64 lines
3.6 KiB
TeX
64 lines
3.6 KiB
TeX
\begin{exercise}[subtitle={Multiplication de fractions}, step={4}, origin={Création}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\searchMode}]
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Faire les calculs suivants
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\begin{multicols}{4}
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\begin{enumerate}[label={\Alph*=}]
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\item $\dfrac{- 6}{3} + \dfrac{- 7}{3}$
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\item $\dfrac{- 10}{5} + \dfrac{6}{5}$
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\item $\dfrac{7}{10} + \dfrac{3}{90}$
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\item $\dfrac{10}{81} + \dfrac{5}{9}$
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\item $\dfrac{7}{9} + \dfrac{3}{10}$
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\item $\dfrac{8}{5} + \dfrac{3}{7}$
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\item $\dfrac{1}{a} + \dfrac{1}{2a}$
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\item $\dfrac{3}{5a} + \dfrac{1}{4a}$
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\end{enumerate}
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\end{multicols}
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\end{exercise}
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\begin{solution}
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\begin{enumerate}[label={\Alph*=}]
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\item $\dfrac{- 6}{3} + \dfrac{- 7}{3}=\dfrac{- 6 - 7}{3}=\dfrac{- 13}{3} = \dfrac{- 13}{3}$
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\item $\dfrac{- 10}{5} + \dfrac{6}{5}=\dfrac{- 10 + 6}{5}=\dfrac{- 4}{5} = \dfrac{- 4}{5}$
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\item $\dfrac{7}{10} + \dfrac{3}{90}=\dfrac{7 \times 9}{10 \times 9} + \dfrac{3}{90}=\dfrac{63}{90} + \dfrac{3}{90}=\dfrac{63 + 3}{90}=\dfrac{66}{90} = \dfrac{11}{15}$
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\item $\dfrac{10}{81} + \dfrac{5}{9}=\dfrac{10}{81} + \dfrac{5 \times 9}{9 \times 9}=\dfrac{10}{81} + \dfrac{45}{81}=\dfrac{10 + 45}{81}=\dfrac{55}{81} = \dfrac{55}{81}$
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\item $\dfrac{7}{9} + \dfrac{3}{10}=\dfrac{7 \times 10}{9 \times 10} + \dfrac{3 \times 9}{10 \times 9}=\dfrac{70}{90} + \dfrac{27}{90}=\dfrac{70 + 27}{90}=\dfrac{97}{90} = \dfrac{97}{90}$
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\item $\dfrac{- 6}{3} + \dfrac{- 7}{3}=\dfrac{- 6 - 7}{3}=\dfrac{- 13}{3} = \dfrac{- 13}{3}$
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\item $\dfrac{1}{a} + \dfrac{1}{2a} = \dfrac{2}{2a} + \dfrac{1}{2a} = \dfrac{2+1}{2a} = \dfrac{3}{2a}$
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\item $\dfrac{3}{5a} + \dfrac{1}{4a} = \dfrac{12}{20a} + \dfrac{5}{20a} = \dfrac{12+5}{2a} = \dfrac{17}{2a}$
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\end{enumerate}
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\end{solution}
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\begin{exercise}[subtitle={Multiplication de fractions}, step={4}, origin={Création}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\searchMode}]
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Faire les calculs suivants
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\begin{multicols}{4}
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\begin{enumerate}[label={\Alph*=}]
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\item $\dfrac{7}{8} \times \dfrac{- 10}{8}$
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\item $B = \dfrac{3}{10} \times \dfrac{7}{10}$
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\item $\dfrac{3}{4} \times \dfrac{9}{12}$
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\item $\dfrac{2}{30} \times \dfrac{4}{10}$
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\item $\dfrac{9}{3} \times \dfrac{9}{7}$
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\item $\dfrac{5}{4} \times \dfrac{3}{7}$
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\item $\dfrac{1}{a} \times \dfrac{1}{2a}$
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\item $\dfrac{3}{5a} \times \dfrac{1}{4a}$
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\end{enumerate}
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\end{multicols}
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\end{exercise}
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\begin{solution}
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\begin{enumerate}[label={\Alph*=}]
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\item $\dfrac{7}{8} \times \dfrac{- 10}{8}=\dfrac{7(- 10)}{8 \times 8}=\dfrac{- 70}{64} = \dfrac{- 35}{32}$
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\item $\dfrac{3}{10} \times \dfrac{7}{10}=\dfrac{3 \times 7}{10 \times 10}=\dfrac{21}{100} = \dfrac{21}{100}$
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\item $\dfrac{3}{4} \times \dfrac{9}{12}=\dfrac{3 \times 9}{4 \times 12}=\dfrac{27}{48} = \dfrac{9}{16}$
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\item $\dfrac{2}{30} \times \dfrac{4}{10}=\dfrac{2 \times 4}{30 \times 10}=\dfrac{8}{300} = \dfrac{2}{75}$
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\item $\dfrac{9}{3} \times \dfrac{9}{7}=\dfrac{9 \times 9}{3 \times 7}=\dfrac{81}{21} = \dfrac{27}{7}$
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\item $\dfrac{7}{8} \times \dfrac{- 10}{8}=\dfrac{7(- 10)}{8 \times 8}=\dfrac{- 70}{64} = \dfrac{- 35}{32}$
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\item $\dfrac{1}{a} \times \dfrac{1}{2a} = \dfrac{1\times 1}{a\times 2a} = \dfrac{1}{2a^2}$
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\item $\dfrac{3}{5a} \times \dfrac{1}{4a} = \dfrac{3\times 1}{5a\times 4a} = \dfrac{3}{20a^2}$
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\end{enumerate}
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\end{solution}
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