{5} { \psline(\i,0)(\i,4)}
\endpspicture
 
\begin{itemize}
    \item Colorie la moitié haute du tableau.
    \item Combien de carreaux as-tu coloriés ? \dotfill
    \item Combien y a-t-il de carreaux en tout ? \dotfill
    \vskip 0.4cm
    \item $\dfrac{\textrm{Carreaux coloriés}}{\textrm{Carreaux}}=\dfrac{\dots\ldots\ldots}{\ldots\ldots\dots}$
\end{itemize}
 
\columnbreak
 
\pspicture(-3,0)(6,4)
\psframe(0,0)(6,4)
\multido{\i=1+1}{3} { \psline(0,\i)(6,\i)}
\multido{\i=2+2}{2} { \psline(\i,0)(\i,4)}
\endpspicture
 
\begin{itemize}
    \item Colorie la moitié haute du tableau.
    \item Combien de carreaux as-tu coloriés ? \dotfill
    \item Combien y a-t-il de carreaux en tout ? \dotfill
    \vskip 0.4cm
    \item $\dfrac{\textrm{Carreaux coloriés}}{\textrm{Carreaux}}=\dfrac{\dots\ldots\ldots}{\ldots\ldots\dots}$
\end{itemize}
\end{multicols}
 
Dans chaque tableau, tu as colorié la moitié des carreaux. Donc,
on peut affirmer que
$$\dfrac{1}{2}=\dfrac{\dots\ldots\ldots}{\dots\ldots\ldots}=\dfrac{\dots\ldots\ldots}{\dots\ldots\ldots}$$
 
 \vskip 0.5cm
\exo Dans chaque cas, colorier la quantité indiquée
 
\psset{xunit=1 cm}
\newpsstyle{blanc}{fillstyle=solid, fillcolor=white}
\pspicture(0,0.5)(2,3.6)
\multirput(0,0.25){6}
{\psellipse[style=blanc](1,0.8)(1,0.2) \psframe[style=blanc, linecolor=white](0,0.8)(2,1)
\psline(0,0.8)(0,1)(2,1)(2,0.8) \psellipse[style=blanc](1,1)(1,0.2)}
\endpspicture
\hfill
\pspicture(0,0.5)(2,3.6)
\multirput(0,0.25){10}
{\psellipse[style=blanc](1,0.8)(1,0.2) \psframe[style=blanc, linecolor=white](0,0.8)(2,1)
\psline(0,0.8)(0,1)(2,1)(2,0.8) \psellipse[style=blanc](1,1)(1,0.2)}
\endpspicture
\hfill
\pspicture(0,0.5)(2,3.6)
\multirput(0,0.25){9}
{\psellipse[style=blanc](1,0.8)(1,0.2) \psframe[style=blanc, linecolor=white](0,0.8)(2,1)
\psline(0,0.8)(0,1)(2,1)(2,0.8) \psellipse[style=blanc](1,1)(1,0.2)}
\endpspicture
\hfill
\pspicture(0,0.5)(2,3.6)
\multirput(0,0.25){4}
{\psellipse[style=blanc](1,0.8)(1,0.2) \psframe[style=blanc, linecolor=white](0,0.8)(2,1)
\psline(0,0.8)(0,1)(2,1)(2,0.8) \psellipse[style=blanc](1,1)(1,0.2)}
\endpspicture
\hfill
\pspicture(0,0.5)(2,3.6)
\multirput(0,0.25){8}
{\psellipse[style=blanc](1,0.8)(1,0.2) \psframe[style=blanc, linecolor=white](0,0.8)(2,1)
\psline(0,0.8)(0,1)(2,1)(2,0.8) \psellipse[style=blanc](1,1)(1,0.2)}
\endpspicture
\hfill
\\
Quantité : $\dfrac{5}{6}$ \hfill
Quantité : $\dfrac{3}{10}$ \hfill
Quantité : $\dfrac{2}{3}$ \hfill
Quantité : $\dfrac{1}{2}$ \hfill
Quantité : $\dfrac{3}{4}$ \\
 
 
 
 \vskip 0.5cm
\exo Dans chaque cas, indiquer sous forme fractionnaire, la quantité coloriée
 
