To add the fractions \( \frac{5}{9} + \frac{2}{22} + \frac{15}{33} \), you need to find a common denominator. Here are the steps:

### Step 1: Simplify the fractions
We already simplified the fractions:
- \( \frac{5}{9} \) (already simplified)
- \( \frac{2}{22} = \frac{1}{11} \)
- \( \frac{15}{33} = \frac{5}{11} \)

### Step 2: Find the Least Common Denominator (LCD)
The denominators are 9 and 11 (since \( \frac{1}{11} \) and \( \frac{5}{11} \) share the same denominator).

The LCD of 9 and 11 is \( 9 \times 11 = 99 \).

### Step 3: Convert each fraction to have the LCD as the denominator
1. Convert \( \frac{5}{9} \):
   \[
   \frac{5}{9} = \frac{5 \times 11}{9 \times 11} = \frac{55}{99}
   \]

2. Convert \( \frac{1}{11} \):
   \[
   \frac{1}{11} = \frac{1 \times 9}{11 \times 9} = \frac{9}{99}
   \]

3. Convert \( \frac{5}{11} \):
   \[
   \frac{5}{11} = \frac{5 \times 9}{11 \times 9} = \frac{45}{99}
   \]

### Step 4: Add the fractions
Now add the fractions:
\[
\frac{55}{99} + \frac{9}{99} + \frac{45}{99} = \frac{55 + 9 + 45}{99} = \frac{109}{99}
\]

### Step 5: Simplify if possible
Since \( \frac{109}{99} \) is already in its simplest form, the result is:
\[
\frac{109}{99} \text{ or } 1 \frac{10}{99}
\]

Would you like more details or have any questions?

Here are some related questions you might consider:

1. How do you add fractions with unlike denominators?
2. What is the least common multiple (LCM), and how is it used in fraction addition?
3. How do you convert improper fractions to mixed numbers?
4. How do you simplify complex fractions?
5. What are other methods for finding a common denominator?

**Tip:** When adding fractions with different denominators, always find the least common denominator to make the process easier and ensure the fractions can be added correctly.

Learn how to add fractions \( \frac{5}{9} + \frac{2}{22} + \frac{15}{33} \) with a step-by-step solution. Understand the concept of finding a common denominator and simplifying fractions. Suitable for students in Grades 6-8.

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