Question

Simplify:
(i) $\left(\frac{3}{2}\times \frac{1}{6}\right)+\left(\frac{5}{3}\times \frac{7}{2}\right)-\left(\frac{13}{8}\times \frac{4}{3}\right)$

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

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

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

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)(\frac{3}{2}\times \frac{1}{6})+(\frac{5}{3}\times \frac{7}{2})-(\frac{13}{8}\times \frac{4}{3}) \\ =\frac{1}{4}+\frac{35}{6}-\frac{13}{6} \\ =\frac{1\times 3+35\times 2-13\times 2}{12} \\ =\frac{3+70-26}{12} \\ =\frac{47}{12} \\ \left(\mathrm{ii}\right)(\frac{1}{4}\times \frac{2}{7})-(\frac{5}{14}\times \frac{-2}{3})+(\frac{3}{7}\times \frac{9}{2}) \\ =\frac{1}{14}-\frac{-5}{21}+\frac{27}{14} \\ =\frac{1\times 3+5\times 2+27\times 3}{42} \\ =\frac{94}{42}=\frac{47}{21} \\ \left(\mathrm{iii}\right)(\frac{13}{9}\times \frac{-15}{2})+(\frac{7}{3}\times \frac{8}{5})+(\frac{3}{5}\times \frac{1}{2}) \\ =\frac{-13\times 5}{6}+\frac{7\times 8}{15}+\frac{3}{10} \\ =\frac{-65}{6}+\frac{56}{15}+\frac{3}{10} \\ =\frac{-65\times 5+56\times 2+3\times 3}{30} \\ =\frac{-204}{30}=\frac{-34}{5} \\ \left(\mathrm{iv}\right)(\frac{3}{11}\times \frac{5}{6})-(\frac{9}{12}\times \frac{4}{3})+(\frac{5}{13}\times \frac{6}{15}) \\ =\frac{5}{22}-1+\frac{2}{13} \\ =\frac{5\times 13-286+2\times 22}{286} \\ =\frac{65-286+44}{286} \\ =\frac{-177}{286} \end{gathered}$$