\psset{xunit=1 cm}
\newpsstyle{blanc}{fillstyle=solid, fillcolor=white}
\newpsstyle{gris}{fillstyle=solid, fillcolor=gray}
\pspicture(0,0.3)(2,3.6)
\multirput(0,0.25){4}
{\psellipse[style=gris](1,0.8)(1,0.2) \psframe[style=gris, linecolor=gray](0,0.8)(2,1)
\psline(0,0.8)(0,1)(2,1)(2,0.8) \psellipse[style=gris](1,1)(1,0.2)}
\multirput(0,0.25){5}
{\psellipse[style=blanc](1,1.8)(1,0.2) \psframe[style=blanc, linecolor=white](0,1.8)(2,2)
\psline(0,1.8)(0,2)(2,2)(2,1.8) \psellipse[style=blanc](1,2)(1,0.2)}
\endpspicture
\hfill
\pspicture(0,0.3)(2,3.6)
\multirput(0,0.25){4}
{\psellipse[style=gris](1,0.8)(1,0.2) \psframe[style=gris, linecolor=gray](0,0.8)(2,1)
\psline(0,0.8)(0,1)(2,1)(2,0.8) \psellipse[style=gris](1,1)(1,0.2)}
\multirput(0,0.25){6}
{\psellipse[style=blanc](1,1.8)(1,0.2) \psframe[style=blanc, linecolor=white](0,1.8)(2,2)
\psline(0,1.8)(0,2)(2,2)(2,1.8) \psellipse[style=blanc](1,2)(1,0.2)}
\endpspicture
\hfill
\pspicture(0,0.3)(2,3.6)
\multirput(0,0.25){6}
{\psellipse[style=gris](1,0.8)(1,0.2) \psframe[style=gris, linecolor=gray](0,0.8)(2,1)
\psline(0,0.8)(0,1)(2,1)(2,0.8) \psellipse[style=gris](1,1)(1,0.2)}
\multirput(0,0.25){4}
{\psellipse[style=blanc](1,2.3)(1,0.2) \psframe[style=blanc, linecolor=white](0,2.3)(2,2.7)
\psline(0,2.3)(0,2.5)(2,2.5)(2,2.3) \psellipse[style=blanc](1,2.5)(1,0.2)}
\endpspicture
\hfill
\pspicture(0,0.3)(2,3.6)
\multirput(0,0.25){2}
{\psellipse[style=gris](1,0.8)(1,0.2) \psframe[style=gris, linecolor=gray](0,0.8)(2,1)
\psline(0,0.8)(0,1)(2,1)(2,0.8) \psellipse[style=gris](1,1)(1,0.2)}
\multirput(0,0.25){5}
{\psellipse[style=blanc](1,1.3)(1,0.2) \psframe[style=blanc, linecolor=white](0,1.3)(2,1.7)
\psline(0,1.3)(0,1.5)(2,1.5)(2,1.3) \psellipse[style=blanc](1,1.5)(1,0.2)}
\endpspicture
\hfill
\pspicture(0,0.3)(2,3.6)
\multirput(0,0.25){6}
{\psellipse[style=gris](1,0.8)(1,0.2) \psframe[style=gris, linecolor=gray](0,0.8)(2,1)
\psline(0,0.8)(0,1)(2,1)(2,0.8) \psellipse[style=gris](1,1)(1,0.2)}
\multirput(0,0.25){6}
{\psellipse[style=blanc](1,2.3)(1,0.2) \psframe[style=blanc, linecolor=white](0,2.3)(2,2.7)
\psline(0,2.3)(0,2.5)(2,2.5)(2,2.3) \psellipse[style=blanc](1,2.5)(1,0.2)}
\endpspicture
\\
Quantité : $\dfrac{\dots}{\dots}$ \hfill
Quantité : $\dfrac{\dots}{\dots}$ \hfill
Quantité : $\dfrac{\dots}{\dots}$ \hfill
Quantité : $\dfrac{\dots}{\dots}$ \hfill
Quantité : $\dfrac{\dots}{\dots}$ \\
 
