\(a,\frac{5}{7}+\frac{7}{13}+\frac{19}{13}+\frac{6}{5}+\frac{9}{7}+\frac{9}{5}.\)
\(=\left(\frac{5}{7}+\frac{9}{7}\right)+\left(\frac{7}{13}+\frac{19}{13}\right)+\left(\frac{6}{5}+\frac{9}{5}\right)\)
\(=\frac{14}{7}+\frac{26}{13}+\frac{15}{5}=2+2+3=7\)
\(b,\frac{1}{10}+\frac{20}{100}+\frac{300}{1000}+\frac{4000}{10000}\)
\(=\frac{1}{10}+\frac{2}{10}+\frac{3}{10}+\frac{4}{10}=\frac{1+2+3+4}{10}=\frac{10}{10}=1\)