What will come in place of question mark (?) .
`2 1/2 - 5 2/3 + 1 1/5 div 1 1/5 = ?`

Options

A. `(13)/(6)`
B. `- (13)/(6)`
C. `6/(13)`
D. `- 6/(13)`

Answer

To solve the expression \(2 \frac{1}{2} - 5 \frac{2}{3} + \frac{1 \frac{1}{5}}{1 \frac{1}{5}} = ?\), we will follow the order of operations and convert the mixed fractions to improper fractions where necessary.

### Step-by-Step Solution:

1. **Convert Mixed Numbers to Improper Fractions:**
- \(2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}\)
- \(5 \frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{17}{3}\)
- \(1 \frac{1}{5} = \frac{1 \times 5 + 1}{5} = \frac{6}{5}\)

Now the expression becomes:
\[ \frac{5}{2} - \frac{17}{3} + \frac{6}{5} \div \frac{6}{5} \]

2. **Perform the Division:**
- Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{6}{5} \div \frac{6}{5} = 1 \]

So now our expression simplifies to:
\[ \frac{5}{2} - \frac{17}{3} + 1 \]

3. **Convert 1 to a Fraction:**
- \(1 = \frac{2}{2}\)

Now the expression is:
\[ \frac{5}{2} - \frac{17}{3} + \frac{2}{2} \]

4. **Combine the Fractions:**
- To combine these fractions, we need a common denominator. The least common multiple (LCM) of 2 and 3 is 6.
- Convert each fraction:
- \(\frac{5}{2} = \frac{5 \times 3}{2 \times 3} = \frac{15}{6}\)
- \(\frac{17}{3} = \frac{17 \times 2}{3 \times 2} = \frac{34}{6}\)
- \(\frac{2}{2} = \frac{2 \times 3}{2 \times 3} = \frac{6}{6}\)

Now the expression is:
\[ \frac{15}{6} - \frac{34}{6} + \frac{6}{6} \]

5. **Combine the Numerators:**
- Combine the fractions:
\[ \frac{15 - 34 + 6}{6} = \frac{-13}{6} \]

### Final Answer:
The final result is:
\[ ? = -\frac{13}{6} \]