\(\frac{4}{7}\times\frac{5}{6}+\frac{4}{7}\times\frac{1}{6}\)
\(=\frac{4}{7}\times\left(\frac{5}{6}+\frac{1}{6}\right)\)
\(=\frac{4}{7}\times1\)
\(=\frac{4}{7}\)
\(\frac{7}{9}\times\frac{8}{5}-\frac{7}{9}\times\frac{3}{5}\)
\(=\frac{7}{9}\times\left(\frac{8}{5}-\frac{3}{5}\right)\)
\(=\frac{7}{9}\times1\)
\(=\frac{7}{9}\)
\(\frac{3}{5}\times\frac{7}{9}-\frac{3}{5}\times\frac{2}{9}\)
\(=\frac{3}{5}\times\left(\frac{7}{9}-\frac{2}{9}\right)\)
\(=\frac{3}{5}\times\frac{5}{9}\)
\(=\frac{1}{3}\)
\(\frac{2}{5}\times\frac{3}{4}\times\frac{3}{5}=\frac{3}{10}\times\frac{3}{5}=\frac{9}{50}\)
\(\frac{5}{9}\times\frac{1}{4}+\frac{4}{9}\times\frac{3}{12}\)
\(=\frac{5}{9}\times\frac{1}{4}+\frac{4}{9}\times\frac{1}{4}\)
\(=\frac{1}{4}\times\left(\frac{5}{9}+\frac{4}{9}\right)\)
\(=\frac{1}{4}\times1\)
\(=\frac{1}{4}\)
\(\frac{2006}{2005}\times\frac{3}{4}-\frac{3}{4}\times\frac{1}{2005}\)
\(=\frac{3}{4}\times\left(\frac{2006}{2005}-\frac{1}{2005}\right)\)
\(=\frac{3}{4}\times1\)
\(=\frac{3}{4}\)
