Find \( -3 \frac{3}{4}\left(-2 \frac{5}{6}\right) \). Write in the simplest form

To calculate \( -3 \frac{3}{4}\left(-2 \frac{5}{6}\right) \), we first convert the mixed numbers to improper fractions. For \( -3 \frac{3}{4} \): \[ -3 \frac{3}{4} = -\left(3 \times 4 + 3\right)/4 = -\frac{15}{4} \] For \( -2 \frac{5}{6} \): \[ -2 \frac{5}{6} = -\left(2 \times 6 + 5\right)/6 = -\frac{17}{6} \] Now, we can multiply the two improper fractions: \[ -\frac{15}{4} \times -\frac{17}{6} = \frac{15 \times 17}{4 \times 6} = \frac{255}{24} \] Next, we simplify \( \frac{255}{24} \). We find the greatest common divisor (GCD) of 255 and 24, which is 3. Now we divide both the numerator and the denominator by 3: \[ \frac{255 \div 3}{24 \div 3} = \frac{85}{8} \] Finally, we can convert this improper fraction back into a mixed number: \[ \frac{85}{8} = 10 \frac{5}{8} \] Thus, the simplest form of the expression is: \[ \boxed{10 \frac{5}{8}} \]