1: \(\dfrac{3}{4}+\dfrac{-7}{12}-\dfrac{2}{3}=\dfrac{9}{12}-\dfrac{7}{12}-\dfrac{8}{12}=-\dfrac{6}{12}=-\dfrac{1}{2}\)
2: \(\dfrac{1}{3}+\dfrac{3}{4}-\dfrac{7}{18}=\dfrac{12}{36}+\dfrac{27}{36}-\dfrac{14}{36}=\dfrac{25}{36}\)
3: \(\dfrac{4}{5}+\dfrac{2}{7}-\dfrac{7}{10}=\dfrac{1}{10}+\dfrac{2}{7}=\dfrac{7}{70}+\dfrac{20}{70}=\dfrac{27}{70}\)
4: \(-\dfrac{4}{5}+\dfrac{1}{4}-\dfrac{7}{2}\)
\(=-\dfrac{16}{20}+\dfrac{5}{20}-\dfrac{70}{20}=\dfrac{-81}{20}\)
5: \(\dfrac{2}{3}-\dfrac{5}{6}+\dfrac{1}{12}\)
\(=\dfrac{8}{12}-\dfrac{10}{12}+\dfrac{1}{12}=-\dfrac{1}{12}\)
6: \(\dfrac{5}{6}+\dfrac{2}{9}-\dfrac{9}{18}\)
\(=\dfrac{15}{18}+\dfrac{4}{18}-\dfrac{9}{18}=\dfrac{10}{18}=\dfrac{5}{9}\)
7: \(\dfrac{7}{12}+\dfrac{3}{8}-\dfrac{1}{4}\)
\(=\dfrac{14}{24}+\dfrac{9}{24}-\dfrac{6}{24}\)
\(=\dfrac{17}{24}\)
8: \(-\dfrac{1}{6}+\left(-\dfrac{2}{5}\right)-\dfrac{1}{2}\)
\(=-\dfrac{5}{30}-\dfrac{12}{30}-\dfrac{15}{30}\)
\(=-\dfrac{32}{30}=-\dfrac{16}{15}\)
9: \(\dfrac{5}{6}+\dfrac{3}{8}-\dfrac{11}{24}\)
\(=\dfrac{20}{24}+\dfrac{9}{24}-\dfrac{11}{24}=\dfrac{18}{24}=\dfrac{3}{4}\)
10: \(\dfrac{3}{4}+\dfrac{-7}{12}-\dfrac{2}{3}=\dfrac{9}{12}-\dfrac{7}{12}-\dfrac{8}{12}=-\dfrac{6}{12}=-\dfrac{1}{2}\)
11: \(3-\left[\dfrac{1}{2}+\left(\dfrac{3}{5}-\dfrac{1}{10}\right)\right]\)
\(=3-\left[\dfrac{1}{2}+\left(\dfrac{6}{10}-\dfrac{1}{10}\right)\right]\)
\(=3-\left[\dfrac{1}{2}+\dfrac{1}{2}\right]=3-1=2\)
12: \(\dfrac{19}{23}+\dfrac{28}{17}+\dfrac{4}{23}-\dfrac{11}{17}\)
\(=\left(\dfrac{19}{23}+\dfrac{4}{23}\right)+\left(\dfrac{28}{17}-\dfrac{11}{17}\right)\)
\(=\dfrac{23}{23}+\dfrac{17}{17}=1+1=2\)
13) \(2\dfrac{2}{3}-1\dfrac{2}{5}+1\dfrac{3}{10}-\left(\dfrac{2}{5}-\dfrac{5}{6}\right)+\dfrac{4}{15}-1\dfrac{1}{3}\)
= \(\dfrac{8}{3}-\dfrac{7}{5}+\dfrac{13}{10}-\left(\dfrac{12}{30}-\dfrac{25}{30}\right)+\dfrac{4}{15}-\dfrac{4}{3}\)
= \(\dfrac{8}{3}-\dfrac{7}{5}+\dfrac{13}{10}-\dfrac{-13}{30}+\dfrac{4}{15}-\dfrac{4}{3}\)
= \(\dfrac{80}{30}-\dfrac{42}{30}+\dfrac{39}{30}+\dfrac{13}{30}+\dfrac{8}{30}-\dfrac{40}{30}\)
= \(\dfrac{80-42+39+13+8-40}{30}\)
= \(\dfrac{58}{30}=\dfrac{29}{15}\)
