Question

Using appropriate properties, find: $\frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}$

Answer 1

$\frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}$
$=\frac{-2}{3}\times \frac{3}{5}-\frac{3}{5}\times \frac{1}{6}+\frac{5}{2}$ [By commutative property]
$=\frac{3}{5}(\frac{-2}{3}-\frac{1}{6})+\frac{5}{2}$
[ reverse of distributive over subtraction ]
$=\frac{3}{5}\left(\frac{-4-1}{6}\right)+\frac{5}{2}$
$=\frac{3}{5}\left(\frac{-5}{6}\right)+\frac{5}{2}$
$=\frac{-15}{30}+\frac{5}{2}$
$=\frac{-1}{2}+\frac{5}{2}$
$=\frac{-1+5}{2}$
$=\frac{4}{2}=2$