To multiply the fractions \(-\frac{1}{4}\) and \(-\frac{4}{5}\), we follow these steps:
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Multiply the numerators: \(-1 \times -4 = 4\)
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Multiply the denominators: \(4 \times 5 = 20\)
Putting it together, we have:
\[ -\frac{1}{4} \times -\frac{4}{5} = \frac{4}{20} \]
Now, we can simplify \(\frac{4}{20}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
\[ \frac{4 \div 4}{20 \div 4} = \frac{1}{5} \]
Therefore, the result of the multiplication is:
\[ -\frac{1}{4} \times -\frac{4}{5} = \frac{1}{5} \]