a: \(\frac29-\left(\frac12\right)^2+\frac{5}{18}\)

\(=\frac29-\frac14+\frac{5}{18}\)

\(=\frac{8}{36}-\frac{9}{36}+\frac{10}{36}=\frac{9}{36}=\frac14\)

b: \(17\frac13\cdot\left(-\frac57\right)-10\frac13\cdot\left(-\frac57\right)-\frac27\)

\(=\left(17+\frac13-10-\frac13\right)\cdot\left(-\frac57\right)-\frac27\)

\(=7\cdot\left(-\frac57\right)-\frac27=-5-\frac27=-\frac{37}{7}\)

c: \(-\frac{5}{17}\cdot\frac{31}{33}+\frac{-5}{17}\cdot\frac{2}{33}+2\frac{5}{17}\)

\(=-\frac{5}{17}\left(\frac{31}{33}+\frac{2}{33}\right)+2+\frac{5}{17}\)

\(=-\frac{5}{17}+2+\frac{5}{17}=2\)

d: \(-\frac{15}{4}\left(\frac{7}{10}-\frac35\right)\)

\(=-\frac{15}{4}\left(\frac{7}{10}-\frac{6}{10}\right)=-\frac{15}{4}\cdot\frac{1}{10}=-\frac{15}{40}=-\frac38\)

e: \(\frac{-22}{17}\cdot\frac{23}{33}+\frac{-22}{17}\cdot\frac{10}{33}+2\frac{5}{17}\)

\(=-\frac{22}{17}\left(\frac{23}{33}+\frac{10}{33}\right)+2+\frac{5}{17}\)

\(=-\frac{22}{17}+2+\frac{5}{17}=-1+2=1\)

f: \(-\frac83\cdot\frac{2}{11}-\frac83:\frac{11}{9}-\frac53\)

\(=-\frac83\cdot\frac{2}{11}-\frac83\cdot\frac{9}{11}-\frac53=-\frac83\left(\frac{2}{11}+\frac{9}{11}\right)-\frac53\)

\(=-\frac83-\frac53=-\frac{13}{3}\)

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