To solve $-\frac{5}{6} + (-2 \frac{1}{2})$, follow these steps:

Step 1: Convert the mixed number to an improper fraction

The mixed number $-2 \frac{1}{2}$ is converted as follows: $-2 \frac{1}{2} = -\left(2 + \frac{1}{2}\right) = -\frac{4}{2} - \frac{1}{2} = -\frac{5}{2}.$

Now the problem becomes: $-\frac{5}{6} + \left(-\frac{5}{2}\right).$

Step 2: Find a common denominator

The denominators are $6$ and $2$. The least common denominator (LCD) is $6$.

Convert $-\frac{5}{2}$ to have a denominator of $6$: $-\frac{5}{2} = -\frac{15}{6}.$

Now rewrite the expression: $-\frac{5}{6} + \left(-\frac{15}{6}\right).$

Step 3: Add the fractions

Since the denominators are the same, add the numerators: $-\frac{5}{6} + \left(-\frac{15}{6}\right) = \frac{-5 - 15}{6} = \frac{-20}{6}.$

Step 4: Simplify the fraction

Simplify $-\frac{20}{6}$ by dividing the numerator and denominator by their greatest common divisor (GCD), which is $2$: $-\frac{20}{6} = -\frac{10}{3}.$

Final Answer:

$-\frac{10}{3}, \text{ or equivalently } -3 \frac{1}{3}.$

Would you like a detailed breakdown of a specific step? Let me know!

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Related Questions:

1. How do you find the least common denominator for fractions?
2. How do you convert between mixed numbers and improper fractions?
3. Why is simplifying fractions important in final answers?
4. How do you handle negative signs in fraction addition?
5. How do you check if your final answer is correct?

Tip:

Always simplify fractions in your final answer unless specifically told otherwise!