To multiply \(-2 \frac{1}{5}\) by \(-8\), let's first convert \(-2 \frac{1}{5}\) into an improper fraction.
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Convert the mixed number \( -2 \frac{1}{5} \) to an improper fraction: \[ -2 \frac{1}{5} = -\left(2 \times 5 + 1\right)/5 = -\frac{10 + 1}{5} = -\frac{11}{5} \]
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Now multiply \(-\frac{11}{5}\) by \(-8\): \[ -\frac{11}{5} \times -8 = \frac{11 \times 8}{5} = \frac{88}{5} \]
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Convert \(\frac{88}{5}\) back into a mixed number:
- Divide \(88\) by \(5\): \[ 88 \div 5 = 17 \quad \text{(with a remainder of 3)} \] So, \(88 = 5 \times 17 + 3\).
Thus, \(\frac{88}{5}\) can be expressed as: \[ 17 \frac{3}{5} \]
The final answer is: \[ \boxed{17 \frac{3}{5}} \]