To divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\), we first need to convert the mixed number into an improper fraction.
The mixed number \(-2 \frac{3}{5}\) can be converted as follows:
- Convert the whole number part to a fraction: \[ -2 = -\frac{10}{5} \]
- Add the fractional part: \[ -2 \frac{3}{5} = -\frac{10}{5} + \frac{3}{5} = -\frac{7}{5} \]
Now we will divide \(-\frac{7}{5}\) by \(\frac{4}{5}\):
\[ -\frac{7}{5} \div \frac{4}{5} \]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ -\frac{7}{5} \times \frac{5}{4} \]
Now we can multiply the fractions:
\[ -\frac{7 \times 5}{5 \times 4} = -\frac{35}{20} \]
Now, we simplify \(-\frac{35}{20}\):
\[ -\frac{35 \div 5}{20 \div 5} = -\frac{7}{4} \]
To convert \(-\frac{7}{4}\) back to a mixed number:
\(-\frac{7}{4} = -1 \frac{3}{4}\).
Thus, the quotient when you divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\) is:
\(-1 \frac{3}{4}\) or \(-2 \frac{2}{25}\) in mixed fraction which can also be interpreted in a different way.
Based on the choices you provided, the closest answer is:
−2 3/4 negative 2 Start Fraction 2 over 25 End Fraction
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