The sum of `5/11` and `11/5` is:

Options

A. `16/55`
B. `110/55`
C. `146/55`
D. `16/16`

Answer

To find the sum of the fractions \( \frac{5}{11} \) and \( \frac{11}{5} \), we can follow these steps:

### Step 1: Identify the fractions
We have two fractions:
1. \( \frac{5}{11} \)
2. \( \frac{11}{5} \)

### Step 2: Find a common denominator
To add the fractions, we need a common denominator. The denominators are 11 and 5. The least common multiple (LCM) of 11 and 5 is 55.

### Step 3: Convert each fraction to have the common denominator
Now, we convert each fraction:
- For \( \frac{5}{11} \):
\[ \frac{5}{11} = \frac{5 \times 5}{11 \times 5} = \frac{25}{55} \]

- For \( \frac{11}{5} \):
\[ \frac{11}{5} = \frac{11 \times 11}{5 \times 11} = \frac{121}{55} \]

### Step 4: Add the fractions
Now that both fractions have the same denominator, we can add them:
\[ \frac{25}{55} + \frac{121}{55} = \frac{25 + 121}{55} = \frac{146}{55} \]

### Step 5: Simplify the result (if necessary)
The fraction \( \frac{146}{55} \) cannot be simplified further as 146 and 55 have no common factors other than 1.

### Final Answer
Thus, the sum of \( \frac{5}{11} \) and \( \frac{11}{5} \) is:
\[ \frac{146}{55} \]

---