Question: Divide. Simplify your answer.
−3 3/4 ÷ −6 4/5
1. **State the problem:** We need to divide the mixed number $$-3 \frac{3}{4}$$ by the mixed number $$-6 \frac{4}{5}$$ and simplify the result.
2. **Convert mixed numbers to improper fractions:**
$$-3 \frac{3}{4} = -\left(3 + \frac{3}{4}\right) = -\frac{15}{4}$$
$$-6 \frac{4}{5} = -\left(6 + \frac{4}{5}\right) = -\frac{34}{5}$$
3. **Rewrite the division as multiplication by the reciprocal:**
$$-\frac{15}{4} \div -\frac{34}{5} = -\frac{15}{4} \times -\frac{5}{34}$$
4. **Multiply the numerators and denominators:**
$$\frac{-15 \times -5}{4 \times 34} = \frac{75}{136}$$
5. **Simplify the fraction if possible:**
Check for common factors between 75 and 136. Since 75 factors as $$3 \times 5^2$$ and 136 factors as $$2^3 \times 17$$, there are no common factors.
6. **Final answer:**
$$\boxed{\frac{75}{136}}$$
The simplified result of dividing $$-3 \frac{3}{4}$$ by $$-6 \frac{4}{5}$$ is $$\frac{75}{136}$$.