To solve the equation \( \frac{2}{3} + \frac{x}{9} = \frac{11}{9} \), we need to find the value of \( x \).

### Step 1: Convert \( \frac{2}{3} \) to a fraction with a denominator of 9
\[
\frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}
\]

### Step 2: Substitute into the equation
\[
\frac{6}{9} + \frac{x}{9} = \frac{11}{9}
\]

### Step 3: Combine the fractions on the left-hand side
Since the denominators are the same, you can add the numerators:
\[
\frac{6 + x}{9} = \frac{11}{9}
\]

### Step 4: Set the numerators equal to each other
\[
6 + x = 11
\]

### Step 5: Solve for \( x \)
\[
x = 11 - 6 = 5
\]

**Final Answer:** The missing numerator is \( \boxed{5} \).

Would you like further details or have any questions?

### Related Questions:
1. How do you add fractions with different denominators?
2. What steps are involved in solving equations with fractions?
3. How can you check if your solution to a fraction equation is correct?
4. What is the significance of finding a common denominator in fraction problems?
5. How do you solve equations with multiple fractions on each side?

**Tip:** Always make sure the denominators are the same when adding or subtracting fractions, so you can directly combine the numerators.

Learn how to solve the fraction equation 2/3 + x/9 = 11/9 step-by-step. This problem involves adding fractions and solving equations with fractions. Suitable for students in Grades 5-8.

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