To solve the expression \(-\frac{3}{8} \cdot \frac{2}{5}\), follow these steps:
1. Multiply the numerators: The numerators are \(-3\) and \(2\). When you multiply these together, you get:
[tex]\[
-3 \times 2 = -6
\][/tex]
2. Multiply the denominators: The denominators are \(8\) and \(5\). When you multiply these together, you get:
[tex]\[
8 \times 5 = 40
\][/tex]
3. Form the new fraction: Combine the results from the previous steps to form the new fraction:
[tex]\[
-\frac{6}{40}
\][/tex]
4. Simplify the fraction: Find the greatest common divisor (GCD) of 6 and 40 to simplify the fraction. The GCD of 6 and 40 is 2. Divide both the numerator and the denominator by 2:
[tex]\[
\frac{-6 \div 2}{40 \div 2} = \frac{-3}{20}
\][/tex]
So, the simplified value of the expression \(-\frac{3}{8} \cdot \frac{2}{5}\) is:
[tex]\[
\boxed{-\frac{3}{20}}
\][/tex]
