Question

Using appropriate properties find

$\frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}$

Answer 1

$\frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}$

$=\frac{-2}{3}\times \frac{3}{5}-\frac{3}{5}\times \frac{1}{6}+\frac{5}{2}$

$=(\frac{-2}{3}-\frac{1}{6})\frac{3}{5}+\frac{5}{2}$ [Distributive property]

$=\left(\frac{-2\times 2-1}{6}\right)\frac{3}{5}+\frac{5}{2}$

$=\frac{-4-1}{6}\times \frac{3}{5}+\frac{5}{2}$

$=\frac{-5}{6}\times \frac{3}{5}+\frac{5}{2}$

$=\frac{-1}{2}+\frac{5}{2}$

$=\frac{-1+5}{2}$

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