\documentclass[a4paper,11pt]{article}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage[french]{babel}
\usepackage[a4paper,top=3.2cm,bottom=2cm,left=2cm,right=2cm]{geometry}
\usepackage{graphicx}
\usepackage[export]{adjustbox}
\usepackage{fancyhdr}
\usepackage{qrcode}
\usepackage[table]{xcolor}
\usepackage{amsmath,amssymb}
\usepackage{enumitem}
% Puces nettes (babel-french remplace sinon la puce par un tiret « – » peu pro).
% Vaut pour TOUTES les fiches qui importent ce module. AtBeginDocument pour
% passer après la personnalisation des listes faite par babel-french.
\AtBeginDocument{%
  \setlist[itemize]{leftmargin=1.8em,itemsep=0.5ex,topsep=0.4ex,parsep=0pt}%
  \setlist[itemize,1]{label=\textcolor{red!75!black}{\small\textbullet}}%
  \setlist[itemize,2]{label=\textcolor{red!75!black}{\scriptsize\textbullet}}%
}
% Titres compacts (gain de place vertical, fiches plus denses) — vaut pour tous.
\usepackage{titlesec}
\titlespacing*{\section}{0pt}{1.4ex}{0.6ex}
\titlespacing*{\subsection}{0pt}{1.0ex}{0.3ex}
% multicol : listes denses (calcul mental) sur 2 colonnes — neutre tant qu'il
% n'est pas utilisé, dispo pour tous les générateurs.
\usepackage{multicol}
\setlength{\columnsep}{1.5em}
% needspace : empêche un titre d'exercice de rester orphelin en bas de page
% (réserve quelques lignes ; sinon le titre passe à la page suivante avec sa
% liste). Neutre tant qu'il n'est pas appelé — dispo pour tous les générateurs.
\usepackage{needspace}
\usepackage{tikz}
\usetikzlibrary{decorations.text}

\usepackage{tgheros}
\pagestyle{fancy}
\fancyhf{}
\setlength{\headheight}{75pt}
\setlength{\headsep}{10pt}

\newcommand{\logowouf}{%
\begin{tikzpicture}[baseline={(current bounding box.center)},scale=0.55,
                    line cap=round,line join=round]
    \path[use as bounding box] (-2.20,-1.45) rectangle (2.20,2.20);
    \path[
        postaction={decorate},
        decoration={
            text along path,
            text={|\fontfamily{qhv}\bfseries\fontsize{9}{9}\selectfont|site2wouf.fr},
            text align={center},
            raise=0.03ex
        }
    ] (-1.29,0.48) arc[start angle=160,end angle=20,radius=1.29];
    \begin{scope}[xshift=-0.06cm]
        \fill[black] (-0.66,0.14) ellipse (0.21 and 0.31);
        \fill[black] ( 0.66,0.14) ellipse (0.21 and 0.31);
        \fill[black] (-0.23,0.49) ellipse (0.22 and 0.35);
        \fill[black] ( 0.23,0.49) ellipse (0.22 and 0.35);
        \fill[black]
            (0,-0.10)
            .. controls (-0.36,-0.02) and (-0.63,-0.24) .. (-0.58,-0.58)
            .. controls (-0.52,-0.93) and (-0.16,-1.12) .. (0,-0.90)
            .. controls (0.16,-1.12) and (0.52,-0.93) .. (0.58,-0.58)
            .. controls (0.63,-0.24) and (0.36,-0.02) .. (0,-0.10)
            -- cycle;
    \end{scope}
\end{tikzpicture}%
}

\newcommand{\titre}{Opérations sur les entiers}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 55}

