(i) \((\frac{3}{2}\times \frac{1}{6})+(\frac{5}{3}\times \frac{7}{2})-(\frac{13}{8}\times \frac{4}{3})\)

= \(\frac{3}{12}+\frac{35}{6}-\frac{52}{24}\)

= \(\frac{3\times 2+35\times 4-52\times 1}{24}\)

= \(\frac{6+140-52}{24}\)

= \(\frac{94}{24}\)

= \(\frac{47}{12}\)

 (ii) \((\frac{1}{4}\times \frac{2}{7})-(\frac{5}{14}\times \frac{-2}{3})+(\frac{3}{7}\times \frac{9}{2})\)

= \(\frac{2}{28}+\frac{10}{42}+\frac{27}{14}\)

= \(\frac{3\times 2+10\times 2+27\times 6}{84}\)

= \(\frac{6+20+162}{84}\)

= \(\frac{188}{84}\)

= \(\frac{47}{21}\)

 (iii) \((\frac{13}{9}\times \frac{-15}{2})+(\frac{7}{3}\times \frac{8}{5})+(\frac{3}{5}\times \frac{1}{2})\)

= \(\frac{13\times -15}{9\times 2}+\frac{7\times 8}{3\times 5}+\frac{3\times 1}{5\times 2}\)

= \(\frac{-65}{6}+\frac{56}{15}+\frac{3}{10}\)

= \(\frac{-65\times 5+56\times 2-3\times 3}{30}\)

= \(\frac{-204}{30}\)

(iv) \((\frac{3}{11}\times \frac{5}{6})-(\frac{9}{12}\times \frac{4}{3})+(\frac{5}{13}\times \frac{6}{15})\)

= \(\frac{3\times 5}{11\times 6}-\frac{36}{36}+\frac{30}{13\times 15}\)

= \(\frac{15}{66}-1+\frac{1}{13}\)

= \(\frac{15\times 13-858+66}{858}\)

= \(\frac{-597}{858}\)