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.