a: \(\dfrac{3}{5}+\left|-\dfrac{5}{3}\right|-\dfrac{-1}{2}+\dfrac{1}{-4}\)
\(=\dfrac{3}{5}+\dfrac{5}{3}+\dfrac{1}{2}-\dfrac{1}{4}\)
\(=\dfrac{9+25}{15}+\dfrac{1}{4}=\dfrac{34}{15}+\dfrac{1}{4}=\dfrac{136}{60}+\dfrac{15}{60}=\dfrac{151}{60}\)
b: \(1\dfrac{3}{5}-\left|\dfrac{5}{2}\right|+\dfrac{-1}{4}+\dfrac{1}{8}\)
\(=\dfrac{8}{5}-\dfrac{5}{2}-\dfrac{1}{4}+\dfrac{1}{8}\)
\(=\dfrac{8}{5}-\dfrac{20}{8}-\dfrac{2}{8}+\dfrac{1}{8}=\dfrac{8}{5}-\dfrac{21}{8}=\dfrac{64-105}{40}=\dfrac{-41}{40}\)
c: \(\dfrac{1}{5}+\left|-\dfrac{5}{2}\right|-\dfrac{-1}{2}+\dfrac{-1}{4}\)
\(=\dfrac{1}{5}-\dfrac{1}{4}+\dfrac{5}{2}+\dfrac{1}{2}\)
\(=-\dfrac{1}{20}+3=\dfrac{59}{20}\)
d: \(\left|\dfrac{5}{-4}\right|-\left|\dfrac{1}{-3}\right|+\dfrac{-5}{6}-4\dfrac{1}{2}\)
\(=\dfrac{5}{4}-\dfrac{1}{3}-\dfrac{5}{6}-\dfrac{9}{2}\)
\(=\dfrac{15}{12}-\dfrac{4}{12}-\dfrac{10}{12}-\dfrac{54}{12}=\dfrac{-53}{12}\)
e: \(\dfrac{5}{8}-\left|-\dfrac{1}{12}\right|-3\dfrac{1}{4}+\left|-\dfrac{5}{6}\right|\)
\(=\dfrac{5}{8}-\dfrac{1}{12}-\dfrac{13}{4}+\dfrac{5}{6}\)
\(=\dfrac{15}{24}-\dfrac{2}{24}-\dfrac{78}{24}+\dfrac{20}{24}\)
\(=\dfrac{-45}{24}=-\dfrac{15}{8}\)
f: \(\dfrac{3}{-7}+\left|-\dfrac{5}{12}\right|+3\dfrac{1}{4}+\left|-\dfrac{5}{6}\right|\)
\(=-\dfrac{3}{7}+\dfrac{5}{12}+\dfrac{13}{4}+\dfrac{5}{6}\)
\(=-\dfrac{3}{7}+\dfrac{5}{12}+\dfrac{39}{12}+\dfrac{10}{12}\)
\(=-\dfrac{3}{7}+\dfrac{54}{12}=-\dfrac{3}{7}+\dfrac{9}{2}=\dfrac{-6}{14}+\dfrac{63}{14}=\dfrac{57}{14}\)
g: \(1\dfrac{3}{5}-\left|\dfrac{1}{-4}\right|+\dfrac{2}{-3}-\left|-\dfrac{1}{2}\right|\)
\(=\dfrac{8}{5}-\dfrac{5}{4}-\dfrac{2}{3}-\dfrac{1}{2}\)
\(=\dfrac{96}{60}-\dfrac{75}{60}-\dfrac{40}{60}-\dfrac{30}{60}=-\dfrac{49}{60}\)
h: \(2\dfrac{1}{3}-\left|-\dfrac{5}{6}\right|+1\dfrac{5}{12}-\left|-\dfrac{7}{2}\right|\)
\(=\dfrac{7}{3}-\dfrac{5}{6}+\dfrac{17}{12}-\dfrac{7}{2}\)
\(=\dfrac{28}{12}-\dfrac{10}{12}+\dfrac{17}{12}-\dfrac{42}{12}=-\dfrac{7}{12}\)
i: \(2\dfrac{3}{4}-5\dfrac{1}{3}+\left|\dfrac{11}{-6}\right|+\dfrac{13}{-12}\)
\(=\dfrac{11}{4}-\dfrac{16}{3}+\dfrac{11}{6}-\dfrac{13}{12}\)
\(=\dfrac{33}{12}-\dfrac{64}{12}+\dfrac{22}{12}-\dfrac{13}{12}=-\dfrac{22}{12}=-\dfrac{11}{6}\)