Ответ:

\(2\frac29=\frac{20}{9}\), \(0.9=\frac9{10}\), \(-2\frac13=-\frac73\).

\(\frac{20}{9}+\frac9{10}\cdot\left(-\frac73\right)=\frac{20}{9}-\frac{21}{10}=\frac{200-189}{90}=\frac{11}{90}\).

Ответ: \(\frac{11}{90}\).