\(a)\)
\(\dfrac{12}{-21}-\dfrac{-5}{35}+\dfrac{2}{7}\)
\(=\dfrac{-12}{21}+\dfrac{-5}{35}+\dfrac{2}{7}\)
\(=\dfrac{-420}{735}+\dfrac{-105}{735}+\dfrac{2}{7}\)
\(=\dfrac{-5}{7}+\dfrac{2}{7}\)
\(=\dfrac{-3}{7}\)
\(b)\)
\(\dfrac{2}{5}+\dfrac{-1}{6}-\dfrac{3}{4}-\dfrac{-2}{3}\)
\(=\dfrac{12}{30}+\dfrac{-5}{30}-\dfrac{3}{4}-\dfrac{-2}{3}\)
\(=\dfrac{7}{30}-\dfrac{3}{4}-\dfrac{-2}{3}\)
\(=\dfrac{28}{120}-\dfrac{90}{120}-\dfrac{-2}{3}\)
\(=\dfrac{-31}{60}-\dfrac{-2}{3}\)
\(=\dfrac{-31}{60}-\dfrac{-40}{60}\)
\(=\dfrac{3}{20}\)
\(c)\)
\(\dfrac{12}{18}+\dfrac{-16}{48}-\dfrac{8}{12}\)
\(=\dfrac{576}{864}+\dfrac{-288}{864}-\dfrac{8}{12}\)
\(=\dfrac{1}{3}-\dfrac{8}{12}\)
\(=\dfrac{4}{12}-\dfrac{8}{12}\)
\(=\dfrac{-1}{3}\)
\(d)\)
\(\dfrac{7}{10}-\dfrac{-3}{4}+\dfrac{-5}{6}-\dfrac{1}{5}+\dfrac{-2}{3}\)
\(=\dfrac{28}{40}-\dfrac{-30}{40}+\dfrac{-5}{6}-\dfrac{1}{5}+\dfrac{-2}{3}\)
\(=\dfrac{29}{20}+\dfrac{-5}{6}-\dfrac{1}{5}+\dfrac{-2}{3}\)
\(=\dfrac{174}{120}+\dfrac{-100}{120}-\dfrac{1}{5}+\dfrac{-2}{3}\)
\(=\dfrac{37}{60}-\dfrac{1}{5}+\dfrac{-2}{3}\)
\(=\dfrac{37}{60}-\dfrac{12}{60}+\dfrac{-2}{3}\)
\(=\dfrac{5}{12}+\dfrac{-2}{3}\)
\(=\dfrac{5}{12}+\dfrac{-8}{12}\)
\(=\dfrac{-1}{4}\)
