To determine the quotient of \(-3 \frac{3}{5} \div -\frac{7}{8}\), we first need to convert the mixed number \(-3 \frac{3}{5}\) into an improper fraction.
-
Convert \(-3 \frac{3}{5}\): \[ -3 \frac{3}{5} = -\left(3 \times 5 + 3\right) / 5 = -\left(15 + 3\right) / 5 = -\frac{18}{5} \]
-
Now we have: \[ -\frac{18}{5} \div -\frac{7}{8} \]
-
Dividing by a fraction is the same as multiplying by its reciprocal: \[ -\frac{18}{5} \div -\frac{7}{8} = -\frac{18}{5} \times -\frac{8}{7} \]
-
When we multiply these fractions: \[ \frac{18 \times 8}{5 \times 7} = \frac{144}{35} \]
-
Now, we can convert \(\frac{144}{35}\) into a mixed number:
- Divide 144 by 35, which gives: \[ 144 \div 35 = 4 \quad \text{(remainder)} \quad 144 - (35 \times 4) = 144 - 140 = 4 \] Thus, \(\frac{144}{35} = 4 \frac{4}{35}\).
The final answer is:
\[ \boxed{4 \frac{4}{35}} \]