a.
\(\frac{6}{7}+\frac{5}{8}\div5-\frac{3}{16}\times\left(-2\right)^2=\frac{6}{7}+\frac{5}{8}\times\frac{1}{5}-\frac{3}{16}\times4=\frac{6}{7}+\frac{1}{8}-\frac{3}{4}=\frac{48}{56}+\frac{7}{56}-\frac{42}{56}=\frac{13}{56}\)
b.
\(\frac{2}{3}+\frac{1}{3}\times\left(-\frac{4}{9}+\frac{5}{6}\right)\div\frac{7}{12}=\frac{2}{3}+\frac{1}{3}\times\left(-\frac{8}{18}+\frac{15}{18}\right)\times\frac{12}{7}=\frac{2}{3}+\frac{7}{18}\times\frac{4}{7}=\frac{2}{3}+\frac{2}{9}=\frac{6}{9}+\frac{2}{9}=\frac{8}{9}\)
c.
\(\left[6+\left(\frac{1}{3}\right)^3-\left|-2\right|\right]\div\frac{3}{2}=\left(6+\frac{1^3}{3^3}-2\right)\times\frac{2}{3}=\left(4+\frac{1}{27}\right)\times\frac{2}{3}=\left(\frac{108}{27}+\frac{1}{27}\right)\times\frac{2}{3}=\frac{109}{27}\times\frac{2}{3}=\frac{218}{81}\)
d.
\(\left(-2\right)^3\times\left(-\frac{1}{24}\right)+\left(\frac{4}{3}-\frac{11}{6}\right)\div\frac{5}{12}\)\(=\left(-8\right)\times\left(-\frac{1}{24}\right)+\left(\frac{8}{6}-\frac{11}{6}\right)\times\frac{12}{5}=\frac{1}{3}+\left(-\frac{3}{6}\right)\times\frac{12}{5}=\frac{1}{3}-\frac{6}{5}=\frac{5}{15}-\frac{18}{15}\)\(=-\frac{13}{15}\)
