To solve the sum of the fractions \( \frac{5}{12} + \frac{9}{11} \), we need to find a common denominator.

### Step-by-Step Solution:

1. **Find the Least Common Denominator (LCD):**

   The denominators are 12 and 11. The least common denominator (LCD) of 12 and 11 is \( 12 \times 11 = 132 \).

2. **Convert Fractions to Have the Same Denominator:**

   \[
   \frac{5}{12} = \frac{5 \times 11}{12 \times 11} = \frac{55}{132}
   \]
   \[
   \frac{9}{11} = \frac{9 \times 12}{11 \times 12} = \frac{108}{132}
   \]

3. **Add the Fractions:**

   Now, we add the fractions:

   \[
   \frac{55}{132} + \frac{108}{132} = \frac{55 + 108}{132} = \frac{163}{132}
   \]

4. **Simplify the Fraction (if needed):**

   Since 163 and 132 have no common factors other than 1, the fraction is already in its simplest form.

5. **Convert to Mixed Number:**

   \[
   \frac{163}{132} = 1 \frac{31}{132}
   \]

### Final Answer:

\[
\frac{5}{12} + \frac{9}{11} = \frac{163}{132} \text{ or } 1 \frac{31}{132}
\]

Would you like more details on this, or do you have any other questions?

### Related Questions:

1. How do you find the least common denominator for two fractions?
2. What are the steps for converting an improper fraction to a mixed number?
3. How do you simplify fractions to their lowest terms?
4. How can you add fractions with different denominators quickly?
5. What is the difference between a proper and an improper fraction?

**Tip:** Always check if the fraction can be simplified to its lowest terms to make calculations easier!

Learn how to add fractions with different denominators by solving the problem 5/12 + 9/11. This guide includes a step-by-step solution involving the least common denominator (LCD) and fraction addition. Suitable for students in Grades 6-8.

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