To multiply the mixed numbers \(-2 \frac{1}{2}\) and \(-1 \frac{3}{5}\), we first convert them to improper fractions.
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Convert \(-2 \frac{1}{2}\): \[ -2 \frac{1}{2} = -\left(2 \times 2 + 1\right)/2 = -\frac{5}{2} \]
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Convert \(-1 \frac{3}{5}\): \[ -1 \frac{3}{5} = -\left(1 \times 5 + 3\right)/5 = -\frac{8}{5} \]
Now, we multiply the two improper fractions: \[ -\frac{5}{2} \times -\frac{8}{5} \]
Since the product of two negative numbers is positive: \[ \frac{5 \times 8}{2 \times 5} = \frac{40}{10} = 4 \]
Now, we write the answer as a decimal: \[ 4 = 4.0 \]
Thus, the answer is: \[ \boxed{4.0} \]