exo47.tex

%@P:exocorcp
%@Dif:3
Calcule astucieusement les produits suivants :
\[\Eqalign{
A&=0,2\times43,57\times5\kern5mm&B&=0,25\times4,5\times4\kern5mm&C&=4\times3,5\times0,5\times2,5\kern5mm&D&=1,25\times7\times8\times0,6\cr
}\]
%@Correction:
\[\Eqalign{
A&=\rnode{A1}{0,2}\times43,57\times\rnode{B1}{5}\kern5mm&B&=\rnode{A2}{0,25}\times4,5\times\rnode{B2}{4}\kern5mm&C&=\rnode{A3}{4}\times3,5\times0,5\times\rnode{B3}{2,5}\kern5mm&D&=\rnode{A4}{1,25}\times7\times\rnode{B4}{8}\times0,6\cr
\cr
A&=\rnode{C1}{1}\times43,57&B&=\rnode{C2}{1}\times4,5&C&=\rnode{C3}{10}\times\rnode{D3}{3,5}\times0,5&D&=\rnode{C4}{10}\times7\times\rnode{D4}{0,6}\cr
\cr
A&=43,57&B&=4,5&C&=\rnode{E3}{35}\times0,5&D&=\rnode{E4}{6}\times7\cr
\cr
&&&&C&=17,5&D&=42\cr
}\]
\ncline[linecolor=gray,nodesep=1mm]{->}{A1}{C1}
\ncline[linecolor=gray]{->}{B1}{C1}
\ncline[linecolor=gray,nodesep=1mm]{->}{A2}{C2}
\ncline[linecolor=gray]{->}{B2}{C2}
\ncline[linecolor=gray,nodesep=1mm]{->}{A3}{C3}
\ncline[linecolor=gray]{->}{B3}{C3}
\ncline[linecolor=gray,nodesep=1mm]{->}{C3}{E3}
\ncline[linecolor=gray]{->}{D3}{E3}
\ncline[linecolor=gray,nodesep=1mm]{->}{A4}{C4}
\ncline[linecolor=gray]{->}{B4}{C4}
\ncline[linecolor=gray,nodesep=1mm]{->}{C4}{E4}
\ncline[linecolor=gray]{->}{D4}{E4}