284 lines
10 KiB
TeX
284 lines
10 KiB
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{Information chiffrée 1 - Exercices}
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\date{Septembre 2021}
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\begin{document}
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\maketitle
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\begin{exercise}[subtitle={Égalité de fractions}]
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Déterminer les valeurs manquantes
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\begin{multicols}{4}
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\begin{enumerate}[label=\alph*)]
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%- set A = random_list(["a", "b", "a*c", "b*c"], conditions = ["a != b"], min_max=(2, 9), rejected=[0, 1])
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\item $\dfrac{\Var{A[0]}}{\Var{A[1]}} = \dfrac{\ldots}{\Var{A[3]}}$
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%- set B = random_list(["a", "b", "a*c", "b*c"], conditions = ["a != b"], min_max=(2, 9), rejected=[0, 1])
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\item $\dfrac{\Var{B[0]}}{\Var{B[1]}} = \dfrac{\ldots}{\Var{B[3]}}$
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%- set C = random_list(["a", "b", "a*c", "b*c"], conditions = ["a != b", "a*b>0"], min_max=(-9, 9), rejected=[0, 1])
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\item $\dfrac{\Var{C[0]}}{\Var{C[1]}} = \dfrac{\ldots}{\Var{C[3]}}$
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%- set D = random_list(["a", "b", "a*c", "b*c"], conditions = ["a != b", "a*b<0"], min_max=(-9, 9), rejected=[0, 1])
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\item $\dfrac{\Var{D[0]}}{\Var{D[1]}} = \dfrac{\ldots}{\Var{D[3]}}$
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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}{4}
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\begin{enumerate}[label=\alph*)]
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\item $\dfrac{\Var{A[0]}}{\Var{A[1]}} = \dfrac{\Var{A[2]}}{\Var{A[3]}}$
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\item $\dfrac{\Var{B[0]}}{\Var{B[1]}} = \dfrac{\Var{B[2]}}{\Var{B[3]}}$
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\item $\dfrac{\Var{C[0]}}{\Var{C[1]}} = \dfrac{\Var{C[2]}}{\Var{C[3]}}$
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\item $\dfrac{\Var{D[0]}}{\Var{D[1]}} = \dfrac{\Var{D[2]}}{\Var{D[3]}}$
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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={Comparaison}]
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Comparer les fractions suivantes
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\begin{multicols}{4}
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\begin{enumerate}[label=\alph*)]
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%- set A1 = Fraction.random()
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%- set A2 = Fraction.random()
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\item $\Var{A1}$ et $\Var{A2}$
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%- set B1 = Fraction.random()
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%- set B2 = Fraction.random()
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\item $\Var{B1}$ et $\Var{B2}$
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%- set C1 = Fraction.random()
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%- set C2 = Fraction.random()
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\item $\Var{C1}$ et $\Var{C2}$
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%- set D1 = Fraction.random()
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%- set D2 = Fraction.random()
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\item $\Var{D1}$ et $\Var{D2}$
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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}{4}
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\begin{enumerate}[label=\alph*)]
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\item
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%- if A1 > A2
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$\Var{A1}$ > $\Var{A2}$
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%- elif A1 < A2
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$\Var{A1}$ < $\Var{A2}$
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%- else
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$\Var{A1}$ = $\Var{A2}$
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%- endif
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\item
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%- if B1 > B2
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$\Var{B1}$ > $\Var{B2}$
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%- elif B1 < B2
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$\Var{B1}$ < $\Var{B2}$
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%- else
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$\Var{B1}$ = $\Var{B2}$
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%- endif
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\item
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%- if C1 > C2
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$\Var{C1}$ > $\Var{C2}$
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%- elif C1 < C2
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$\Var{C1}$ < $\Var{C2}$
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%- else
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$\Var{C1}$ = $\Var{C2}$
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%- endif
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\item
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%- if D1 > D2
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$\Var{D1}$ > $\Var{D2}$
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%- elif D1 < D2
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$\Var{D1}$ < $\Var{D2}$
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%- else
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$\Var{D1}$ = $\Var{D2}$
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%- endif
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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={Additions}]
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Faire les calculs suivants
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\begin{multicols}{4}
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\begin{enumerate}[label={\Alph*=}]
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%- set A = Expression.random("{a} / {b} + {c} / {b}", ["a!=b", "c!=b", "b > 1"], min_max=(1, 10))
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\item $\Var{A}$
