Question

Using appropriate properties find:
(i) -2/3 x 3/5 + 5/2 - 3/5 x 1/6

(ii) 2/5 x (-3/7) - 1/6 x 3/2 + 1/14 x 2/5

Answer 1

Using appropriate properties find:
(i) -2/3 x 3/5 + 5/2 - 3/5 x 1/6

we know that in 1st and last term 3/5 is common

$= > \frac{ - 2}{3} \times \frac{3}{5} + \frac{5}{2} - \frac{3}{5} \times \frac{1}{6} \\ \\ \\ = > \frac{ - 2}{3} \times \frac{3}{5} - \frac{3}{5} \times \frac{1}{6} + \frac{5}{2}\\ \\ \\ = > \frac{3}{5} ( \frac{ - 2}{3} - \frac{1}{6} ) + \frac{5}{2} \\ \\ = > \frac{3}{5} ( \frac{ - 4 - 1}{6} ) + \frac{5}{2} \\ \\ = > \frac{3}{5} \times \frac{ - 5}{6} + \frac{5}{2} \\ \\ = > \frac{ - 1}{2} + \frac{5}{2} \\ \\ = > \frac{ - 1 + 5}{2} \\ \\ = > \frac{4}{2} \\ \\ = > 2$
(ii) 2/5 x (-3/7) - 1/6 x 3/2 + 1/14 x 2/5

take common 2/5 from first and last term

$\frac{2}{5} ( \frac{ - 3}{7} + \frac{1}{14} ) - \frac{1}{6} \times \frac{3}{2} \\ \\ = > \frac{2}{5} ( \frac{ - 6 + 1}{14}) - \frac{1}{6} \times \frac{3}{2} \\ \\ = > \frac{2}{5} \times \frac{ - 5}{14} - \frac{1}{4} \\ \\ = > \frac{ - 1}{7} - \frac{1}{4} \\ \\ = > \frac{ - 4 -7 }{28} \\ \\ = > \frac{ - 11}{28}$