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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.