a) \(A=\dfrac{5}{13}+\dfrac{-5}{17}+\dfrac{-21}{41}+\dfrac{8}{13}+\dfrac{-20}{41}\)
\(A=\left(\dfrac{5}{13}+\dfrac{8}{13}\right)+\left(\dfrac{-21}{41}+\dfrac{-20}{41}\right)+\dfrac{-5}{17}\)
\(A=\dfrac{13}{13}+\dfrac{-41}{41}+\dfrac{-5}{17}\)
\(A=1-1+\dfrac{-5}{17}\)
\(A=\dfrac{-5}{17}\)
b) \(B=\dfrac{4}{9}+\dfrac{23}{37}-\dfrac{22}{9}+\dfrac{14}{37}+1\)
\(B=\left(\dfrac{4}{9}-\dfrac{22}{9}\right)+\left(\dfrac{23}{37}+\dfrac{14}{37}\right)+1\)
\(B=\dfrac{-18}{9}+\dfrac{37}{37}+1\)
\(B=-2+1+1\)
\(B=0\)
c) \(C=\dfrac{11}{15}\cdot\dfrac{12}{13}-\dfrac{7}{30}+\dfrac{11}{15}\cdot\dfrac{14}{13}\)
\(C=\dfrac{11}{15}\cdot\left(\dfrac{12}{13}+\dfrac{14}{13}\right)-\dfrac{7}{30}\)
\(C=\dfrac{11}{15}\cdot\dfrac{26}{13}-\dfrac{7}{30}\)
\(C=\dfrac{11}{15}\cdot2-\dfrac{7}{30}\)
\(C=\dfrac{22}{15}-\dfrac{7}{30}\)
\(C=\dfrac{37}{30}\)
d) \(D=\dfrac{27}{13}:\dfrac{9}{7}+\dfrac{12}{13}:\dfrac{9}{7}\)
\(D=\left(\dfrac{27}{13}+\dfrac{12}{13}\right):\dfrac{9}{7}\)
\(D=\dfrac{39}{13}:\dfrac{9}{7}\)
\(D=3\cdot\dfrac{7}{9}\)
\(D=\dfrac{3\cdot7}{9}\)
\(D=\dfrac{7}{3}\)
