Let's simplify the expression:

\[
\frac{2}{6} + \frac{4}{18} + \frac{2}{8}
\]

### Step 1: Simplify each fraction.
- \(\frac{2}{6}\) simplifies to \(\frac{1}{3}\) because \(2 \div 2 = 1\) and \(6 \div 2 = 3\).
- \(\frac{4}{18}\) simplifies to \(\frac{2}{9}\) because \(4 \div 2 = 2\) and \(18 \div 2 = 9\).
- \(\frac{2}{8}\) simplifies to \(\frac{1}{4}\) because \(2 \div 2 = 1\) and \(8 \div 2 = 4\).

So, the expression becomes:

\[
\frac{1}{3} + \frac{2}{9} + \frac{1}{4}
\]

### Step 2: Find a common denominator.
The least common denominator (LCD) of 3, 9, and 4 is 36.

Now, convert each fraction to have a denominator of 36:
- \(\frac{1}{3} = \frac{12}{36}\) (because \(1 \times 12 = 12\) and \(3 \times 12 = 36\))
- \(\frac{2}{9} = \frac{8}{36}\) (because \(2 \times 4 = 8\) and \(9 \times 4 = 36\))
- \(\frac{1}{4} = \frac{9}{36}\) (because \(1 \times 9 = 9\) and \(4 \times 9 = 36\))

### Step 3: Add the fractions.
\[
\frac{12}{36} + \frac{8}{36} + \frac{9}{36} = \frac{12 + 8 + 9}{36} = \frac{29}{36}
\]

So, the simplified result is:

\[
\frac{29}{36}
\]

Would you like any more details or have any questions?

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Here are some related questions you might be interested in:
1. How do you find the least common denominator?
2. How can fractions be simplified more quickly?
3. What is the general method for adding fractions with different denominators?
4. How do you convert improper fractions to mixed numbers?
5. How can you add mixed numbers?
6. What is the process for subtracting fractions with unlike denominators?
7. Can you multiply fractions without finding a common denominator?
8. How do you divide fractions?

**Tip:** Always simplify fractions as much as possible before performing arithmetic operations.

Learn how to simplify and add fractions 2/6, 4/18, and 2/8 with a step-by-step solution. Understand the concept of finding a common denominator and adding fractions. Suitable for students in Grades 6-8.

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