a. \(\dfrac{3}{4}\) + \(\dfrac{-4}{5}\) - \(\dfrac{1}{2}\) = \(\dfrac{-1}{20}\) - \(\dfrac{1}{2}\) = \(\dfrac{-11}{20}\)
b. (4 - \(\dfrac{5}{12}\) ): 2 + \(\dfrac{5}{24}\)
= \(\dfrac{43}{12}\) : 2 + \(\dfrac{5}{24}\)
= \(\dfrac{43}{24}\) + \(\dfrac{5}{24}\)
=\(\dfrac{48}{24}\) = 2
2.2
\(\dfrac{4}{7}\) .x - \(\dfrac{2}{3}\) = \(\dfrac{1}{5}\)
\(\dfrac{4}{7}\) x = \(\dfrac{1}{5}\) + \(\dfrac{2}{3}\)
\(\dfrac{4}{7}\) . x = \(\dfrac{13}{15}\)
x = \(\dfrac{91}{60}\)
2.1
\(a)\dfrac{3}{4}+\dfrac{-4}{5}-\dfrac{1}{2}\\ =\dfrac{3\times5}{4\times5}+\dfrac{-4\times4}{5\times4}-\dfrac{1\times10}{2\times10}\\ =\dfrac{15}{20}+\dfrac{-16}{20}-\dfrac{10}{20}\\ =\dfrac{15-16-10}{20}\\ =\dfrac{-11}{20}\)
\(b)\left(4-\dfrac{5}{12}\right):2+\dfrac{5}{24}\\ =\left(\dfrac{4\times12}{1\times12}-\dfrac{5}{12}\right):2+\dfrac{5}{24}\\ =\left(\dfrac{48}{12}-\dfrac{5}{12}\right):2+\dfrac{5}{24}\\ =\left(\dfrac{48-5}{12}\right):2+\dfrac{5}{24}\\ =\dfrac{43}{12}:2+\dfrac{5}{24}\\ =\dfrac{43}{12}\times\dfrac{1}{2}+\dfrac{5}{24}\\ =\dfrac{43}{24}+\dfrac{5}{24}\\ =\dfrac{43+5}{24}\\ =\dfrac{48}{24}\\ =2\)
\(2.2\\ \dfrac{4}{7}\times x-\dfrac{2}{3}=\dfrac{1}{5}\\ \dfrac{4}{7}\times x=\dfrac{1}{5}+\dfrac{2}{3}\\ \dfrac{4}{7}\times x=\dfrac{1\times3}{5\times3}+\dfrac{2\times5}{3\times5}\\ \dfrac{4}{7}\times x=\dfrac{3}{15}+\dfrac{10}{15}\\ \dfrac{4}{7}\times x=\dfrac{13}{15}\\ x=\dfrac{13}{15}:\dfrac{4}{7}\\ x=\dfrac{13}{15}\times\dfrac{7}{4}\\ x=\dfrac{91}{60}\)