Feat: ajoute les exercices techniques pour les calculs de fractions
All checks were successful
continuous-integration/drone/push Build is passing
All checks were successful
continuous-integration/drone/push Build is passing
This commit is contained in:
parent
5d333b26b0
commit
15c6dac685
64
2nd/01_Proportion_et_fractions/1_exercises_tech.tex
Normal file
64
2nd/01_Proportion_et_fractions/1_exercises_tech.tex
Normal file
@ -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}
|
||||
Binary file not shown.
@ -22,5 +22,6 @@
|
||||
\maketitle
|
||||
|
||||
\input{exercises.tex}
|
||||
\input{1_exercises_tech.tex}
|
||||
|
||||
\end{document}
|
||||
|
||||
12
2nd/01_Proportion_et_fractions/bopytex_config.py
Normal file
12
2nd/01_Proportion_et_fractions/bopytex_config.py
Normal file
@ -0,0 +1,12 @@
|
||||
# bopytex_config.py
|
||||
from mapytex.calculus.random import expression as random_expression
|
||||
from mapytex import render
|
||||
import random
|
||||
|
||||
random.seed(0) # Controlling the seed allows to make subject reproductible
|
||||
|
||||
render.set_render("tex")
|
||||
|
||||
direct_access = {
|
||||
"random_expression": random_expression,
|
||||
}
|
||||
@ -43,16 +43,17 @@
|
||||
\end{exercise}
|
||||
|
||||
\begin{solution}
|
||||
\def\arraystretch{2}
|
||||
\begin{enumerate}
|
||||
\item $\frac{120}{150} = \frac{4}{5} = 0.8 = 80\%$
|
||||
\item $\frac{5}{22} \approx 0.22 = 22\%$
|
||||
\item $\dfrac{120}{150} = \dfrac{4}{5} = 0.8 = 80\%$
|
||||
\item $\dfrac{5}{22} \approx 0.22 = 22\%$
|
||||
\item
|
||||
|
||||
\begin{tabular}{|p{4cm}|*{4}{c|}}
|
||||
\hline
|
||||
Camping & Les flots bleu & Cascade magique & Le tronc dégarni & La vallée plate\\
|
||||
\hline
|
||||
Proportion en fraction & $\frac{0}{35}$ & $\frac{10}{15}$ & $\frac{40}{75}$ & $\frac{100}{200}$ \\
|
||||
Proportion en fraction & $\dfrac{0}{35}$ & $\dfrac{10}{15}$ & $\dfrac{40}{75}$ & $\dfrac{100}{200}$ \\
|
||||
\hline
|
||||
Proportion en décimal & 0 & 0.66 & 0.53 & 0.5 \\
|
||||
\hline
|
||||
@ -60,6 +61,7 @@
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{enumerate}
|
||||
\def\arraystretch{1.5}
|
||||
\end{solution}
|
||||
|
||||
|
||||
@ -106,29 +108,31 @@
|
||||
\end{exercise}
|
||||
|
||||
\begin{solution}
|
||||
\def\arraystretch{2}
|
||||
\begin{tabular}{|*{4}{c|}}
|
||||
\hline
|
||||
Proportion & Fraction irréductible & Effectifs associés & Valeur décimale \\
|
||||
\hline
|
||||
10\% & $\frac{1}{10}$ & 10 pour 100, c'est comme 1 pour 10 & 0.1\\
|
||||
10\% & $\dfrac{1}{10}$ & 10 pour 100, c'est comme 1 pour 10 & 0.1\\
|
||||
\hline
|
||||
20\% & $\frac{1}{5}$ & 20 pour 100, c'est comme 1 pour 5 & 0.2\\
|
||||
20\% & $\dfrac{1}{5}$ & 20 pour 100, c'est comme 1 pour 5 & 0.2\\
|
||||
\hline
|
||||
25\% & $\frac{1}{4}$ & 25 pour 100, c'est comme 1 pour 4 & 0.25\\
|
||||
25\% & $\dfrac{1}{4}$ & 25 pour 100, c'est comme 1 pour 4 & 0.25\\
|
||||
\hline
|
||||
33.3\% & $\frac{333}{1000}$ & 33.3 pour 100, c'est comme 333 pour 1000 & 0.333\\
|
||||
33.3\% & $\dfrac{333}{1000}$ & 33.3 pour 100, c'est comme 333 pour 1000 & 0.333\\
|
||||
\hline
|
||||
50\% & $\frac{1}{2}$ & 50 pour 100, c'est comme 1 pour 2 & 0.5 \\
|
||||
50\% & $\dfrac{1}{2}$ & 50 pour 100, c'est comme 1 pour 2 & 0.5 \\
|
||||
\hline
|
||||
60\% & $\frac{3}{5}$ & 60 pour 100, c'est comme 3 pour 5 & 0.6 \\
|
||||
60\% & $\dfrac{3}{5}$ & 60 pour 100, c'est comme 3 pour 5 & 0.6 \\
|
||||
\hline
|
||||
66.7\% & $\frac{667}{1000}$ & 66.7 pour 100, c'est comme 667 pour 1000 & 0.667\\
|
||||
66.7\% & $\dfrac{667}{1000}$ & 66.7 pour 100, c'est comme 667 pour 1000 & 0.667\\