\newpage
 
 \vskip 0.5cm
\exo
\begin{questions}
    \item Pour chaque grille quelle est la fraction : $\dfrac{nombre\ de\ cases\ noires}{nombre\ de\ cases\ au\ total}$ ?
    \item Ranger ces fractions $f_1$, $f_2$ et $f_3$ par ordre croissant. Quelle est la figure la
    plus sombre ?
\end{questions}
 
\medskip
\psset{unit=0.5cm}%
\pspicture*(0,-2)(6,6) %\psgrid
\newpsstyle{S}{fillstyle=solid,fillcolor=black}
\psgrid[gridcolor=black,gridwidth=0.1pt,subgriddiv=0,gridlabels=0](0,0)(6,6)
\psframe[style=S](5,4)(6,5) \psframe[style=S](0,0)(1,1)
\psframe[style=S](0,2)(1,3) \psframe[style=S](0,3)(1,4)
\psframe[style=S](1,2)(2,3) \psframe[style=S](1,4)(2,5)
\psframe[style=S](1,5)(2,6) \psframe[style=S](2,0)(3,1)
\psframe[style=S](2,1)(3,2) \psframe[style=S](4,1)(5,2)
\psframe[style=S](5,1)(6,2) \psframe[style=S](2,3)(3,4)
\psframe[style=S](3,4)(4,5) \psframe[style=S](4,3)(5,4)
\psframe[style=S](4,5)(5,6) \psframe[style=S](5,3)(6,4)
\put(1,-1.5){$f_1=\dfrac{\ldots\ldots\ldots}{\ldots\ldots\ldots}$}
\endpspicture
\hfill \pspicture*(0,-2)(9,5)
\newpsstyle{S}{fillstyle=solid,fillcolor=black}
\psgrid[gridcolor=black,gridwidth=0.1pt,subgriddiv=0,gridlabels=0](0,0)(9,5)
\psframe[style=S](0,0)(1,5) \psframe[style=S](2,0)(3,5)
\psframe[style=S](4,0)(5,5) \psframe[style=S](6,0)(7,5)
\psframe[style=S](8,0)(9,5) \psframe[style=S](0,2)(9,3)
\put(2,-1.5){$f_2=\dfrac{\ldots\ldots\ldots}{\ldots\ldots\ldots}$}
\endpspicture
\hfill
\psset{unit=0.17cm}%
\begin{pspicture*}(3.05,-4)(21.9,18) %\psgrid
\psset{dotstyle=x, dotscale=2.0, linewidth=0.02}
\psline[linecolor=black](7.795534,17.590638)(17.195534,17.557305)
\psline[linecolor=black](17.195534,17.557305)(21.866667,9.400000)
\psline[linecolor=black](21.866667,9.400000)(17.137800,1.276028)
\psline[linecolor=black](17.137800,1.276028)(7.737800,1.309361)
\psline[linecolor=black](7.737800,1.309361)(3.066667,9.466666)
\psline[linecolor=black](3.066667,9.466666)(7.795534,17.590638)
\psline[linecolor=black](7.795534,17.590638)(17.137800,1.276028)
\psline[linecolor=black](3.066667,9.466666)(21.866667,9.400000)
\psline[linecolor=black](17.195534,17.557305)(7.737800,1.309361)
\psline[linecolor=black](12.495534,17.573972)(5.402233,5.388013)
\psline[linecolor=black](19.531101,13.478653)(12.437800,1.292694)
\psline[linecolor=black](19.502233,5.338014)(12.495534,17.573972)
\psline[linecolor=black](5.431101,13.528652)(12.437800,1.292694)
\psline[linecolor=black](5.402233,5.388013)(19.502233,5.338014)
\psline[linecolor=black](5.431101,13.528652)(19.531101,13.478653)
\pspolygon[fillstyle=solid, fillcolor=black] (7.795534,17.590638)
(10.131101,13.511986) (12.495534,17.573972)
\pspolygon[fillstyle=solid, fillcolor=black] (12.495534,17.573972)
(14.831101,13.495319) (17.195534,17.557305)
\pspolygon[fillstyle=solid, fillcolor=black] (5.431101,13.528652)
(10.131101,13.511986) (7.766667,9.450000)
\pspolygon[fillstyle=solid, fillcolor=black] (10.131101,13.511986)
(12.466667,9.433333) (14.831101,13.495319)
\pspolygon[fillstyle=solid, fillcolor=black] (14.831101,13.495319)
(19.531101,13.478653) (17.166667,9.416667)
\pspolygon[fillstyle=solid, fillcolor=black] (3.066667,9.466666)
(7.766667,9.450000) (5.402233,5.388013)
\pspolygon[fillstyle=solid, fillcolor=black] (7.766667,9.450000)
(10.102233,5.371347) (12.466667,9.433333)
\pspolygon[fillstyle=solid, fillcolor=black] (12.466667,9.433333)
(17.166667,9.416667) (14.802233,5.354680)
\pspolygon[fillstyle=solid, fillcolor=black] (21.866667,9.400000)
(19.502233,5.338014) (17.166667,9.416667)
\pspolygon[fillstyle=solid, fillcolor=black] (17.137800,1.276028)
(19.502233,5.338014) (14.802233,5.354680)
\pspolygon[fillstyle=solid, fillcolor=black] (10.102233,5.371347)
(14.802233,5.354680) (12.437800,1.292694)
\pspolygon[fillstyle=solid, fillcolor=black] (7.737800,1.309361)
(10.102233,5.371347) (5.402233,5.388013)
\put(6,-2){$f_3=\dfrac{\ldots\ldots\ldots}{\ldots\ldots\ldots}$}
\end{pspicture*}
\hfill
\\
 
