To divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\), we first convert the mixed number \(-2 \frac{3}{5}\) into an improper fraction.
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Convert \(-2\) to a fraction: \(-2\) can be rewritten as \(-\frac{10}{5}\) (since \(2 \times 5 = 10\)).
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Combine this with \(\frac{3}{5}\): \[ -2 \frac{3}{5} = -\frac{10}{5} + \frac{3}{5} = -\frac{10 - 3}{5} = -\frac{7}{5} \]
Now the division problem can be rewritten as: \[ -\frac{7}{5} \div \frac{4}{5} \]
Next, we change the division into multiplication by the reciprocal: \[ -\frac{7}{5} \times \frac{5}{4} \]
Now, multiply the fractions: \[ = -\frac{7 \times 5}{5 \times 4} = -\frac{35}{20} \]
We can simplify the fraction \(-\frac{35}{20}\):
- Both the numerator and the denominator can be divided by 5. \[ -\frac{35 \div 5}{20 \div 5} = -\frac{7}{4} \]
Thus, the result of \(-2 \frac{3}{5} \div \frac{4}{5}\) is: \[ -\frac{7}{4} \]
Alternatively, this can be expressed as a mixed number: \[ -1 \frac{3}{4} \]
So, the final answer is \(-\frac{7}{4}\) or \(-1 \frac{3}{4}\).