\fancyhead[C]{%
\raisebox{4pt}{%
\begin{minipage}[c]{0.15\textwidth}
    \centering
    \logowouf
\end{minipage}
\begin{minipage}[c]{0.62\textwidth}
    \centering
    {\Large\bfseries \titre\par}
    {\small\color{gray} \soustitre}
\end{minipage}
\begin{minipage}[c]{0.21\textwidth}
    \centering
    \qrcode[height=1.5cm]{https://site2wouf.fr/exercices_operations_entiers.php?x=55}\\[2pt]
    {\small\ttfamily\bfseries\color{red} OPEN0055}
\end{minipage}%
}
}

\begin{document}

\begin{center}
    \small Addition, soustraction, multiplication et division euclidienne posées.
\end{center}
\vspace{0.5em}
\section*{Exercice 1 : Pose et effectue les trois additions suivantes}
\begin{itemize}
\item $1 575  + 3 310 $
\item $2 552  + 5 054 $
\item $1 400  + 3 105 $
\end{itemize}
\section*{Exercice 2 : Pose et effectue les trois soustractions suivantes}
\begin{itemize}
\item $3 404  - 2 568 $
\item $8 999  - 2 975 $
\item $8 500  - 3 961 $
\end{itemize}
\section*{Exercice 3 : Pose et effectue les deux multiplications suivantes}
\begin{itemize}
\item $6 539  \times 3 251 $
\item $7 653  \times 4 219 $
\end{itemize}
\section*{Exercice 4 : Pose et effectue les deux divisions euclidiennes suivantes}
\textcolor{red}{On écrira ensuite l'opération en ligne.}
\begin{itemize}
\item La division (euclidienne) de 6 324  par 8 
\item La division (euclidienne) de 9 863  par 91 
\end{itemize}
\newpage
\section*{\textcolor{red}{Correction}}
\subsection*{Exercice 1}
$1 575  + 3 310  = 4 885 $\\

\begin{center}\begin{tikzpicture}[line width=0.6pt]
  \draw[black] (0.267,1.133) -- (3.467,1.133);
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (3.333,1.667) {1575};
  \node[black, anchor=base, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (0.400,1.267) {+};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (3.333,1.267) {3310};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (3.333,0.733) {4885};
\end{tikzpicture}\end{center}
\par\vspace{0.5em}
$2 552  + 5 054  = 7 606 $\\

\begin{center}\begin{tikzpicture}[line width=0.6pt]
  \draw[black] (0.267,1.133) -- (3.467,1.133);
  \node[red, anchor=base, font=\ttfamily \fontsize{5.3}{6.4}\selectfont] at (3.109,2.067) {1};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (3.333,1.667) {2552};
  \node[black, anchor=base, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (0.400,1.267) {+};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (3.333,1.267) {5054};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (3.333,0.733) {7606};
\end{tikzpicture}\end{center}
\par\vspace{0.5em}
$1 400  + 3 105  = 4 505 $\\

\begin{center}\begin{tikzpicture}[line width=0.6pt]
  \draw[black] (0.267,1.133) -- (3.467,1.133);
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (3.333,1.667) {1400};
  \node[black, anchor=base, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (0.400,1.267) {+};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (3.333,1.267) {3105};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (3.333,0.733) {4505};
\end{tikzpicture}\end{center}
\par\vspace{0.5em}
\subsection*{Exercice 2}
$3 404  - 2 568  = 836 $\\

\begin{center}\begin{tikzpicture}[line width=0.6pt]
  \draw[black] (0.267,1.133) -- (3.467,1.133);
  \node[red, anchor=base, font=\ttfamily \fontsize{5.3}{6.4}\selectfont] at (2.661,2.333) {1};
  \node[red, anchor=base, font=\ttfamily \fontsize{5.3}{6.4}\selectfont] at (2.885,2.333) {1};
  \node[red, anchor=base, font=\ttfamily \fontsize{5.3}{6.4}\selectfont] at (3.109,2.333) {1};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (3.333,1.933) {3404};
  \node[black, anchor=base, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (0.400,1.533) {-};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (3.333,1.533) {2568};
  \node[red, anchor=base, font=\ttfamily \fontsize{5.3}{6.4}\selectfont] at (2.661,1.267) {1};
  \node[red, anchor=base, font=\ttfamily \fontsize{5.3}{6.4}\selectfont] at (2.885,1.267) {1};
  \node[red, anchor=base, font=\ttfamily \fontsize{5.3}{6.4}\selectfont] at (3.109,1.267) {1};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (3.333,0.733) {836};
\end{tikzpicture}\end{center}
\par\vspace{0.5em}
$8 999  - 2 975  = 6 024 $\\