 \vskip 0.5cm
\exo Colorie:
\begin{enumerate}[$\diamond$]
\item $\dfrac{3}{4}$ du losange
% Généré par 0.9.2
\psset{linecolor=black, linewidth=.5pt, arrowsize=2pt 4}
\psset{unit=0.7000cm}
\pspicture(-4.5000,-2.0000)(8.5000,-1.5000)
\rput(3,-6){\pscircle(-2.0000,3.0000){1.5000}
\rput(-2,3){ \SpecialCoor  \multido{\i=20+40}{9}{\psline(1.5;\i)}}
\NormalCoor
\pspolygon(1.3505,4.3750)(2.0000,3.2500)(2.6495,4.3750)
\pspolygon(1.6752,3.8125)(2.3248,3.8125)(2.0000,4.3750)
\pspolygon(2.0000,5.5000)(0.7010,3.2500)(3.2990,3.2500)
\pspolygon(0.0000,2.0000)(0.0000,-1.0000)(3.0000,-1.0000)(3.0000,2.0000)
\psline(1.0000,2.0000)(1.0000,-1.0000)
\psline(2.0000,2.0000)(2.0000,-1.0000)
\psline(0.0000,1.0000)(3.0000,1.0000)
\psline(0.0000,0.0000)(3.0000,0.0000)
\pspolygon(6.0000,4.0000)(4.0000,3.0000)(6.0000,2.0000)(8.0000,3.0000)
\psline(6.0000,4.0000)(6.0000,2.0000)
\psline(4.0000,3.0000)(8.0000,3.0000)}
\endpspicture
\item $\dfrac{2}{3}$ du disque,
\item $\dfrac{5}{9}$ du carré
\item $\dfrac{3}{8}$ du triangle équilatéral
\end{enumerate}
 