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%- set B = Expression.random("{a} / {b} + {c} / {b}", ["a!=b", "c!=b", "b > 1"], min_max=(-10, 10))
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\item $\Var{B}$
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%- set C = Expression.random("{a} / {b} + {c}", ["a!=b", "b > 1"], min_max=(1, 10))
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\item $\Var{C}$
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%- set D = Expression.random("{a} / {b} + {c}", ["a!=b", "b > 1"], min_max=(-10, 10))
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\item $\Var{D}$
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%- set E = Expression.random("{a} / {b} + {c} / {k*b}", ["a!=b", "c!=b", "b > 1"], min_max=(1, 10))
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\item $\Var{E}$
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%- set F = Expression.random("{a} / {b} + {c} / {k*b}", ["a!=b", "c!=b", "b > 1", "k > 1"], min_max=(-10, 10))
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\item $\Var{F}$
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%- set G = Expression.random("{a} / {b} + {c} / {d}", ["a!=b", "c!=d", "b > 1", "d > 1"], min_max=(0, 10))
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\item $\Var{G}$
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%- set H = Expression.random("{a} / {b} + {c} / {d}", ["a!=b", "c!=d", "b > 1", "d > 1"], min_max=(-10, 10))
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\item $\Var{H}$
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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{enumerate}[label={\Alph*=}]
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\item $\Var{A.simplify().explain() | join('=')}$
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\item $\Var{B.simplify().explain() | join('=')}$
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\item $\Var{C.simplify().explain() | join('=')}$
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\item $\Var{D.simplify().explain() | join('=')}$
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\item $\Var{E.simplify().explain() | join('=')}$
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\item $\Var{F.simplify().explain() | join('=')}$
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\item $\Var{G.simplify().explain() | join('=')}$
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\item $\Var{H.simplify().explain() | join('=')}$
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\end{enumerate}
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\end{solution}
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\begin{exercise}[subtitle={Multiplications}]
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Faire les calculs suivants
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\begin{multicols}{4}
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\begin{enumerate}[label={\Alph*=}]
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%- set A = Expression.random("{a} / {b} * {c}", ["a!=b", "b > 1"], min_max=(1, 10))
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\item $\Var{A}$
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%- set B = Expression.random("{a} / {b} * {c}", ["a!=b", "b > 1"], min_max=(-10, 10))
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\item $\Var{B}$
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%- set C = Expression.random("{a} / {b} * {c} / {b}", ["a!=b", "c!=b", "b > 1"], min_max=(1, 10))
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\item $\Var{C}$
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%- set D = Expression.random("{a} / {b} * {c} / {b}", ["a!=b", "c!=b", "b > 1"], min_max=(-10, 10))
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\item $\Var{D}$
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%- set E = Expression.random("{a} / {b} * {c} / {k*b}", ["a!=b", "c!=b", "b > 1"], min_max=(1, 10))
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\item $\Var{E}$
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%- set F = Expression.random("{a} / {b} * {c} / {k*b}", ["a!=b", "c!=b", "b > 1", "k > 1"], min_max=(-10, 10))
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\item $\Var{F}$
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%- set G = Expression.random("{a} / {b} * {c} / {d}", ["a!=b", "c!=d", "b > 1", "d > 1"], min_max=(0, 10))
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\item $\Var{G}$
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%- set H = Expression.random("{a} / {b} * {c} / {d}", ["a!=b", "c!=d", "b > 1", "d > 1"], min_max=(-10, 10))
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\item $\Var{H}$
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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}{2}
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\begin{enumerate}[label={\Alph*=}]
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\item $\Var{A.simplify().explain() | join('=')} = \Var{A.simplify().simplify()}$
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\item $\Var{B.simplify().explain() | join('=')} = \Var{B.simplify().simplify()}$
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\item $\Var{C.simplify().explain() | join('=')} = \Var{C.simplify().simplify()}$
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\item $\Var{D.simplify().explain() | join('=')} = \Var{D.simplify().simplify()}$
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\item $\Var{E.simplify().explain() | join('=')} = \Var{E.simplify().simplify()}$
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\item $\Var{F.simplify().explain() | join('=')} = \Var{F.simplify().simplify()}$
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\item $\Var{G.simplify().explain() | join('=')} = \Var{G.simplify().simplify()}$
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\item $\Var{H.simplify().explain() | join('=')} = \Var{H.simplify().simplify()}$
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\end{enumerate}
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\end{multicols}
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\end{solution}
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\pagebreak
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\printsolutions
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%
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% \section{Ajouts de fractions}
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%
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% \begin{itemize}
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% \item Fraction avec le même dénominateur
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% \Block{set e = Expression.random("{a} / {b} + {c} / {b}", ["b > 1"], min_max=(1, 10))}
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% \begin{align*}
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% A = \Var{e}
