Correction exercice Préparer l'avaluation

$\begin{array}{l}
\mathrm{J}=\left(\dfrac{1}{8}-\dfrac{7}{12}\right) \div\left(\dfrac{7}{6}+\dfrac{7}{16}\right) \\
\mathrm{J}=\left(\dfrac{6}{48}-\dfrac{28}{48}\right) \div\left(\dfrac{56}{48}+\dfrac{21}{48}\right) \\
\mathrm{J}=\left(\dfrac{-22}{48}\right) \div\left(\dfrac{77}{48}\right)=\left(\dfrac{-22}{48}\right) \times\left(\dfrac{48}{77}\right) \\
\mathrm{J}=\dfrac{-22}{77}\\
\mathrm{J}=\dfrac{-2}{7}\\
&\\
M=\dfrac{\dfrac{1}{8}+\dfrac{7}{12}}{\dfrac{5}{6}-\dfrac{4}{15}}=\dfrac{\dfrac{6}{48}+\dfrac{28}{48}}{\dfrac{25}{30}-\dfrac{8}{30}} \\
M=\dfrac{34}{48} \div \dfrac{17}{30}=\dfrac{34}{48} \times \dfrac{30}{17} \\
M=\dfrac{2 \times 17}{6 \times 2 \times 4} \times \dfrac{6 \times 5}{17}\\
M=\dfrac{5}{4}\\
&\\
&\\
\mathrm{K}=\dfrac{1}{8}-\dfrac{7}{12} \div \dfrac{7}{6}+\dfrac{7}{12} \\
\mathrm{K}=\dfrac{1}{8}-\dfrac{1}{2}+\dfrac{7}{12} \\
\mathrm{K}=\dfrac{3}{24}-\dfrac{12}{24}+\dfrac{14}{24} \\
\mathrm{K}=\dfrac{5}{24}\\
&\\
\mathrm{N}=\dfrac{\dfrac{5}{3}-\dfrac{7}{9}}{\dfrac{1}{4}-\dfrac{1}{2}}=\dfrac{\dfrac{15}{9}-\dfrac{7}{9}}{\dfrac{1}{4}-\dfrac{2}{4}} \\
\mathrm{N}=\dfrac{8}{9} \div \dfrac{-1}{4}=\dfrac{8}{9} \times \dfrac{-4}{1} \\
\mathrm{N}=\dfrac{-32}{9}\\
&\\
\mathrm{L}=\left(\dfrac{1}{8}+\dfrac{7}{12}\right) \times\left(\dfrac{6}{5} \div \dfrac{4}{15}\right) \\
\mathrm{L}=\left(\dfrac{3}{24}+\dfrac{14}{24}\right) \times\left(\dfrac{18}{15} \div \dfrac{4}{15}\right) \\
\mathrm{L}=\dfrac{17}{4 \times 6} \times\left(\dfrac{3 \times 6}{4}\right) \\
\mathrm{L}=\dfrac{51}{16}
\end{array}$
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