\(\frac{27}{23}+\frac{5}{21}-\frac{4}{23}+\frac{6}{21}+\frac{1}{2}\)
= \(\left(\frac{27}{23}-\frac{4}{23}\right)+\left(\frac{5}{21}+\frac{6}{21}\right)+\frac{1}{2}\)
= 1 + \(\frac{11}{21}+\frac{1}{2}\)
= \(\frac{42}{42}+\frac{22}{42}+\frac{21}{42}\)
= \(\frac{85}{42}\)