From 15c6dac685997f4382cb7ffbe97ea0865dccf024 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 1 Sep 2022 18:17:22 +0200 Subject: [PATCH] Feat: ajoute les exercices techniques pour les calculs de fractions --- .../1_exercises_tech.tex | 64 +++++++++++++++ .../all_exercises.pdf | Bin 40516 -> 45294 bytes .../all_exercises.tex | 1 + .../bopytex_config.py | 12 +++ 2nd/01_Proportion_et_fractions/exercises.tex | 68 +++++++++------- 2nd/01_Proportion_et_fractions/solutions.pdf | Bin 28126 -> 31751 bytes 2nd/01_Proportion_et_fractions/solutions.tex | 3 +- .../tpl_exercises_tech.tex | 76 ++++++++++++++++++ 8 files changed, 191 insertions(+), 33 deletions(-) create mode 100644 2nd/01_Proportion_et_fractions/1_exercises_tech.tex create mode 100644 2nd/01_Proportion_et_fractions/bopytex_config.py create mode 100644 2nd/01_Proportion_et_fractions/tpl_exercises_tech.tex diff --git a/2nd/01_Proportion_et_fractions/1_exercises_tech.tex b/2nd/01_Proportion_et_fractions/1_exercises_tech.tex new file mode 100644 index 0000000..1b37ba2 --- /dev/null +++ b/2nd/01_Proportion_et_fractions/1_exercises_tech.tex @@ -0,0 +1,64 @@ +\begin{exercise}[subtitle={Multiplication de fractions}, step={3}, origin={Création}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\searchMode}] + Faire les calculs suivants + \begin{multicols}{4} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{- 6}{3} + \dfrac{- 7}{3}$ + \item $\dfrac{- 10}{5} + \dfrac{6}{5}$ + + \item $\dfrac{7}{10} + \dfrac{3}{90}$ + \item $\dfrac{10}{81} + \dfrac{5}{9}$ + + \item $\dfrac{7}{9} + \dfrac{3}{10}$ + \item $\dfrac{8}{5} + \dfrac{3}{7}$ + + \item $\dfrac{1}{a} + \dfrac{1}{2a}$ + \item $\dfrac{3}{5a} + \dfrac{1}{4a}$ + \end{enumerate} + \end{multicols} + +\end{exercise} + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{- 6}{3} + \dfrac{- 7}{3}=\dfrac{- 6 - 7}{3}=\dfrac{- 13}{3} = \dfrac{- 13}{3}$ + \item $\dfrac{- 10}{5} + \dfrac{6}{5}=\dfrac{- 10 + 6}{5}=\dfrac{- 4}{5} = \dfrac{- 4}{5}$ + \item $\dfrac{7}{10} + \dfrac{3}{90}=\dfrac{7 \times 9}{10 \times 9} + \dfrac{3}{90}=\dfrac{63}{90} + \dfrac{3}{90}=\dfrac{63 + 3}{90}=\dfrac{66}{90} = \dfrac{11}{15}$ + \item $\dfrac{10}{81} + \dfrac{5}{9}=\dfrac{10}{81} + \dfrac{5 \times 9}{9 \times 9}=\dfrac{10}{81} + \dfrac{45}{81}=\dfrac{10 + 45}{81}=\dfrac{55}{81} = \dfrac{55}{81}$ + \item $\dfrac{7}{9} + \dfrac{3}{10}=\dfrac{7 \times 10}{9 \times 10} + \dfrac{3 \times 9}{10 \times 9}=\dfrac{70}{90} + \dfrac{27}{90}=\dfrac{70 + 27}{90}=\dfrac{97}{90} = \dfrac{97}{90}$ + \item $\dfrac{- 6}{3} + \dfrac{- 7}{3}=\dfrac{- 6 - 7}{3}=\dfrac{- 13}{3} = \dfrac{- 13}{3}$ + \item $\dfrac{1}{a} + \dfrac{1}{2a} = \dfrac{2}{2a} + \dfrac{1}{2a} = \dfrac{2+1}{2a} = \dfrac{3}{2a}$ + \item $\dfrac{3}{5a} + \dfrac{1}{4a} = \dfrac{12}{20a} + \dfrac{5}{20a} = \dfrac{12+5}{2a} = \dfrac{17}{2a}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Multiplication de fractions}, step={3}, origin={Création}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\searchMode}] + Faire les calculs suivants + \begin{multicols}{4} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{7}{8} \times \dfrac{- 10}{8}$ + \item $B = \dfrac{3}{10} \times \dfrac{7}{10}$ + + \item $\dfrac{3}{4} \times \dfrac{9}{12}$ + \item $\dfrac{2}{30} \times \dfrac{4}{10}$ + + \item $\dfrac{9}{3} \times \dfrac{9}{7}$ + \item $\dfrac{5}{4} \times \dfrac{3}{7}$ + + \item $\dfrac{1}{a} * \dfrac{1}{2a}$ + \item $\dfrac{3}{5a} * \dfrac{1}{4a}$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\dfrac{7}{8} \times \dfrac{- 10}{8}=\dfrac{7(- 10)}{8 \times 8}=\dfrac{- 70}{64} = \dfrac{- 35}{32}$ + \item $\dfrac{3}{10} \times \dfrac{7}{10}=\dfrac{3 \times 7}{10 \times 10}=\dfrac{21}{100} = \dfrac{21}{100}$ + \item $\dfrac{3}{4} \times \dfrac{9}{12}=\dfrac{3 \times 9}{4 \times 12}=\dfrac{27}{48} = \dfrac{9}{16}$ + \item $\dfrac{2}{30} \times \dfrac{4}{10}=\dfrac{2 \times 4}{30 \times 10}=\dfrac{8}{300} = \dfrac{2}{75}$ + \item $\dfrac{9}{3} \times \dfrac{9}{7}=\dfrac{9 \times 9}{3 \times 7}=\dfrac{81}{21} = \dfrac{27}{7}$ + \item $\dfrac{7}{8} \times \dfrac{- 10}{8}=\dfrac{7(- 10)}{8 \times 8}=\dfrac{- 70}{64} = \dfrac{- 35}{32}$ + \item $\dfrac{1}{a} \times \dfrac{1}{2a} = \dfrac{1\times 1}{a\times 2a} = \dfrac{1}{2a^2}$ + \item $\dfrac{3}{5a} \times \dfrac{1}{4a} = \dfrac{3\times 1}{5a\times 4a} = \dfrac{3}{20a^2}$ + \end{enumerate} +\end{solution} diff --git a/2nd/01_Proportion_et_fractions/all_exercises.pdf b/2nd/01_Proportion_et_fractions/all_exercises.pdf index 9fe4f56e36efea0dbaada0fcf89bfe9c0ea4f865..c4da229b1fa040344f8c05a50482e14fa78acd05 100644 GIT binary patch delta 40765 zcmZs>V{G8x6ZT!(wr$(CZQJ&DYnxl!cDu#awzk^Z?bg=w%YEPPp8t7ul9SBjOfuKx zntXz-0UPmLL~q9z`1+4S(-Y+`E0Bh$S0C_A@)5t+z{i$OQ7aFnzbnFyVf_z4!>rkl{Fkma_y1zYr 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a/2nd/01_Proportion_et_fractions/solutions.tex +++ b/2nd/01_Proportion_et_fractions/solutions.tex @@ -22,7 +22,6 @@ \maketitle \input{exercises.tex} -%\printcollection{banque} -%\printsolutions{exercises} +\input{1_exercises_tech.tex} \end{document} diff --git a/2nd/01_Proportion_et_fractions/tpl_exercises_tech.tex b/2nd/01_Proportion_et_fractions/tpl_exercises_tech.tex new file mode 100644 index 0000000..c1bda40 --- /dev/null +++ b/2nd/01_Proportion_et_fractions/tpl_exercises_tech.tex @@ -0,0 +1,76 @@ +\begin{exercise}[subtitle={Multiplication de fractions}, step={3}, origin={Création}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\searchMode}] + Faire les calculs suivants + \begin{multicols}{4} + \begin{enumerate}[label={\Alph*=}] + %- set A = random_expression("{a} / {b} + {c} / {b}", ["a!=b", "c!=b", "b > 1"], global_config={"rejected":[-1, 0, 1]}) + \item $\Var{A}$ + %- set B = random_expression("{a} / {b} + {c} / {b}", ["a!=b", "c!=b", "b > 1"], global_config={"rejected":[-1, 0, 1]}) + \item $\Var{B}$ + + %- set C = random_expression("{a} / {b} + {c} / {d*b}", ["a!=b", "c!=b", "b > 1"], global_config={"min_max":(1, 10)}) + \item $\Var{C}$ + %- set D = random_expression("{a} / {d*b} + {c} / {b}", ["a!=b", "c!=b", "b > 1"], global_config={"min_max":(1, 10)}) + \item $\Var{D}$ + + %- set E = random_expression("{a} / {b} + {c} / {d}", ["a!=b", "c!