To find the value of the given expression, let's break it down into individual terms and solve each one step by step:
The expression to be evaluated is:
[tex]\[ -\frac{2}{3} \times \frac{3}{5} + \frac{5}{2} - \frac{3}{5} \times \frac{1}{6} \][/tex]
### Step 1: Simplify the first term:
[tex]\[ -\frac{2}{3} \times \frac{3}{5} \][/tex]
Multiply the numerators and the denominators:
[tex]\[ -\frac{2 \times 3}{3 \times 5} = -\frac{6}{15} \][/tex]
Simplify the fraction:
[tex]\[ -\frac{6}{15} = -\frac{2}{5} \][/tex]
In decimal form:
[tex]\[ -\frac{2}{5} = -0.4 \][/tex]
### Step 2: Identify the second term:
The second term is [tex]\(\frac{5}{2}\)[/tex], which directly converts to:
[tex]\[ 2.5 \][/tex]
### Step 3: Simplify the third term:
[tex]\[ -\frac{3}{5} \times \frac{1}{6} \][/tex]
Multiply the numerators and the denominators:
[tex]\[ -\frac{3 \times 1}{5 \times 6} = -\frac{3}{30} \][/tex]
Simplify the fraction:
[tex]\[ -\frac{3}{30} = -\frac{1}{10} \][/tex]
In decimal form:
[tex]\[ -\frac{1}{10} = -0.1 \][/tex]
### Step 4: Combine the results:
Add the simplified terms together:
[tex]\[ -0.4 + 2.5 + (-0.1) \][/tex]
First, sum [tex]\(-0.4\)[/tex] and [tex]\(-0.1\)[/tex]:
[tex]\[ -0.4 - 0.1 = -0.5 \][/tex]
Then add [tex]\( -0.5 \)[/tex] to [tex]\( 2.5 \)[/tex]:
[tex]\[ 2.5 - 0.5 = 2.0 \][/tex]
### Conclusion:
The value of the expression [tex]\(\-\frac{2}{3} \times \frac{3}{5}+\frac{5}{2}-\frac{3}{5} \times \frac{1}{6}\)[/tex] is:
[tex]\[ \boxed{2.0} \][/tex]
So, the final result is [tex]\(2.0\)[/tex].
