Question

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

Answer 1

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

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

Interchange the second and third terms

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

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

[Since, Using, distributive property of rational numbers over subtraction:

$(a\times b)-(a\times c)=a\times (b-c)$]

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

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

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

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

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

$=\frac{4}{2}$

$=2$

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