a) \(2\frac{7}{21}+4\frac{5}{23}+1\frac{18}{23}\)
\(=\left(2+4+1\right)+\left(\frac{7}{21}+\frac{5}{23}+\frac{18}{23}\right)\)
\(=7+1\frac{1}{3}=8\frac{1}{3}\)
b) \(\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}+\frac{1}{8\times9}\)
=\(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)
=\(\frac{1}{5}-\frac{1}{9}=\frac{4}{45}\)