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

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

To find: Here we have to find the value of the given expression.

Solution:

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

First let us simplify each term:

$\frac{2}{3}\ \times\ \frac{3}{5}\ =\ \frac{2}{5}$

$\frac{3}{5}\ \times\ \frac{1}{6}\ =\ \frac{1}{10}$

So expression will become

$=\ -\frac{2}{5}\ +\ \frac{5}{2}\ -\ \frac{1}{10}$

LCM of 5, 2, 10: 10

Adjust fractions based on the LCM:

$=\ -\frac{4}{10}\ +\ \frac{25}{10}\ -\ \frac{1}{10}$

Since the denominators are equal, combine the fractions:

$=\ \frac{-\ 4\ +\ 25\ -\ 1}{10}$

Add/Subtract the numbers: 

$=\ \frac{20}{10}$

Divide the numbers:

$=\ \mathbf{2}$

So, value of given expression is 2.