`#3107.101107`
`g)`
\(\dfrac{4}{19}\cdot\dfrac{-3}{7}+\dfrac{-3}{7}\cdot\dfrac{15}{19}+\dfrac{5}{7}\)
\(=\dfrac{-3}{7}\left(\dfrac{4}{19}+\dfrac{15}{19}\right)+\dfrac{5}{7}\)
\(=\dfrac{-3}{7}\cdot1+\dfrac{5}{7}\)
\(=-\dfrac{3}{7}+\dfrac{5}{7}=\dfrac{2}{7}\)
`h)`
\(\dfrac{5}{9}\cdot\dfrac{7}{13}+\dfrac{5}{9}\cdot\dfrac{9}{13}-\dfrac{5}{9}\cdot\dfrac{3}{13}\)
\(=\dfrac{5}{9}\cdot\left(\dfrac{7}{13}+\dfrac{9}{13}-\dfrac{3}{13}\right)\)
\(=\dfrac{5}{9}\cdot\left(\dfrac{7+9-3}{13}\right)\)
\(=\dfrac{5}{9}\cdot1=\dfrac{5}{9}\)
`i)`
\(\left(\dfrac{-4}{5}+\dfrac{4}{3}\right)+\left(\dfrac{-5}{4}+\dfrac{14}{5}\right)-\dfrac{7}{3}\)
\(=\dfrac{-4}{5}+\dfrac{4}{3}+\dfrac{-5}{4}+\dfrac{14}{5}-\dfrac{7}{3}\)
\(=\left(-\dfrac{4}{5}+\dfrac{14}{5}\right)+\left(\dfrac{4}{3}-\dfrac{7}{3}\right)-\dfrac{5}{4}\)
\(=\dfrac{10}{5}+\dfrac{-3}{3}-\dfrac{5}{4}\)
\(=2-1-\dfrac{5}{4}\)
\(=1-\dfrac{5}{4}\)
\(=-\dfrac{1}{4}\)
`j)`
\(\dfrac{8}{3}\cdot\dfrac{2}{5}\cdot\dfrac{3}{8}\cdot10\cdot\dfrac{19}{92}\)
\(=\left(\dfrac{8}{3}\cdot\dfrac{3}{8}\right)\cdot\left(\dfrac{2}{5}\cdot10\right)\cdot\dfrac{19}{92}\)
\(=1\cdot\dfrac{20}{5}\cdot\dfrac{19}{92}\)
\(=4\cdot\dfrac{19}{92}=\dfrac{19}{23}\)
`k)`
\(\dfrac{-5}{7}\cdot\dfrac{2}{11}+\dfrac{-5}{7}\cdot\dfrac{9}{14}+1\dfrac{5}{7}\)
\(=-\dfrac{5}{7}\cdot\dfrac{2}{11}-\dfrac{5}{7}\cdot\dfrac{9}{14}+1+\dfrac{5}{7}\)
\(=\dfrac{5}{7}\cdot\left(-\dfrac{2}{11}-\dfrac{9}{14}+1\right)+1\)
\(=\dfrac{5}{7}\cdot\dfrac{27}{154}+1\)
\(=\dfrac{135}{1078}+1=\dfrac{1213}{1078}\)
`l)`
\(\dfrac{12}{19}\cdot\dfrac{7}{15}\cdot\dfrac{-13}{17}\cdot\dfrac{19}{12}\cdot\dfrac{17}{13}\)
\(=\left(\dfrac{12}{19}\cdot\dfrac{19}{12}\right)\cdot\left(-\dfrac{13}{17}\cdot\dfrac{17}{13}\right)\cdot\dfrac{7}{15}\)
\(=1\cdot\left(-1\right)\cdot\dfrac{7}{15}=-\dfrac{7}{15}\)