Evaluate: a. `8 (2)/(7) + 11 (5)/(7) + 2 (1)/(7)`

Answer

To evaluate the expression \( 8 \frac{2}{7} + 11 \frac{5}{7} + 2 \frac{1}{7} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert each mixed number into an improper fraction.

1. **For \( 8 \frac{2}{7} \)**:
\[ 8 \frac{2}{7} = \frac{8 \times 7 + 2}{7} = \frac{56 + 2}{7} = \frac{58}{7} \]

2. **For \( 11 \frac{5}{7} \)**:
\[ 11 \frac{5}{7} = \frac{11 \times 7 + 5}{7} = \frac{77 + 5}{7} = \frac{82}{7} \]

3. **For \( 2 \frac{1}{7} \)**:
\[ 2 \frac{1}{7} = \frac{2 \times 7 + 1}{7} = \frac{14 + 1}{7} = \frac{15}{7} \]

### Step 2: Add the Improper Fractions
Now we can add the three improper fractions together:
\[ \frac{58}{7} + \frac{82}{7} + \frac{15}{7} \]

Since they all have the same denominator, we can add the numerators directly:
\[ = \frac{58 + 82 + 15}{7} = \frac{155}{7} \]

### Step 3: Final Answer
The final answer is:
\[ \frac{155}{7} \]