=b", "gcd(b, d) == 1"], global_config={"min_max":(1, 10)}) + \item $\Var{E}$ + %- set F = random_expression("{a} / {b} + {c} / {d}", ["a!=b", "c!=b", "gcd(b, d) == 1"], global_config={"min_max":(1, 10)}) + \item $\Var{F}$ + + \item $\dfrac{1}{a} + \dfrac{1}{2a}$ + \item $\dfrac{3}{5a} + \dfrac{1}{4a}$ + \end{enumerate} + \end{multicols} + +\end{exercise} + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\Var{A.simplify().explain() | join('=')} = \Var{A.simplify().simplified}$ + \item $\Var{B.simplify().explain() | join('=')} = \Var{B.simplify().simplified}$ + \item $\Var{C.simplify().explain() | join('=')} = \Var{C.simplify().simplified}$ + \item $\Var{D.simplify().explain() | join('=')} = \Var{D.simplify().simplified}$ + \item $\Var{E.simplify().explain() | join('=')} = \Var{E.simplify().simplified}$ + \item $\Var{A.simplify().explain() | join('=')} = \Var{A.simplify().simplified}$ + \item $\dfrac{1}{a} + \dfrac{1}{2a} = \dfrac{2}{2a} + \dfrac{1}{2a} = \dfrac{2+1}{2a} = \dfrac{3}{2a}$ + \item $\dfrac{3}{5a} + \dfrac{1}{4a} = \dfrac{12}{20a} + \dfrac{5}{20a} = \dfrac{12+5}{2a} = \dfrac{17}{2a}$ + \end{enumerate} +\end{solution} + +\begin{exercise}[subtitle={Multiplication de fractions}, step={3}, origin={Création}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\searchMode}] + Faire les calculs suivants + \begin{multicols}{4} + \begin{enumerate}[label={\Alph*=}] + %- set A = random_expression("{a} / {b} * {c} / {b}", ["a!=b", "c!=b", "b > 1"], global_config={"rejected":[-1, 0, 1]}) + \item $\Var{A}$ + %- set B = random_expression("{a} / {b} * {c} / {b}", ["a!=b", "c!=b", "b > 1"], global_config={"rejected":[-1, 0, 1]}) + \item $B = \Var{B}$ + + %- set C = random_expression("{a} / {b} * {c} / {d*b}", ["a!=b", "c!=b", "b > 1"], global_config={"min_max":(1, 10)}) + \item $\Var{C}$ + %- set D = random_expression("{a} / {d*b} * {c} / {b}", ["a!=b", "c!=b", "b > 1"], global_config={"min_max":(1, 10)}) + \item $\Var{D}$ + + %- set E = random_expression("{a} / {b} * {c} / {d}", ["a!=b", "c!=b", "gcd(b, d) == 1"], global_config={"min_max":(1, 10)}) + \item $\Var{E}$ + %- set F = random_expression("{a} / {b} * {c} / {d}", ["a!=b", "c!=b", "gcd(b, d) == 1"], global_config={"min_max":(1, 10)}) + \item $\Var{F}$ + + \item $\dfrac{1}{a} * \dfrac{1}{2a}$ + \item $\dfrac{3}{5a} * \dfrac{1}{4a}$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{solution} + \begin{enumerate}[label={\Alph*=}] + \item $\Var{A.simplify().explain() | join('=')} = \Var{A.simplify().simplified}$ + \item $\Var{B.simplify().explain() | join('=')} = \Var{B.simplify().simplified}$ + \item $\Var{C.simplify().explain() | join('=')} = \Var{C.simplify().simplified}$ + \item $\Var{D.simplify().explain() | join('=')} = \Var{D.simplify().simplified}$ + \item $\Var{E.simplify().explain() | join('=')} = \Var{E.simplify().simplified}$ + \item $\Var{A.simplify().explain() | join('=')} = \Var{A.simplify().simplified}$ + \item $\dfrac{1}{a} \times \dfrac{1}{2a} = \dfrac{1\times 1}{a\times 2a} = \dfrac{1}{2a^2}$ + \item $\dfrac{3}{5a} \times \dfrac{1}{4a} = \dfrac{3\times 1}{5a\times 4a} = \dfrac{3}{20a^2}$ + \end{enumerate} +\end{solution}