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Simplify:
(i) $ \left(\frac{25}{8} \times \frac{2}{5}\right)-\left(\frac{3}{5} \times \frac{-10}{9}\right) $
(ii) $ \left(\frac{1}{2} \times \frac{1}{4}\right)+\left(\frac{1}{2} \times 6\right) $
(iii) $ \left(-5 \times \frac{2}{15}\right)=\left(-6 \times \frac{2}{9}\right) $
(iv) $ \left(\frac{-9}{4} \times \frac{5}{3}\right)+\left(\frac{13}{2} \times \frac{5}{6}\right) $
(v) $ \left(\frac{-4}{3} \times \frac{12}{-5}\right)+\left(\frac{3}{7} \times \frac{21}{15}\right) $
(vi) $ \left(\frac{13}{5} \times \frac{8}{3}\right)-\left(\frac{-5}{2} \times \frac{11}{3}\right) $
(vii) $ \left(\frac{13}{7} \times \frac{11}{26}\right)-\left(\frac{-4}{3} \times \frac{5}{6}\right) $
(viii) $ \left(\frac{8}{5} \times \frac{-3}{2}\right)+\left(\frac{-3}{10} \times \frac{11}{16}\right) $
To do:
We have to simplify the given expressions.
Solution:
(i) $(\frac{25}{8} \times \frac{2}{5})-(\frac{3}{5} \times \frac{-10}{9})=\frac{25 \times 2}{8 \times 5}-\frac{3 \times(-10)}{5 \times 9}$
$=\frac{5 \times 1}{4 \times 1}-\frac{1 \times(-2)}{1 \times 3}$
$=\frac{5}{4}-\frac{-2}{3}$
$=\frac{15+8}{12}$
$=\frac{23}{12}$
(ii) $(\frac{1}{2} \times \frac{1}{4})+(\frac{1}{2} \times 6)=\frac{1 \times 1}{2 \times 4}+\frac{1}{2} \times \frac{6}{1}$
$=\frac{1}{8}+\frac{3}{1}$
$=\frac{1+24}{8}$
$=\frac{25}{8}$
(iii) $(-5 \times \frac{2}{15})-(-6 \times \frac{2}{9})=\frac{-2}{3}-\frac{-2\times2}{3}$
$=\frac{-2}{3}+\frac{4}{3}$
$=\frac{-2+4}{3}$
$=\frac{2}{3}$
(iv) $(\frac{-9}{4} \times \frac{5}{3})+(\frac{13}{2} \times \frac{5}{6})=\frac{-9 \times 5}{4 \times 3}+\frac{13 \times 5}{2 \times 6}$
$=\frac{-3 \times 5}{4 \times 1}+\frac{65}{12}$
$=\frac{-15}{4}+\frac{65}{12}$
$=\frac{-45+65}{12}$
$=\frac{20}{12}$
$=\frac{5}{3}$
(v) $(\frac{-4}{3} \times \frac{12}{-5})+(\frac{3}{7} \times \frac{21}{15})=\frac{-4 \times 12}{3 \times(-5)}+\frac{3 \times 21}{7 \times 15}$
$=\frac{-4 \times 4}{1 \times(-5)}+\frac{1 \times 3}{1 \times 5}$
$=\frac{-16}{-5}+\frac{3}{5}$
$=\frac{16}{5}+\frac{3}{5}$
$=\frac{16+3}{5}$
$=\frac{19}{5}$
(vi) $(\frac{13}{5} \times \frac{8}{3})-(\frac{-5}{2} \times \frac{11}{3})=\frac{13 \times 8}{5 \times 3}-\frac{-5 \times 11}{2 \times 3}$
$=\frac{104}{15}-\frac{-55}{6}$
$=\frac{208+275}{30}$
$=\frac{483}{30}$
$=\frac{161}{10}$
(vii) $(\frac{13}{7} \times \frac{11}{26})-(\frac{-4}{3} \times \frac{5}{6})=\frac{13 \times 11}{7 \times 26}-\frac{-4 \times 5}{3 \times 6}$
$=\frac{1 \times 11}{7 \times 2}-\frac{-2 \times 5}{3 \times 3}$
$=\frac{11}{14}-\frac{-10}{9}$
$=\frac{99+140}{126}$
$=\frac{239}{126}$
(viii) $(\frac{8}{5} \times \frac{-3}{2})+(\frac{-3}{10} \times \frac{11}{16})=\frac{8 \times(-3)}{5 \times 2}+\frac{-3 \times 11}{10 \times 16}$
$=\frac{4 \times(-3)}{5 \times 1}+\frac{-3 \times 11}{10 \times 16}$
$=\frac{-12}{5}+\frac{-33}{160}$
$=\frac{-384-33}{160}$
$=\frac{-417}{160}$
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