The given expression is:

\[
\frac{8}{9} + \left( -\frac{5}{6} \right)
\]

To solve this, we'll first find a common denominator for the fractions $\frac{8}{9}$ and $-\frac{5}{6}$.

### Step 1: Find the least common denominator (LCD)
The denominators are 9 and 6. The least common denominator of 9 and 6 is 18.

### Step 2: Convert both fractions to have the same denominator
- For $\frac{8}{9}$, we multiply both the numerator and the denominator by 2:
  \[
  \frac{8}{9} = \frac{8 \times 2}{9 \times 2} = \frac{16}{18}
  \]

- For $-\frac{5}{6}$, we multiply both the numerator and the denominator by 3:
  \[
  -\frac{5}{6} = \frac{-5 \times 3}{6 \times 3} = \frac{-15}{18}
  \]

### Step 3: Add the fractions
Now that both fractions have the same denominator, we can add them:
\[
\frac{16}{18} + \frac{-15}{18} = \frac{16 - 15}{18} = \frac{1}{18}
\]

### Final Answer:
\[
\frac{8}{9} + \left( -\frac{5}{6} \right) = \frac{1}{18}
\]

Would you like more details on any step or have any questions?

Here are five related questions to explore:
1. How do you find the least common denominator for more complex fractions?
2. What happens if both fractions are negative?
3. Can you solve a similar problem with three fractions?
4. What is the importance of simplifying fractions before adding them?
5. How do you subtract fractions with unlike denominators?

**Tip:** Always simplify your answer if possible to ensure clarity.

$$ \frac{8}{9} + \left(-\frac{5}{6}\right) $$

Learn how to add fractions with different denominators by finding a common denominator. This example problem, $\frac{8}{9} + (-\frac{5}{6})$, involves finding the least common denominator (LCD) and converting fractions before performing the addition. Suitable for students in Grades 5-7.

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