\begin{center}\begin{tikzpicture}[line width=0.6pt]
  \draw[black] (0.267,1.133) -- (3.467,1.133);
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (3.333,1.933) {8999};
  \node[black, anchor=base, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (0.400,1.533) {-};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (3.333,1.533) {2975};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (3.333,0.733) {6024};
\end{tikzpicture}\end{center}
\par\vspace{0.5em}
$8 500  - 3 961  = 4 539 $\\

\begin{center}\begin{tikzpicture}[line width=0.6pt]
  \draw[black] (0.267,1.133) -- (3.467,1.133);
  \node[red, anchor=base, font=\ttfamily \fontsize{5.3}{6.4}\selectfont] at (2.661,2.333) {1};
  \node[red, anchor=base, font=\ttfamily \fontsize{5.3}{6.4}\selectfont] at (2.885,2.333) {1};
  \node[red, anchor=base, font=\ttfamily \fontsize{5.3}{6.4}\selectfont] at (3.109,2.333) {1};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (3.333,1.933) {8500};
  \node[black, anchor=base, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (0.400,1.533) {-};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (3.333,1.533) {3961};
  \node[red, anchor=base, font=\ttfamily \fontsize{5.3}{6.4}\selectfont] at (2.661,1.267) {1};
  \node[red, anchor=base, font=\ttfamily \fontsize{5.3}{6.4}\selectfont] at (2.885,1.267) {1};
  \node[red, anchor=base, font=\ttfamily \fontsize{5.3}{6.4}\selectfont] at (3.109,1.267) {1};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.6}{12.7}\selectfont] at (3.333,0.733) {4539};
\end{tikzpicture}\end{center}
\par\vspace{0.5em}
\subsection*{Exercice 3}
$6 539  \times 3 251  = 21 258 289 $\\

\begin{center}\begin{tikzpicture}[line width=0.6pt]
  \draw[black] (0.257,2.636) -- (3.729,2.636);
  \draw[black] (0.257,1.157) -- (3.729,1.157);
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.2}{12.3}\selectfont] at (3.600,3.150) {6539};
  \node[black, anchor=base, font=\ttfamily \fontsize{10.2}{12.3}\selectfont] at (0.386,2.764) {\(\times\)};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.2}{12.3}\selectfont] at (3.600,2.764) {3251};
  \node[black, anchor=base east, font=\ttfamily \fontsize{8.8}{10.5}\selectfont] at (3.600,2.250) {6539};
  \node[black, anchor=base east, font=\ttfamily \fontsize{8.8}{10.5}\selectfont] at (3.407,1.929) {32695};
  \node[black, anchor=base east, font=\ttfamily \fontsize{8.8}{10.5}\selectfont] at (3.214,1.607) {13078};
  \node[black, anchor=base east, font=\ttfamily \fontsize{8.8}{10.5}\selectfont] at (3.021,1.286) {19617};
  \node[black, anchor=base, font=\ttfamily \fontsize{8.8}{10.5}\selectfont] at (0.386,1.286) {+};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.2}{12.3}\selectfont] at (3.600,0.771) {21258289};
\end{tikzpicture}\end{center}
\par\vspace{0.5em}
$7 653  \times 4 219  = 32 288 007 $\\

\begin{center}\begin{tikzpicture}[line width=0.6pt]
  \draw[black] (0.257,2.636) -- (3.729,2.636);
  \draw[black] (0.257,1.157) -- (3.729,1.157);
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.2}{12.3}\selectfont] at (3.600,3.150) {7653};
  \node[black, anchor=base, font=\ttfamily \fontsize{10.2}{12.3}\selectfont] at (0.386,2.764) {\(\times\)};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.2}{12.3}\selectfont] at (3.600,2.764) {4219};
  \node[black, anchor=base east, font=\ttfamily \fontsize{8.8}{10.5}\selectfont] at (3.600,2.250) {68877};
  \node[black, anchor=base east, font=\ttfamily \fontsize{8.8}{10.5}\selectfont] at (3.407,1.929) {7653};
  \node[black, anchor=base east, font=\ttfamily \fontsize{8.8}{10.5}\selectfont] at (3.214,1.607) {15306};
  \node[black, anchor=base east, font=\ttfamily \fontsize{8.8}{10.5}\selectfont] at (3.021,1.286) {30612};
  \node[black, anchor=base, font=\ttfamily \fontsize{8.8}{10.5}\selectfont] at (0.386,1.286) {+};
  \node[black, anchor=base east, font=\ttfamily \fontsize{10.2}{12.3}\selectfont] at (3.600,0.771) {32288007};
\end{tikzpicture}\end{center}
\par\vspace{0.5em}
\subsection*{Exercice 4}
Division de 6 324  par 8 ~:\\