 
 \vskip 1cm
\exo On a représenté trois baguettes de pain prédécoupées. Dans chaque cas, indiquer par une fraction la quantité grisée.
\psset{unit=0.4cm}%
\begin{enumerate}[a)$\diamond$]
% -------------- 9/6
\item \pspicture*(0,0)(12,1)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(0,1)(0,0)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(12,1)(12,0)
\multido{\i=2+2}{4}{\pspolygon[fillstyle=solid,fillcolor=gray](\i,1)(\i,0)(10,0)(10,1)}
\endpspicture \quad
\pspicture*(0,0)(12,1)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(0,1)(0,0)
\pspolygon[fillstyle=solid,fillcolor=white,linearc=.5](6,0)(6,1)(12,1)(12,0)
\multido{\i=2+2}{2}{\pspolygon[fillstyle=solid,fillcolor=gray](\i,1)(\i,0)(10,0)(10,1)}
\multido{\i=6+2}{2}{\pspolygon[fillstyle=solid,fillcolor=white](\i,1)(\i,0)(10,0)(10,1)}
\endpspicture \quad
\pspicture*(0,0)(12,1)
\pspolygon[fillstyle=solid,fillcolor=white,linearc=.5](6,0)(6,1)(0,1)(0,0)
\pspolygon[fillstyle=solid,fillcolor=white,linearc=.5](6,0)(6,1)(12,1)(12,0)
\multido{\i=2+2}{4}{\pspolygon[fillstyle=solid,fillcolor=white](\i,1)(\i,0)(10,0)(10,1)}
\endpspicture
% ------------------------------ 5/3
\item \pspicture*(0,0)(12,1)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(0,1)(0,0)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(12,1)(12,0)
\pspolygon[fillstyle=solid,fillcolor=gray](4,1)(4,0)(8,0)(8,1)
\endpspicture \quad
\pspicture*(0,0)(12,1)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(0,1)(0,0)
\pspolygon[fillstyle=solid,fillcolor=white,linearc=.5](6,0)(6,1)(12,1)(12,0)
\pspolygon[fillstyle=solid,fillcolor=gray](4,1)(4,0)(8,0)(8,1)
\endpspicture \quad
\pspicture*(0,0)(12,1)
\pspolygon[fillstyle=solid,fillcolor=white,linearc=.5](6,0)(6,1)(0,1)(0,0)
\pspolygon[fillstyle=solid,fillcolor=white,linearc=.5](6,0)(6,1)(12,1)(12,0)
\pspolygon[fillstyle=solid,fillcolor=white](4,1)(4,0)(8,0)(8,1)
\endpspicture
% ------------------------------ 10/4
\item \pspicture*(0,0)(12,1)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(0,1)(0,0)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(12,1)(12,0)
\multido{\i=3+3}{3}{\pspolygon[fillstyle=solid,fillcolor=gray](\i,1)(\i,0)(9,0)(9,1)}
\endpspicture \quad
\pspicture*(0,0)(12,1)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(0,1)(0,0)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(12,1)(12,0)
\multido{\i=3+3}{3}{\pspolygon[fillstyle=solid,fillcolor=gray](\i,1)(\i,0)(9,0)(9,1)}
\endpspicture \quad
\pspicture*(0,0)(12,1)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(0,1)(0,0)
\pspolygon[fillstyle=solid,fillcolor=white,linearc=.5](6,0)(6,1)(12,1)(12,0)
\multido{\i=3+3}{1}{\pspolygon[fillstyle=solid,fillcolor=gray](\i,1)(\i,0)(9,0)(9,1)}
\multido{\i=6+3}{2}{\pspolygon[fillstyle=solid,fillcolor=white](\i,1)(\i,0)(9,0)(9,1)}
\endpspicture
% ------------------------------------ 3/6
\item \pspicture*(0,0)(12,1)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(0,1)(0,0)
\pspolygon[fillstyle=solid,fillcolor=white,linearc=.5](6,0)(6,1)(12,1)(12,0)
\multido{\i=2+2}{2}{\pspolygon[fillstyle=solid,fillcolor=gray](\i,1)(\i,0)(10,0)(10,1)}
\multido{\i=6+2}{2}{\pspolygon[fillstyle=solid,fillcolor=white](\i,1)(\i,0)(10,0)(10,1)}
\endpspicture \quad
\pspicture*(0,0)(12,1)
\pspolygon[fillstyle=solid,fillcolor=white,linearc=.5](6,0)(6,1)(0,1)(0,0)
\pspolygon[fillstyle=solid,fillcolor=white,linearc=.5](6,0)(6,1)(12,1)(12,0)
\multido{\i=2+2}{4}{\pspolygon[fillstyle=solid,fillcolor=white](\i,1)(\i,0)(10,0)(10,1)}
\endpspicture \quad
\pspicture*(0,0)(12,1)
\pspolygon[fillstyle=solid,fillcolor=white,linearc=.5](6,0)(6,1)(0,1)(0,0)
\pspolygon[fillstyle=solid,fillcolor=white,linearc=.5](6,0)(6,1)(12,1)(12,0)
\multido{\i=2+2}{4}{\pspolygon[fillstyle=solid,fillcolor=white](\i,1)(\i,0)(10,0)(10,1)}
\endpspicture
% ------------------------------4/3
\item \pspicture*(0,0)(12,1)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(0,1)(0,0)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(12,1)(12,0)
\pspolygon[fillstyle=solid,fillcolor=gray](4,1)(4,0)(8,0)(8,1)
\endpspicture \quad
\pspicture*(0,0)(12,1)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(0,1)(0,0)
\pspolygon[fillstyle=solid,fillcolor=white,linearc=.5](6,0)(6,1)(12,1)(12,0)
\pspolygon[fillstyle=solid,fillcolor=white](4,1)(4,0)(8,0)(8,1)
\endpspicture \quad
\pspicture*(0,0)(12,1)
\pspolygon[fillstyle=solid,fillcolor=white,linearc=.5](6,0)(6,1)(0,1)(0,0)
\pspolygon[fillstyle=solid,fillcolor=white,linearc=.5](6,0)(6,1)(12,1)(12,0)
\pspolygon[fillstyle=solid,fillcolor=white](4,1)(4,0)(8,0)(8,1)
\endpspicture
% ------------------------------ 9/4
\item \pspicture*(0,0)(12,1)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(0,1)(0,0)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(12,1)(12,0)
\multido{\i=3+3}{3}{\pspolygon[fillstyle=solid,fillcolor=gray](\i,1)(\i,0)(9,0)(9,1)}
\endpspicture \quad
\pspicture*(0,0)(12,1)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(0,1)(0,0)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(12,1)(12,0)
\multido{\i=3+3}{3}{\pspolygon[fillstyle=solid,fillcolor=gray](\i,1)(\i,0)(9,0)(9,1)}
\endpspicture \quad
\pspicture*(0,0)(12,1)
\pspolygon[fillstyle=solid,fillcolor=gray,linearc=.5](6,0)(6,1)(0,1)(0,0)
\pspolygon[fillstyle=solid,fillcolor=white,linearc=.5](6,0)(6,1)(12,1)(12,0)
\multido{\i=3+3}{2}{\pspolygon[fillstyle=solid,fillcolor=white](\i,1)(\i,0)(9,0)(9,1)}
\endpspicture
 
