help me
1: \(\dfrac{-5}{17}\cdot\dfrac{31}{33}+\dfrac{-5}{17}\cdot\dfrac{2}{33}+1\dfrac{5}{17}\)
\(=-\dfrac{5}{17}\left(\dfrac{31}{33}+\dfrac{2}{33}\right)+1+\dfrac{5}{17}\)
\(=-\dfrac{5}{17}+1+\dfrac{5}{17}\)
=1
2: \(\dfrac{5}{7}\cdot\dfrac{-3}{11}+\dfrac{5}{7}\cdot\dfrac{-8}{11}+2\dfrac{5}{7}\)
\(=\dfrac{5}{7}\left(-\dfrac{3}{11}-\dfrac{8}{11}\right)+2+\dfrac{5}{7}\)
\(=-\dfrac{5}{7}+2+\dfrac{5}{7}\)
=2
3: \(\dfrac{9}{10}\cdot\dfrac{23}{11}-\dfrac{1}{11}\cdot\dfrac{9}{10}+\dfrac{9}{10}\)
\(=\dfrac{9}{10}\left(\dfrac{23}{11}-\dfrac{1}{11}+1\right)\)
\(=\dfrac{9}{10}\left(\dfrac{22}{11}+1\right)=\dfrac{9}{10}\cdot3=\dfrac{27}{10}\)
4: \(\dfrac{5}{4}\cdot\dfrac{8}{15}+\dfrac{-5}{16}\cdot\dfrac{8}{15}-1\)
\(=\dfrac{8}{15}\left(\dfrac{5}{4}-\dfrac{5}{16}\right)-1\)
\(=\dfrac{8}{15}\cdot\left(\dfrac{20}{16}-\dfrac{5}{16}\right)-1\)
\(=\dfrac{8}{15}\cdot\dfrac{15}{16}-1=\dfrac{8}{16}-1=-\dfrac{8}{16}=-\dfrac{1}{2}\)
5: \(\dfrac{-19}{3}\cdot\dfrac{14}{4}+\dfrac{25}{4}\cdot\dfrac{-19}{3}+4\dfrac{3}{4}\)
\(=-\dfrac{19}{4}\left(\dfrac{14}{3}+\dfrac{25}{3}\right)+\dfrac{19}{4}\)
\(=-\dfrac{19}{4}\cdot13+\dfrac{19}{4}=-\dfrac{19}{4}\left(13-1\right)=-\dfrac{19}{4}\cdot12=-19\cdot3=-57\)
6: \(\dfrac{1}{27}\cdot\dfrac{-3}{7}-\dfrac{5}{9}\cdot\dfrac{-3}{7}+\dfrac{1}{9}\)
\(=\dfrac{-1}{9}\cdot\dfrac{3}{7}+\dfrac{15}{63}+\dfrac{1}{9}\)
\(=\dfrac{-3}{63}+\dfrac{15}{63}+\dfrac{7}{63}=\dfrac{15+7-3}{63}=\dfrac{19}{63}\)
