\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}
