a: \(\dfrac{7}{5}-1\dfrac{1}{20}+\dfrac{4}{7}\)
\(=\dfrac{7}{5}-\dfrac{21}{20}+\dfrac{4}{7}\)
\(=\dfrac{28-21}{20}+\dfrac{4}{7}=\dfrac{7}{20}+\dfrac{4}{7}=\dfrac{49+80}{140}\)
\(=\dfrac{129}{140}\)
b: \(\left(8\dfrac{6}{7}+11\dfrac{2}{3}\right)-7\dfrac{6}{7}\)
\(=8+\dfrac{6}{7}+11+\dfrac{2}{3}-7-\dfrac{6}{7}\)
\(=12+\dfrac{2}{3}=\dfrac{38}{3}\)
c: \(\dfrac{5}{13}+\dfrac{-5}{7}+\dfrac{-20}{41}+\dfrac{8}{13}+\dfrac{-21}{41}\)
\(=\left(\dfrac{5}{13}+\dfrac{8}{13}\right)+\left(-\dfrac{20}{41}-\dfrac{21}{41}\right)-\dfrac{5}{7}\)
\(=0-0-\dfrac{5}{7}=-\dfrac{5}{7}\)
d: \(4\dfrac{6}{7}-\left(1\dfrac{5}{13}-3\dfrac{6}{7}\right)+3\dfrac{5}{13}\)
\(=4+\dfrac{6}{7}-1-\dfrac{5}{13}+3+\dfrac{6}{7}+3+\dfrac{5}{13}\)
\(=9+\dfrac{12}{7}=\dfrac{75}{7}\)
e: \(\left(\dfrac{44}{7}-3\dfrac{5}{9}\right)-\left(5\dfrac{2}{7}+\dfrac{4}{9}\right)\)
\(=\dfrac{44}{7}-3-\dfrac{5}{9}-5-\dfrac{2}{7}-\dfrac{4}{9}\)
\(=\left(\dfrac{44}{7}-\dfrac{2}{7}\right)-\left(3+5\right)-\left(\dfrac{5}{9}+\dfrac{4}{9}\right)\)
=6-8-1
=-3
f: \(\left(-\dfrac{2}{5}+\dfrac{3}{7}\right)-\left(\dfrac{4}{9}+\dfrac{12}{20}-\dfrac{13}{35}\right)+\dfrac{7}{35}\)
\(=\dfrac{-14+15}{35}-\dfrac{4}{9}-\dfrac{3}{5}+\dfrac{13}{35}+\dfrac{7}{35}\)
\(=\dfrac{1}{35}+\dfrac{20}{35}-\dfrac{21}{35}-\dfrac{4}{9}\)
\(=-\dfrac{4}{9}\)
