\(a,\dfrac{-1}{7}+\dfrac{8}{13}+\dfrac{-6}{7}-1\dfrac{23}{24}-\dfrac{-5}{13}\\ =\dfrac{-1}{7}+\dfrac{8}{13}+\dfrac{-6}{7}-\dfrac{47}{24}+\dfrac{5}{13}\\ =\left(\dfrac{-1}{7}+\dfrac{-6}{7}\right)+\left(\dfrac{8}{13}+\dfrac{5}{13}\right)-\dfrac{47}{24}\\ =-1+1-\dfrac{47}{24}\\ =0-\dfrac{47}{24}\\ =\dfrac{-47}{24}\)

\(b,\left(7\dfrac{4}{9}+4\dfrac{7}{11}\right)-3\dfrac{4}{9}\\ =7\dfrac{4}{9}+4\dfrac{7}{11}-3\dfrac{4}{9}\\ =\left(7\dfrac{4}{9}-3\dfrac{4}{9}\right)+4\dfrac{7}{11}\\ =4+4\dfrac{7}{11}\\ =\dfrac{44}{11}+\dfrac{51}{11}\\ =\dfrac{95}{11}\)

\(\dfrac{3}{5}\times x+2+40=53\\ \rightarrow\dfrac{3}{5}\times x+2=53-40\\ \rightarrow\dfrac{3}{5}\times x+2=13\\ \rightarrow\dfrac{3}{5}\times x=13-2\\ \rightarrow\dfrac{3}{5}\times x=11\\ \rightarrow x=11:\dfrac{3}{5}\\ \rightarrow x=11\times\dfrac{5}{3}\\ \rightarrow x=\dfrac{55}{3}\)

\(e,\dfrac{-5}{9}+\dfrac{11}{36}-\dfrac{-7}{18}=\dfrac{-5}{9}+\dfrac{11}{36}+\dfrac{7}{18}=\dfrac{-20}{36}+\dfrac{11}{36}+\dfrac{14}{36}=\dfrac{-20+11+14}{36}=\dfrac{5}{36}\\ f,\dfrac{-2}{3}\times\dfrac{4}{5}+\dfrac{1}{5}:\dfrac{9}{11}=\dfrac{-8}{15}+\dfrac{1}{5}:\dfrac{9}{11}=\dfrac{-8}{15}+\dfrac{1}{5}\times\dfrac{11}{9}=\dfrac{-8}{15}+\dfrac{11}{45}=\dfrac{-24}{45}+\dfrac{11}{45}=\dfrac{-13}{45}\)

\(\dfrac{-15}{4}-\dfrac{6}{17}+\dfrac{15}{4}=\left(\dfrac{-15}{4}+\dfrac{15}{4}\right)-\dfrac{6}{7}=0-\dfrac{6}{7}=\dfrac{-6}{7}\)

\(a,-9,9;-9,825;0;1,85;5,36;8,5\\ b,-9,35;-8,58;-4;0,19;\dfrac{-5}{-4};3,75\)