\begin{center}\begin{tikzpicture}[line width=0.6pt]
  \draw[gray] (1.960,2.380) -- (1.960,2.240);
  \draw[gray] (2.240,2.380) -- (2.240,1.680);
  \draw[black] (2.800,2.730) -- (2.800,0.280);
  \draw[black] (2.800,2.380) -- (4.200,2.380);
  \draw[black] (1.330,2.170) -- (1.750,2.170);
  \draw[black] (1.610,1.610) -- (2.030,1.610);
  \draw[black] (1.890,1.050) -- (2.310,1.050);
  \draw[blue] (1.260,2.730) .. controls (1.447,2.823) and (1.633,2.823) .. (1.820,2.730);
  \node[black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.400,2.520) {6};
  \node[black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.680,2.520) {3};
  \node[black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.960,2.520) {2};
  \node[black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (2.240,2.520) {4};
  \node[black, anchor=base west, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (3.080,2.520) {8};
  \node[blue, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (3.080,2.100) {7};
  \node[blue, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (3.360,2.100) {9};
  \node[blue, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (3.640,2.100) {0};
  \node[red, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.680,2.240) {6};
  \node[red, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.400,2.240) {5};
  \node[black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.960,1.960) {2};
  \node[green!55!black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.680,1.960) {7};
  \node[red, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.960,1.680) {2};
  \node[red, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.680,1.680) {7};
  \node[black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (2.240,1.400) {4};
  \node[green!55!black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.960,1.400) {0};
  \node[red, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (2.240,1.120) {0};
  \node[green!55!black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (2.240,0.770) {4};
\end{tikzpicture}\end{center}
\par\vspace{0.3em}
\textcolor{green}{6 324  = 8  \(\times\) 790  + 4  et 4  \(<\) 8 }\\[0.8em]
Division de 9 863  par 91 ~:\\

\begin{center}\begin{tikzpicture}[line width=0.6pt]
  \draw[gray] (1.960,2.380) -- (1.960,2.240);
  \draw[gray] (2.240,2.380) -- (2.240,1.680);
  \draw[black] (2.800,2.730) -- (2.800,0.280);
  \draw[black] (2.800,2.380) -- (4.200,2.380);
  \draw[black] (1.330,2.170) -- (1.750,2.170);
  \draw[black] (1.610,1.610) -- (2.030,1.610);
  \draw[black] (1.610,1.050) -- (2.310,1.050);
  \draw[blue] (1.260,2.730) .. controls (1.447,2.823) and (1.633,2.823) .. (1.820,2.730);
  \node[black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.400,2.520) {9};
  \node[black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.680,2.520) {8};
  \node[black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.960,2.520) {6};
  \node[black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (2.240,2.520) {3};
  \node[black, anchor=base west, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (3.080,2.520) {91};
  \node[blue, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (3.080,2.100) {1};
  \node[blue, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (3.360,2.100) {0};
  \node[blue, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (3.640,2.100) {8};
  \node[red, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.680,2.240) {1};
  \node[red, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.400,2.240) {9};
  \node[black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.960,1.960) {6};
  \node[green!55!black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.680,1.960) {7};
  \node[red, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.960,1.680) {0};
  \node[black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (2.240,1.400) {3};
  \node[green!55!black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.960,1.400) {6};
  \node[green!55!black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.680,1.400) {7};
  \node[red, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (2.240,1.120) {8};
  \node[red, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.960,1.120) {2};
  \node[red, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.680,1.120) {7};
  \node[green!55!black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (2.240,0.770) {5};
  \node[green!55!black, anchor=base, font=\ttfamily \fontsize{8.0}{9.6}\selectfont] at (1.960,0.770) {3};
\end{tikzpicture}\end{center}
\par\vspace{0.3em}
\textcolor{green}{9 863  = 91  \(\times\) 108  + 35  et 35  \(<\) 91 }\\[0.8em]
\end{document}