|
||||
\hline
|
||||
75\% & $\frac{3}{4}$ & 75 pour 100, c'est comme 3 pour 4 & 0.75 \\
|
||||
75\% & $\dfrac{3}{4}$ & 75 pour 100, c'est comme 3 pour 4 & 0.75 \\
|
||||
\hline
|
||||
100\% & 1 & 100 pour 100, c'est comme 1 pour 1 & 1\\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\def\arraystretch{1.5}
|
||||
\end{solution}
|
||||
|
||||
\begin{exercise}[subtitle={Techniques}, step={1}, origin={MEpC}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\trainMode}]
|
||||
@ -148,19 +152,21 @@
|
||||
\end{exercise}
|
||||
|
||||
\begin{solution}
|
||||
\begin{multicols}{3}
|
||||
\begin{enumerate}
|
||||
\item $\frac{20}{100} \times 190 = 38$
|
||||
\item $\frac{2}{3} \times 126 = 84$
|
||||
\item $\frac{42}{100} = \frac{31}{50} = 0.42$
|
||||
\item $\frac{78}{100} = \frac{39}{50} = 0.78$
|
||||
\item $\frac{1,5}{5} = \frac{3}{10} = 0.3$
|
||||
\item $\frac{1500}{2300} = \frac{15}{23} \approx 0.65$
|
||||
\item $\frac{30}{100} \times 400 = 120$
|
||||
\item $\frac{0.6}{100} \times \np{2 000 000} = \np{12 000}$
|
||||
\item $ \frac{14}{0.4} = 35$
|
||||
\item $ \frac{150 000}{0.75} = 200 000$
|
||||
\item $ \frac{5\times 30}{0.24} = 625$
|
||||
\item $\dfrac{20}{100} \times 190 = 38$
|
||||
\item $\dfrac{2}{3} \times 126 = 84$
|
||||
\item $\dfrac{42}{100} = \dfrac{31}{50} = 0.42$
|
||||
\item $\dfrac{78}{100} = \dfrac{39}{50} = 0.78$
|
||||
\item $\dfrac{1,5}{5} = \dfrac{3}{10} = 0.3$
|
||||
\item $\dfrac{1500}{2300} = \dfrac{15}{23} \approx 0.65$
|
||||
\item $\dfrac{30}{100} \times 400 = 120$
|
||||
\item $\dfrac{0.6}{100} \times \np{2 000 000} = \np{12 000}$
|
||||
\item $ \dfrac{14}{0.4} = 35$
|
||||
\item $ \dfrac{150 000}{0.75} = 200 000$
|
||||
\item $ \dfrac{5\times 30}{0.24} = 625$
|
||||
\end{enumerate}
|
||||
\end{multicols}
|
||||
\end{solution}
|
||||
|
||||
\begin{exercise}[subtitle={Radars}, step={1}, origin={MEpC}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\groupMode}]
|
||||
@ -187,11 +193,11 @@
|
||||
\begin{enumerate}
|
||||
\item Est-il possible de trouver deux nombres entiers distincts $a$ et $b$ tels que:
|
||||
\[
|
||||
\frac{1}{a} + \frac{1}{b} = 1
|
||||
\dfrac{1}{a} + \dfrac{1}{b} = 1
|
||||
\]
|
||||
\item Est-il possible de trouver deux nombres entiers distincts $a$, $b$ et $c$ tels que:
|
||||
\[
|
||||
\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1
|
||||
\dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c} = 1
|
||||
\]
|
||||
\item Avec 4 nombres? 5? Et plus?
|
||||
\end{enumerate}
|
||||
@ -213,11 +219,11 @@
|
||||
\end{multicols}
|
||||
\item Indiquez sur les disques les fractions correspondantes
|
||||
\[
|
||||
\frac{1}{2} \qquad
|
||||
\frac{1}{3} \qquad
|
||||
\frac{1}{4} \qquad
|
||||
\frac{1}{8} \qquad
|
||||
\frac{1}{12} \qquad
|
||||
\dfrac{1}{2} \qquad
|
||||
\dfrac{1}{3} \qquad
|
||||
\dfrac{1}{4} \qquad
|
||||
\dfrac{1}{8} \qquad
|
||||
\dfrac{1}{12} \qquad
|
||||
\]
|
||||
\item Reconstituez un disque complet à l'aide de 3 portions.
|
||||
\item Reconstituez un disque complet à l'aide de 4 portions.
|
||||
|
||||
Binary file not shown.
@ -22,7 +22,6 @@
|
||||
\maketitle
|
||||
|
||||
\input{exercises.tex}
|
||||
%\printcollection{banque}
|
||||
%\printsolutions{exercises}
|
||||
\input{1_exercises_tech.tex}
|
||||
|
||||
\end{document}
|
||||
|
||||
76
2nd/01_Proportion_et_fractions/tpl_exercises_tech.tex
Normal file
76
2nd/01_Proportion_et_fractions/tpl_exercises_tech.tex
Normal file
@ -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}
|
||||
Loading…
Reference in New Issue
Block a user