\vskip 0.7cm
 
\centerline{\textbf{Réponses : } \hfill a)= \dotfill~~ b)=
\dotfill~~ c)= \dotfill~~ d)= \dotfill~~ e)=\dotfill~~
f)=\dotfill}
\end{enumerate}
 
 \vskip 0.4cm
\exo
\begin{questions}
\item Relier entre elles les figures dont les parties grisées
correspondent. \item En déduire six égalités de fractions.
\end{questions}
 
\smallskip
\multido{}{5}{Fraction: \dots \hfill } Fraction: \dots \\
 
\psset{unit=0.8cm}%
% -------------- 4/8
\pspicture*(-1,-1)(1,1) \SpecialCoor
\pscircle{1} \pswedge[fillstyle=solid,fillcolor=gray]{1}{0}{180} \multido{\i=0+45}{8}{\psline(1;\i)}
\NormalCoor \endpspicture
\hfill
% -------------- 2/6
\pspicture*(-1,-1)(1,1) \SpecialCoor
\pscircle{1} \pswedge[fillstyle=solid,fillcolor=gray]{1}{60}{180}\multido{\i=0+60}{6}{\psline(1;\i)}
\NormalCoor \endpspicture
\hfill
% -------------- 8/10
\pspicture*(-1,-1)(1,1) \SpecialCoor
\pscircle{1} \pswedge[fillstyle=solid,fillcolor=gray]{1}{36}{324} \multido{\i=0+36}{10}{\psline(1;\i)}
\NormalCoor \endpspicture
\hfill
% -------------- 2/20
\pspicture*(-1,-1)(1,1)
\SpecialCoor
\pscircle{1} \pswedge[fillstyle=solid,fillcolor=gray]{1}{144}{180} \multido{\i=0+18}{20}{\psline(1;\i)}
\NormalCoor \endpspicture
\hfill
% -------------- 2/3
\pspicture*(-1,-1)(1,1) \SpecialCoor
\pscircle{1} \pswedge[fillstyle=solid,fillcolor=gray]{1}{0}{240} \multido{\i=0+120}{3}{\psline(1;\i)}
\NormalCoor \endpspicture
\hfill
% -------------- 5/6
\pspicture*(-1,-1)(1,1) \SpecialCoor
\pscircle{1} \pswedge[fillstyle=solid,fillcolor=gray]{1}{60}{360}\multido{\i=0+60}{6}{\psline(1;\i)}
\NormalCoor \endpspicture
\\
 
