\(A=4\frac{1}{3}+\left(\frac{-1}{3}\right)^2-\frac{\sqrt{100}}{15}-\frac{7}{9}\)
\(=\frac{13}{3}+\frac{1}{9}-\frac{10}{15}-\frac{7}{9}\)
\(=\left(\frac{1}{9}-\frac{7}{9}\right)+\left(\frac{13}{3}-\frac{10}{15}\right)=\frac{-6}{9}+\frac{55}{15}=-\frac{2}{3}+\frac{11}{3}=\frac{9}{3}=3\)