Simplify:

Solution:

(i) $\left(\frac{25}{8} \times \frac{2}{5}\right)-\left(\frac{3}{5} \times \frac{-10}{9}\right)$

$=\frac{5}{4}-\frac{-2}{3}$

$=\frac{5 \times 3+2 \times 4}{12}$

$=\frac{23}{12}$

(ii) $\left(\frac{1}{2} \times \frac{1}{4}\right)+\left(\frac{1}{2} \times 6\right)$

$=\frac{1}{8}+3$

$=\frac{1+3 \times 8}{8}$

$=\frac{25}{8}$

$($ iii $)\left(-5 \times \frac{2}{15}\right)-\left(-6 \times \frac{2}{9}\right)$

$=\frac{-2}{3}-\frac{-4}{3}$

$=\frac{-2+4}{3}$

$=\frac{2}{3}$

$($ iv $)\left(\frac{-9}{4} \times \frac{5}{3}\right)+\left(\frac{13}{2} \times \frac{5}{6}\right)$

$=\frac{-3 \times 5}{4}+\frac{13 \times 5}{12}$

$=\frac{-15}{4}+\frac{65}{12}$

$=\frac{-15 \times 3+65}{12}$

$=\frac{20}{12}=\frac{5}{3}$

$(\mathrm{v})\left(\frac{-4}{3} \times \frac{12}{-5}\right)+\left(\frac{3}{7} \times \frac{21}{15}\right)$

$=\frac{4 \times 4}{5}+\frac{1 \times 3}{5}$

$=\frac{16}{5}+\frac{3}{5}$

$=\frac{16+3}{5}$

$=\frac{19}{5}$

$(\mathrm{vi})\left(\frac{13}{5} \times \frac{8}{3}\right)-\left(\frac{-5}{2} \times \frac{11}{3}\right)$

$=\frac{13 \times 8}{15}-\frac{-5 \times 11}{6}$

$=\frac{104}{15}-\frac{-55}{6}$

$=\frac{104 \times 2+55 \times 5}{30}$

$=\frac{483}{30}$

$($ vii $)\left(\frac{13}{7} \times \frac{11}{26}\right)-\left(\frac{-4}{3} \times \frac{5}{6}\right)$

$=\frac{1 \times 11}{7 \times 2}-\frac{-2 \times 5}{3 \times 3}$

$=\frac{11}{14}-\frac{-10}{9}$

$=\frac{11 \times 9+10 \times 14}{126}$

$=\frac{239}{126}$

$($ viii $)\left(\frac{8}{5} \times \frac{-3}{2}\right)+\left(\frac{-3}{10} \times \frac{11}{16}\right)$

$=\frac{4 \times(-3)}{5}+\frac{-3 \times 11}{10 \times 16}$

$=\frac{-12}{5}+\frac{-33}{160}$

$=\frac{-12 \times 32-33}{160}$

$=\frac{-384-33}{160}$

$=\frac{-417}{160}$