\(\frac{4}{9}\cdot\frac{7}{15}+\frac{31}{30}\cdot\frac{11}{18}+\frac{4}{9}\cdot\frac{8}{15}-\frac{11}{18}\cdot\frac{1}{30}\)
\(=\frac{4}{9}.\left(\frac{7}{15}+\frac{8}{15}\right)+\frac{11}{18}.\left(\frac{31}{30}-\frac{1}{30}\right)\)
\(=\frac{4}{9}+\frac{11}{18}=\frac{8}{18}+\frac{11}{18}=\frac{19}{18}\)