124 lines
3.4 KiB
TeX
124 lines
3.4 KiB
TeX
% vim:ft=tex:
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%
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\documentclass[12pt]{article}
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\usepackage[utf8x]{inputenc}
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\usepackage[francais]{babel}
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\usepackage[T1]{fontenc}
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\usepackage{amssymb}
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\usepackage{amsmath}
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\usepackage{amsfonts}
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\title{
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Snippets pour Opytex \\
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Fractions
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}
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\author{
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Benjamin Bertrand
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}
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\begin{document}
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\maketitle
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\section{Simplifications de fractions}
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\begin{itemize}
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\item Trouver le numérateur quand le dénominateur augmente
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%- set a,b,ans,c = random_list(["{a}", "{b}", "{a*c}", "{b*c}"], conditions = ["a != b"], min_max=(2, 10))
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\begin{align*}
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\dfrac{\Var{a}}{\Var{b}} = \dfrac{\ldots}{\Var{c}}
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\end{align*}
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Solution
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\begin{align*}
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\dfrac{\Var{a}}{\Var{b}} = \dfrac{\Var{ans}}{\Var{c}}
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\end{align*}
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\item Trouver le numérateur quand le dénominateur diminue
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\Block{set a,b,ans,c = random_list(["{a*c}", "{b*c}", "{a}", "{b}"], conditions = ["a != b"], min_max=(2, 10))}
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\begin{align*}
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\dfrac{\Var{a}}{\Var{b}} = \dfrac{\cdots}{\Var{c}}
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\end{align*}
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Solution
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\begin{align*}
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\dfrac{\Var{a}}{\Var{b}} = \dfrac{\Var{ans}}{\Var{c}}
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\end{align*}
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Explications \Var{type(a)} -- \Var{type(b)}
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set f = Expression.from_str(str(int(a)) + " / " + str(int(b)))
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\begin{align*}
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\texttt{f.simplify().explain()|join('=')}
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\end{align*}
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\end{itemize}
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\section{Ajouts de fractions}
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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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\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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\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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\item Une fraction et un entier
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\Block{set e = Expression.random("{c} + {a} / {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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\end{itemize}
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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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\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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\end{document}
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