 
\bigskip
\medskip
 
% -------------- 1/3
\pspicture*(-1,-1)(1,1) \SpecialCoor
\pscircle{1} \pswedge[fillstyle=solid,fillcolor=gray]{1}{240}{360}\multido{\i=0+120}{3}{\psline(1;\i)}
\NormalCoor \endpspicture
\hfill
% -------------- 2/4
\pspicture*(-1,-1)(1,1) \SpecialCoor
\pscircle{1} \pswedge[fillstyle=solid,fillcolor=gray]{1}{180}{360}\multido{\i=0+90}{4}{\psline(1;\i)}
\NormalCoor \endpspicture
\hfill
% -------------- 4/5
\pspicture*(-1,-1)(1,1) \SpecialCoor
\pscircle{1} \pswedge[fillstyle=solid,fillcolor=gray]{1}{72}{360} \multido{\i=0+72}{5}{\psline(1;\i)}
\NormalCoor \endpspicture
\hfill
% -------------- 6/9
\pspicture*(-1,-1)(1,1) \SpecialCoor
\pscircle{1} \pswedge[fillstyle=solid,fillcolor=gray]{1}{120}{360}\multido{\i=0+40}{9}{\psline(1;\i)}
\NormalCoor \endpspicture
\hfill
% -------------- 10/12
\pspicture*(-1,-1)(1,1) \SpecialCoor
\pscircle{1} \pswedge[fillstyle=solid,fillcolor=gray]{1}{210}{150} \multido{\i=0+30}{12}{\psline(1;\i)}
\NormalCoor \endpspicture
\hfill
% -------------- 1/10
\pspicture*(-1,-1)(1,1) \SpecialCoor
\pscircle{1} \pswedge[fillstyle=solid,fillcolor=gray]{1}{180}{216}\multido{\i=0+36}{10}{\psline(1;\i)}
\NormalCoor \endpspicture
\\
 
\multido{}{5}{Fraction: \dots \hfill } Fraction: \dots \\
\vskip 0.1cm
Les 6 égalités de fractions sont : \dotfill
 
\vskip 0.5cm
 
\exo Voici 12 fractions. Quelles sont celles qui sont égales à
$\dfrac{1}{2}$, à $\dfrac{3}{4}$, à $\dfrac{2}{3}$ ?
 
\smallskip
\psframebox{$\dfrac{6}{8}$} \hfill \psframebox{$\dfrac{50}{100}$} \hfill
\psframebox{$\dfrac{9}{12}$} \hfill \psframebox{$\dfrac{18}{27}$} \hfill
\psframebox{$\dfrac{21}{28}$} \hfill \psframebox{$\dfrac{10}{20}$} \hfill
\psframebox{$\dfrac{200}{300}$} \hfill \psframebox{$\dfrac{22}{33}$} \hfill
\psframebox{$\dfrac{7}{14}$} \hfill \psframebox{$\dfrac{4}{6}$} \hfill
\psframebox{$\dfrac{42}{84}$} \hfill \psframebox{$\dfrac{297}{396}$} \hfill \\
 
\bigskip
 
\centerline{$\dfrac{1}{2}=$ \hfill $\dfrac{3}{4}=$ \hfill
$\dfrac{2}{3}=$ \hfill}
 
 \vskip 0.5cm
 
\exo Compléter les égalités suivantes.
 
