\(9\frac{2}{9}+\frac{2}{3}+7\frac{7}{9}=\left(9\frac{2}{9}+7\frac{7}{9}\right)+\frac{2}{3}\)
= 16\(\frac{9}{9}+\frac{2}{3}\)
= 17 + \(\frac{2}{3}=\frac{51}{3}+\frac{2}{3}=\frac{53}{3}\)
\(9\frac{2}{9}+\frac{2}{3}+7\frac{7}{9}=\frac{83}{9}+\frac{2}{3}+\frac{70}{9}\)
\(=\left(\frac{83}{9}+\frac{70}{9}\right)+\frac{2}{3}=17+\frac{2}{3}\)
\(=\frac{17\cdot3+2}{3}=\frac{53}{3}\)