To multiply \(-2 \frac{1}{2}\) by \(-1 \frac{3}{5}\), we first convert these mixed numbers to improper fractions.
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Convert \(-2 \frac{1}{2}\):
- The whole number part is \(-2\), which can be written as \(-\frac{5}{2}\) (since \(2 \times 2 + 1 = 5\)).
- Thus, \(-2 \frac{1}{2} = -\frac{5}{2}\).
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Convert \(-1 \frac{3}{5}\):
- The whole number part is \(-1\), which can be written as \(-\frac{8}{5}\) (since \(1 \times 5 + 3 = 8\)).
- Thus, \(-1 \frac{3}{5} = -\frac{8}{5}\).
Now, we can multiply the two improper fractions:
\[ -\frac{5}{2} \times -\frac{8}{5} \]
Multiplying the numerators and the denominators gives:
\[ \frac{5 \times 8}{2 \times 5} = \frac{40}{10} \]
Now, simplify:
\[ \frac{40}{10} = 4 \]
Finally, as a decimal, the answer is \(4.0\).
So, the result of multiplying \(-2 \frac{1}{2}\) by \(-1 \frac{3}{5}\) is \(4.0\).