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% \end{align*}
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% Solution
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% \begin{align*}
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% \Var{e.simplify().explain() | join('=')}
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% \end{align*}
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%
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% \item Fraction avec un denominateur multiple de l'autre
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% \Block{set e = Expression.random("{a} / {b} + {c} / {b*d}", ["b > 1","d > 1"], min_max=(1, 10))}
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% \begin{align*}
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% A = \Var{e}
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% \end{align*}
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% Solution
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% \begin{align*}
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% \Var{e.simplify().explain() | join('=')}
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% \end{align*}
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%
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% \item Une fraction et un entier
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% \Block{set e = Expression.random("{a} / {b} + {c}", ["b > 1"], min_max=(1, 10))}
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% \begin{align*}
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% A = \Var{e}
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% \end{align*}
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% Solution
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% \begin{align*}
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% \Var{e.simplify().explain() | join('=')}
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% \end{align*}
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%
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% \end{itemize}
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%
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%
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% \section{Multiplications de fractions}
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% \begin{itemize}
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% \item Une fraction et un entier
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% \Block{set e = Expression.random("{c} * {a} / {b}", min_max=(2, 10))}
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% \begin{align*}
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% A = \Var{e}
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% \end{align*}
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% Solution
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% \begin{align*}
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% \Var{e.simplify().explain() | join('=')}
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% \end{align*}
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%
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% \item Fraction avec des dénominateurs quelconques
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% \Block{set e = Expression.random("{a} / {b} * {c} / {d}", ["b > 1","d > 1"], min_max=(1, 10))}
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% \begin{align*}
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% A = \Var{e}
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% \end{align*}
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% Solution
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% \begin{align*}
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% \Var{e.simplify().explain() | join('=')}
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% \end{align*}
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% \end{itemize}
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%
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%
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% \section{Division de fractions}
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% \begin{itemize}
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% \item Une fraction et un entier
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% \Block{set e = Expression.random("{c} / {a} / {b}", min_max=(2, 10))}
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% \begin{align*}
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% A = \Var{e}
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% \end{align*}
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% Solution
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% \begin{align*}
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% \Var{e.simplify().explain() | join('=')}
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% \end{align*}
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%
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% \item Fraction avec des dénominateurs quelconques
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% \Block{set e = Expression.random("({a} / {b}) / ({c} / {d})", ["a != b", "c!= d", "b > 1","d > 1"], min_max=(1, 10))}
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% \begin{align*}
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% A = \Var{e}
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% \end{align*}
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% Solution
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% \begin{align*}
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% \Var{e.simplify().explain() | join('=')}
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% \end{align*}
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% \end{itemize}
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%
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% \section{Tout mélangé}
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% \begin{itemize}
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% \item
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% \Block{set e = Expression.random("{d}/{e}*({c} / {a} + {b})", min_max=(2, 10))}
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% \begin{align*}
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% A = \Var{e}
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% \end{align*}
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% Solution
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% \begin{align*}
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% \Var{e.simplify().explain() | join('=')}
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% \end{align*}
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% \end{itemize}
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\end{document}
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