\begin{questions}
\item $\dfrac{20}{18}=\dfrac{2\*\dots}{2\*\dots}=\dfrac{\dots}{\dots}$
\hfill $\dfrac{30}{48}=\dfrac{6\*\dots}{6\*\dots}=\dfrac{\dots}{\dots}$
\hfill $\dfrac{36}{32}=\dfrac{4\*\dots}{4\*\dots}=\dfrac{\dots}{\dots}$
\hfill $\dfrac{3}{21}=\dfrac{3\*\dots}{3\*\dots}=\dfrac{\dots}{\dots}$ \\
\item $\dfrac{98}{35}=\dfrac{7\*\dots}{7\*\dots}=\dfrac{\dots}{\dots}$
\hfill $\dfrac{99}{44}=\dfrac{11\*\dots}{11\*\dots}=\dfrac{\dots}{\dots}$
\hfill $\dfrac{17}{34}=\dfrac{17\*\dots}{17\*\dots}=\dfrac{\dots}{\dots}$
\hfill $\dfrac{76}{95}=\dfrac{19\*\dots}{19\*\dots}=\dfrac{\dots}{\dots}$ \\
\end{questions}
 
 \vskip 0.5cm
 
\exo Compléter les égalités suivantes en expliquant les calculs :
 
\smallskip
 
\begin{questions}
    \item $\dfrac{1}{6}=\dfrac{\dots\dots}{12}$ ; explication :
    \dotfill
    \item $\dfrac{20}{60}=\dfrac{4}{\dots\dots}$ ; explication :
    \dotfill
    \item $\dfrac{21}{56}=\dfrac{3}{\dots\dots}$ ; explication :
    \dotfill
    \item $\dfrac{6}{24}=\dfrac{\dots\dots}{8}$ ; explication :
    \dotfill
    \item $\dfrac{44}{66}=\dfrac{2}{\dots\dots}$ ; explication :
    \dotfill
    \item $\dfrac{1}{6}=\dfrac{6}{\dots\dots}$ ; explication :
    \dotfill
\end{questions}
 
 \vskip 0.5cm
\exo Mettre une croix dans la (ou les) bonne(s) case(s). On
rappelle d'une fraction est \textit{irréductible} si on ne peut
pas la simplifier par un nombre entier.
\begin{center}
\begin{tabular}{|l|c|c|c|c|c|c|c|c|}
\hline & $\dfrac{\strut 3}{\strut 6}$ &
$\dfrac{15}{10}$ & $\dfrac{11}{2}$ & $\dfrac{4}{12}$ &
$\dfrac{24}{36}$ & $\dfrac{3}{21}$ & $\dfrac{15}{24}$ &
$\dfrac{20}{25}$ \\ \hline Fraction simplifiable par 2 & & & & & &
& & \\ \hline Fraction simplifiable par 3 & & & & & & & & \\\hline
Fraction simplifiable par 4 & & & & & & & & \\ \hline Fraction
simplifiable par 5 & & & & & & & & \\ \hline Fraction irréductible
& & & & & & & & \\ \hline
\end{tabular}
\end{center}
 
 \vskip 0.5cm
% exemple :
\exo Calculer puis simplifier lorsque c'est possible
 
\begin{enumerate}[a)]
    \item $\dfrac{2}{3}\*\dfrac{3}{4} =$ \dotfill
    \item $\dfrac{7}{2}\*\dfrac{5}{2} =$ \dotfill
    \item $\dfrac{2}{3}\*\dfrac{9}{2} =$ \dotfill
\end{enumerate}
 
\vskip 0.5cm
 
\exo Mettre les fractions au même dénominateur, puis classer dans
l'ordre croissssant
\begin{enumerate}[a)]
\item $\dfrac{4}{5}$ \qquad $\dfrac{7}{15}$ \qquad $\dfrac{4}{3}$
\qquad $\dfrac{1}{5}$ \qquad $\dfrac{2}{3}$ \qquad
$\dfrac{3}{15}$\\
 
\vskip 0.3cm
Ordre croissant : \dotfill
 
\item $\dfrac{13}{30}$ \qquad $\dfrac{3}{5}$ \qquad
$\dfrac{6}{20}$ \qquad $\dfrac{3}{4}$ \qquad $\dfrac{2}{3}$ \qquad
$\dfrac{5}{15}$\\
 
\vskip 0.3cm
Ordre croissant : \dotfill
 
 
 
\item $\dfrac{3}{12}$ \qquad $\dfrac{2}{24}$ \qquad $\dfrac{5}{6}$
\qquad $\dfrac{9}{48}$ \qquad $\dfrac{7}{3}$ \qquad
$\dfrac{5}{4}$\\
 
\vskip 0.3cm Ordre croissant : \dotfill
 
\end{enumerate}
\end{document}