To divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\), we can first convert the mixed number into an improper fraction.
Step 1: Convert the mixed number to an improper fraction.
\(-2 \frac{3}{5}\) can be converted as follows:
\[ -2 \frac{3}{5} = -\left(2 \cdot 5 + 3\right) / 5 = -\left(10 + 3\right) / 5 = -\frac{13}{5} \]
Step 2: Set up the division of fractions.
Now, we want to divide \(-\frac{13}{5}\) by \(\frac{4}{5}\). Dividing by a fraction is the same as multiplying by its reciprocal:
\[ -\frac{13}{5} \div \frac{4}{5} = -\frac{13}{5} \cdot \frac{5}{4} \]
Step 3: Multiply the fractions.
When we multiply the fractions, we can simplify:
\[ -\frac{13 \cdot 5}{5 \cdot 4} = -\frac{13}{4} \]
Step 4: Convert to a mixed number if needed.
The quotient \(-\frac{13}{4}\) can be converted to a mixed number:
\(-\frac{13}{4} = -3 \frac{1}{4}\) (since \(13 \div 4 = 3\) with a remainder of 1).
Thus, the quotient when you divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\) is
\(-3 \frac{1}{4}\) or \(-\frac{13}{4}\).
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