Solve: (-3⅓) + (-2.75) - Adding Negative Mixed Numbers and Decimals

$(-3\frac{2}{6})+(-2.75)=$

To solve this problem, we'll convert both numbers to fractions and then perform the addition:

Step 1: Convert $-3\frac{2}{6}$ to an improper fraction.
First, simplify $\frac{2}{6}$ to $\frac{1}{3}$:
$-3\frac{2}{6} = -3\frac{1}{3} = -\left(\frac{3 \times 3 + 1}{3}\right) = -\frac{10}{3}$.

Step 2: Convert $-2.75$ to a fraction.
$-2.75 = -2\frac{75}{100}$. Simplify $\frac{75}{100}$ to $\frac{3}{4}$:
$-2\frac{3}{4} = -\left(\frac{2 \times 4 + 3}{4}\right) = -\frac{11}{4}$.

Step 3: Find a common denominator and add the fractions.
The common denominator for 3 and 4 is 12.
Convert $-\frac{10}{3}$ to $-\frac{40}{12}$ and $-\frac{11}{4}$ to $-\frac{33}{12}$.

Step 4: Add the fractions:
$-\frac{40}{12} + -\frac{33}{12} = -\frac{73}{12}$.

Step 5: Convert $-\frac{73}{12}$ back to a mixed number.
$-\frac{73}{12} = -6\frac{1}{12}$.

Therefore, the solution to the problem is $-6\frac{1}{12}$.