start snippet for opytex - fractions are done!
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Lafrite
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% 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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%
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\begin{align*}
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\dfrac{2}{6} = \dfrac{\ldots}{48}
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\end{align*}
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Solution
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\begin{align*}
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\dfrac{2}{6} = \dfrac{16}{48}
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\end{align*}
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\item Trouver le numérateur quand le dénominateur diminue
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%
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\begin{align*}
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\dfrac{12}{9} = \dfrac{\cdots}{3}
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\end{align*}
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Solution
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\begin{align*}
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\dfrac{12}{9} = \dfrac{4}{3}
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\end{align*}
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Explications
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\begin{align*}
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\frac{ 12 }{ 9 }=\frac{ 4 \times 3 }{ 3 \times 3 }=\frac{ 4 }{ 3 }
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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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\begin{align*}
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A = \frac{ 1 }{ 4 } + \frac{ 5 }{ 4 }
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\end{align*}
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Solution
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\begin{align*}
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\frac{ 1 }{ 4 } + \frac{ 5 }{ 4 }=\frac{ 1 + 5 }{ 4 }=\frac{ 6 }{ 4 }=\frac{ 3 \times 2 }{ 2 \times 2 }=\frac{ 3 }{ 2 }
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\end{align*}
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\item Fraction avec un denominateur multiple de l'autre
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\begin{align*}
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A = \frac{ 10 }{ 7 } + \frac{ 3 }{ 49 }
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\end{align*}
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Solution
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\begin{align*}
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\frac{ 10 }{ 7 } + \frac{ 3 }{ 49 }=\frac{ 10 \times 7 }{ 7 \times 7 } + \frac{ 3 \times 1 }{ 49 \times 1 }=\frac{ 70 }{ 49 } + \frac{ 3 }{ 49 }=\frac{ 70 + 3 }{ 49 }=\frac{ 73 }{ 49 }
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\end{align*}
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\item Fraction avec des dénominateurs premiers entre eux
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\begin{align*}
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A = \frac{ 10 }{ 3 } + \frac{ 4 }{ 2 }
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\end{align*}
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Solution
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\begin{align*}
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\frac{ 10 }{ 3 } + \frac{ 4 }{ 2 }=\frac{ 10 \times 2 }{ 3 \times 2 } + \frac{ 4 \times 3 }{ 2 \times 3 }=\frac{ 20 }{ 6 } + \frac{ 12 }{ 6 }=\frac{ 20 + 12 }{ 6 }=\frac{ 32 }{ 6 }=\frac{ 16 \times 2 }{ 3 \times 2 }=\frac{ 16 }{ 3 }
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\end{align*}
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\item Une fraction et un entier
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\begin{align*}
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A = \frac{ 6 }{ 8 } + 9
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\end{align*}
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Solution
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\begin{align*}
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\frac{ 6 }{ 8 } + 9=\frac{ 6 \times 1 }{ 8 \times 1 } + \frac{ 9 \times 8 }{ 1 \times 8 }=\frac{ 6 }{ 8 } + \frac{ 72 }{ 8 }=\frac{ 6 + 72 }{ 8 }=\frac{ 78 }{ 8 }=\frac{ 39 \times 2 }{ 4 \times 2 }=\frac{ 39 }{ 4 }
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\end{align*}
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\item Une fraction et un entier
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\begin{align*}
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A = 2 + \frac{ 8 }{ 2 }
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\end{align*}
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Solution
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\begin{align*}
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2 + \frac{ 8 }{ 2 }=\frac{ 2 \times 2 }{ 1 \times 2 } + \frac{ 8 \times 1 }{ 2 \times 1 }=\frac{ 4 }{ 2 } + \frac{ 8 }{ 2 }=\frac{ 4 + 8 }{ 2 }=6
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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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\begin{align*}
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A = 5 \times \frac{ 7 }{ 8 }
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\end{align*}
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Solution
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\begin{align*}
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5 \times \frac{ 7 }{ 8 }=\frac{ 7 }{ 8 } \times 5=\frac{ 7 \times 5 }{ 8 }=\frac{ 35 }{ 8 }
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\end{align*}
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\item Fraction avec des dénominateurs quelconques
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\begin{align*}
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A = \frac{ 5 }{ 10 } \times \frac{ 4 }{ 7 }
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\end{align*}
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Solution
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\begin{align*}
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\frac{ 5 }{ 10 } \times \frac{ 4 }{ 7 }=\frac{ 4 }{ 7 } \times \frac{ 5 }{ 10 }=\frac{ 2 \times 2 \times 5 }{ 7 \times 5 \times 2 }=\frac{ 4 \times 5 }{ 7 \times 10 }=\frac{ 20 }{ 70 }=\frac{ 2 \times 10 }{ 7 \times 10 }=\frac{ 2 }{ 7 }
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\end{align*}
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\end{itemize}
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\end{document}
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Binary file not shown.
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@ -0,0 +1,133 @@
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% 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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\Block{set a,b,ans,c = random_str("{a},{b},{a*c},{b*c}", conditions = ["{a} != {b}"], val_min = 2, val_max = 10).split(',')}%
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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_str("{a*c},{b*c},{a},{b}", conditions = ["{a} != {b}"], val_min = 2, val_max = 10).split(',')}%
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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
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\Block{set f = Expression(a + "/" +b)}
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\begin{align*}
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\Var{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"], val_min = 1)}
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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"], val_min = 1)}
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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 premiers entre eux
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\Block{set e = Expression.random("{a} / {b} + {c} / {d}", ["{b} > 1","{d} > 1", "gcd({b},{d}) == 1"], val_min = 1)}
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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"], val_min = 1)}
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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"], val_min = 1)}
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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}", ["{b} > 1"], val_min = 1)}
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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"], val_min = 1)}
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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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