a. $\dfrac{4}{105}\times\dfrac{35}8 =\dfrac{\overset{1}{\cancel4}\times\overset{1}{\cancel{35}}} {\underset{3}{\cancel{105}} \times\underset{2}{\cancel8}} =\dfrac16$.

b. $\dfrac{50}{100}\times\dfrac{10}{100} =\dfrac{50\times 10}{100\times 100} =\dfrac{\overset{1}{\cancel{50}}\times\overset{1}{\cancel{10}}} {\underset{2}{\cancel{100}} \times \underset{10}{\cancel{100}}} =\dfrac1{20}$.

c. $\dfrac87 \times\dfrac{49}{40} =\dfrac{8 \times 49}{7\times 40} =\dfrac{\overset{1}{\cancel 8} \times \overset{7}{\cancel{49}}} {\underset{1}{\cancel 7} \times \underset{5}{\cancel{40}}} =\dfrac{7}{5}$.

d. $\dfrac12\times\dfrac23\times\dfrac34 =\dfrac{1\times \cancel 2 \times \cancel 3}{\cancel 2 \times \cancel 3 \times 4} =\dfrac14$.

e. $\dfrac3{35}\times\dfrac{27}5\times\dfrac{25}{-9} =-\dfrac{\overset{1}{\cancel 3} \times 27 \times \overset{1}{\cancel{25}}} {\underset{7}{\cancel{35}} \times \underset{1}{\cancel 5}\times \underset{3}{\cancel 9}} =\frac{\overset{9}{\cancel{27}}}{\underset{1}{\cancel 3}} =9$.