To solve the problem \(-1 \frac{3}{4} \div \frac{2}{5}\), we first need to convert the mixed number \(-1 \frac{3}{4}\) into an improper fraction.
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Convert \(-1 \frac{3}{4}\) to an improper fraction: \[ -1 \frac{3}{4} = -\left(1 \cdot 4 + 3\right) / 4 = -\left(4 + 3\right) / 4 = -\frac{7}{4} \]
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Now, we divide \(-\frac{7}{4}\) by \(\frac{2}{5}\). Dividing by a fraction is the same as multiplying by its reciprocal: \[ -\frac{7}{4} \div \frac{2}{5} = -\frac{7}{4} \cdot \frac{5}{2} \]
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Multiply the fractions: \[ -\frac{7 \cdot 5}{4 \cdot 2} = -\frac{35}{8} \]
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The result \(-\frac{35}{8}\) can be expressed as a mixed number: \[ -\frac{35}{8} = -4 \frac{3}{8} \]
Thus, the quotient in simplest form is \( \text{negative } 4 \text{ and } 3 \text{ eighths} \).
The correct response is: −4 and 3 eighths