1. The problem is to subtract the mixed number $-3 \frac{1}{6}$ from $-4 \frac{3}{4}$ and express the answer in fraction form. 2. First, convert the mixed numbers to improper fractions. - For $-3 \frac{1}{6}$: multiply the whole number 3 by the denominator 6 and add the numerator 1, then apply the negative sign. $$-3 \frac{1}{6} = -\left(3 \times 6 + 1\right)/6 = -\frac{19}{6}$$ - For $-4 \frac{3}{4}$: multiply the whole number 4 by the denominator 4 and add the numerator 3, then apply the negative sign. $$-4 \frac{3}{4} = -\left(4 \times 4 + 3\right)/4 = -\frac{19}{4}$$ 3. Now subtract $-4 \frac{3}{4}$ from $-3 \frac{1}{6}$: $$-3 \frac{1}{6} - (-4 \frac{3}{4}) = -\frac{19}{6} - \left(-\frac{19}{4}\right) = -\frac{19}{6} + \frac{19}{4}$$ 4. Find a common denominator for $\frac{19}{6}$ and $\frac{19}{4}$. The least common denominator (LCD) of 6 and 4 is 12. 5. Convert both fractions to have denominator 12: $$-\frac{19}{6} = -\frac{19 \times 2}{6 \times 2} = -\frac{38}{12}$$ $$\frac{19}{4} = \frac{19 \times 3}{4 \times 3} = \frac{57}{12}$$ 6. Add the fractions: $$-\frac{38}{12} + \frac{57}{12} = \frac{-38 + 57}{12} = \frac{19}{12}$$ 7. The fraction $\frac{19}{12}$ is an improper fraction and can be left as is or converted to a mixed number $1 \frac{7}{12}$. Final answer: $\frac{19}{12}$