a) \(\dfrac{1}{3}-\dfrac{2}{5}\)
\(=\dfrac{5}{15}-\dfrac{6}{15}\)
\(=\dfrac{-1}{15}\)
b) \(\left(5\dfrac{2}{3}-2\right)-\dfrac{2}{3}\)
\(=\left(5+\dfrac{2}{3}-2\right)-\dfrac{2}{3}\)
\(=3+\dfrac{2}{3}-\dfrac{2}{3}\)
\(=3\)
c) \(\left(\dfrac{2}{5}-1\right)+\left(\dfrac{4}{3}-\dfrac{2}{5}\right)\)
\(=\dfrac{2}{5}-1+\dfrac{4}{3}-\dfrac{2}{5}\)
\(=\left(\dfrac{4}{3}-1\right)+\left(\dfrac{2}{5}-\dfrac{2}{5}\right)\)
\(=\dfrac{1}{3}\)
d) \(\left(1\dfrac{8}{9}+\dfrac{3}{4}\right)-\left(\dfrac{1}{4}-\dfrac{1}{9}\right)\)
\(=\left(1+\dfrac{8}{9}+\dfrac{3}{4}\right)-\left(\dfrac{1}{4}-\dfrac{1}{9}\right)\)
\(=1+\dfrac{8}{9}+\dfrac{3}{4}-\dfrac{1}{4}+\dfrac{1}{9}\)
\(=1+\left(\dfrac{8}{9}+\dfrac{1}{9}\right)+\left(\dfrac{3}{4}-\dfrac{1}{4}\right)\)
\(=1+1+\dfrac{2}{4}\)
\(=2+\dfrac{1}{2}\)
\(=\dfrac{5}{2}\)