To solve the expression \( \frac{1}{3} + \frac{11}{36} + \frac{5}{7} \), we first need to find a common denominator. The denominators are 3, 36, and 7.

### Step-by-Step Solution:

1. **Find the Least Common Denominator (LCD):**
   - The prime factors of 3 are \(3\).
   - The prime factors of 36 are \(2^2 \times 3^2\).
   - The prime factors of 7 are \(7\).

   The LCD is the product of the highest powers of all prime factors involved:
   \[
   \text{LCD} = 2^2 \times 3^2 \times 7 = 4 \times 9 \times 7 = 252
   \]

2. **Convert each fraction to have the LCD as the denominator:**

   \[
   \frac{1}{3} = \frac{1 \times 84}{3 \times 84} = \frac{84}{252}
   \]

   \[
   \frac{11}{36} = \frac{11 \times 7}{36 \times 7} = \frac{77}{252}
   \]

   \[
   \frac{5}{7} = \frac{5 \times 36}{7 \times 36} = \frac{180}{252}
   \]

3. **Add the fractions:**

   \[
   \frac{84}{252} + \frac{77}{252} + \frac{180}{252} = \frac{84 + 77 + 180}{252} = \frac{341}{252}
   \]

4. **Simplify the fraction if possible:**

   The greatest common divisor (GCD) of 341 and 252 is 1, so the fraction \(\frac{341}{252}\) is already in its simplest form.

### Final Answer:
\[
\frac{1}{3} + \frac{11}{36} + \frac{5}{7} = \frac{341}{252}
\]

Would you like more details or have any questions? Here are some related questions to consider:

1. How do you find the least common denominator (LCD) of multiple fractions?
2. What is the process for converting fractions to have the same denominator?
3. Can you explain how to add fractions with different denominators?
4. How do you simplify a fraction to its lowest terms?
5. What are prime factors and how do you find them?
6. Why is it important to find a common denominator when adding fractions?
7. How can you check if your answer is correct when adding fractions?
8. Can you solve \( \frac{2}{5} + \frac{3}{10} + \frac{4}{15} \)?

**Tip:** When working with fractions, always remember to simplify your final answer if possible by finding the greatest common divisor (GCD) of the numerator and the denominator.

Learn how to add fractions 1/3, 11/36, and 5/7 with a step-by-step solution. Find the least common denominator, convert fractions, add them, and simplify the result. Suitable for Grades 6-8.

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