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To solve the given problem, we need to add the mixed numbers \(2 \frac{6}{15}\) and \(2 \frac{2}{3}\), and express the result as a mixed number in its simplest form.

### Step 1: Convert the Mixed Numbers to Improper Fractions
1. Convert \(2 \frac{6}{15}\) to an improper fraction:
   \[
   2 \frac{6}{15} = \frac{2 \times 15 + 6}{15} = \frac{30 + 6}{15} = \frac{36}{15}
   \]

2. Convert \(2 \frac{2}{3}\) to an improper fraction:
   \[
   2 \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}
   \]

### Step 2: Find the Least Common Denominator (LCD)
The denominators are 15 and 3. The least common denominator of 15 and 3 is 15.

### Step 3: Convert Fractions to Equivalent Fractions with the LCD
1. \(\frac{36}{15}\) is already with denominator 15.
2. Convert \(\frac{8}{3}\) to a fraction with denominator 15:
   \[
   \frac{8}{3} \times \frac{5}{5} = \frac{40}{15}
   \]

### Step 4: Add the Fractions
Now, add the fractions:
\[
\frac{36}{15} + \frac{40}{15} = \frac{36 + 40}{15} = \frac{76}{15}
\]

### Step 5: Convert the Improper Fraction Back to a Mixed Number
\(\frac{76}{15}\) as a mixed number is:
\[
76 \div 15 = 5 \text{ remainder } 1 \quad \text{so,} \quad \frac{76}{15} = 5 \frac{1}{15}
\]

Thus, the answer is \(5 \frac{1}{15}\) in its simplest form.

Would you like more details or have any questions?

### Related Questions
1. How do you convert mixed numbers to improper fractions?
2. How do you find the least common denominator of two fractions?
3. How can you simplify an improper fraction to a mixed number?
4. What are some strategies for adding fractions with different denominators?
5. How do you simplify fractions to their simplest form?

**Tip:** Always check if your final answer can be simplified further to ensure it is in its simplest form!

Calculate 2 6/15 + 2 2/3. Give your answer as a mixed number in its simplest form.

Learn how to add the mixed numbers 2 6/15 and 2 2/3 and express the result as a mixed number in its simplest form. The solution covers converting mixed numbers to improper fractions, finding a common denominator, and simplifying the answer.

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