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: \[ -2 = -\frac{10}{5} \] So, \[ -2 \frac{3}{5} = -\frac{10}{5} + \frac{3}{5} = -\frac{7}{5} \]
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Now we need to divide \(-\frac{7}{5}\) by \(\frac{4}{5}\). Dividing by a fraction is the same as multiplying by its reciprocal: \[ -\frac{7}{5} \div \frac{4}{5} = -\frac{7}{5} \times \frac{5}{4} \]
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Multiply the fractions: \[ -\frac{7 \times 5}{5 \times 4} = -\frac{35}{20} \]
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Simplify \(-\frac{35}{20}\):
- Both the numerator and denominator can be divided by 5: \[ -\frac{35 \div 5}{20 \div 5} = -\frac{7}{4} \]
Therefore, the quotient when you divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\) is \(-\frac{7}{4}\) or \(-1 \frac{3}{4}\) in mixed number form.
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