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The problem is asking to add \( \frac{1}{9} + \frac{5}{6} \), simplify the result, and express it as a mixed number if appropriate.

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

- Convert \( \frac{1}{9} \) to a fraction with denominator 18:
  \[
  \frac{1}{9} = \frac{2}{18}
  \]

- Convert \( \frac{5}{6} \) to a fraction with denominator 18:
  \[
  \frac{5}{6} = \frac{15}{18}
  \]

### Step 2: Add the fractions.
Now that both fractions have the same denominator, we can add them:
\[
\frac{2}{18} + \frac{15}{18} = \frac{17}{18}
\]

### Step 3: Check if the result can be simplified or written as a mixed number.
The fraction \( \frac{17}{18} \) is already in its simplest form and cannot be converted into a mixed number, as the numerator is less than the denominator.

### Final Answer: 
The sum is \( \frac{17}{18} \), so the correct option is the first one: \( \frac{17}{18} \).

Would you like any further details on the steps? Here are some follow-up questions:

1. How do you find the least common denominator (LCD)?
2. Why is \( \frac{17}{18} \) in its simplest form?
3. What is the process for converting improper fractions into mixed numbers?
4. Can \( \frac{5}{6} \) be simplified before adding it to \( \frac{1}{9} \)?
5. What are the rules for adding fractions with different denominators?

**Tip**: Always simplify fractions before finalizing your answer—it makes calculations easier!

Add. Simplify the answer and write the answer as a mixed number if appropriate: 1/9 + 5/6.

This problem involves adding fractions with different denominators: 1/9 + 5/6. It explains finding the least common denominator (LCD) and simplifying the answer. Learn how to add fractions and simplify the result to its simplest form.

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