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!