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 \(-2 \frac{1}{2}\) to an improper fraction: \[ -2 \frac{1}{2} = -\left(2 \times 2 + 1\right)/2 = -5/2 \]
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Convert \(-1 \frac{3}{5}\) to an improper fraction: \[ -1 \frac{3}{5} = -\left(1 \times 5 + 3\right)/5 = -8/5 \]
Now we multiply the two improper fractions: \[ (-\frac{5}{2}) \times (-\frac{8}{5}) = \frac{5 \times 8}{2 \times 5} = \frac{40}{10} = 4 \]
So, the answer is \(4\).
Thus, the answer is: \[ \boxed{4} \]