\(A=\dfrac{1^2}{1.2}\times\dfrac{2^2}{2.3}\times\dfrac{3^2}{3.4}\times\dfrac{4^2}{4.5}\times\dfrac{5^2}{5.6}\\ A=\dfrac{1.2.3.4.5}{1.2.3.4.5}\times\dfrac{1.2.3.4.5}{2.3.4.5.6}\\ A=1\times\dfrac{1}{6}=\dfrac{1}{6}\)

\(a,\dfrac{11}{10}-\dfrac{2}{3}+\dfrac{4}{5}=\dfrac{33-20+24}{30}=\dfrac{37}{30}\\ b,\dfrac{18}{15}+\dfrac{3}{5}-\dfrac{7}{45}=\dfrac{54+27-7}{45}=\dfrac{74}{45}\)

\(\dfrac{-8}{9}\)

\(\dfrac{-7}{9}\)

\(\overline{aaa}:\left(37a\right)+997=\left(100a+10a+a\right):\left(37a\right)+997=111a:\left(37a\right)+997=3+997=1000\)

\(\overline{aa}:\left(37a\right)+997=11a:\left(37a\right)+997=\dfrac{11}{37}+997=997\)\(\dfrac{11}{37}\)

\(\dfrac{26}{81}+\dfrac{4}{27}=\dfrac{26}{81}+\dfrac{4\times3}{27\times3}=\dfrac{26}{81}+\dfrac{12}{81}=\dfrac{38}{81}\)

\(\dfrac{5}{64}+\dfrac{7}{8}=\dfrac{5}{64}+\dfrac{7\times8}{8\times8}=\dfrac{5}{64}+\dfrac{56}{64}=\dfrac{61}{64}\)