`13 1/2-[4 1/2-{3-(2-1/2)}]` is equal to:

Options

A. `9 1/2`
B. `10 1/2`
C. `10 3/4`
D. `13 1/2`

Answer

To solve the expression \( 13 \frac{1}{2} - [4 \frac{1}{2} - \{3 - (2 - \frac{1}{2})\}] \), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Convert Mixed Numbers to Improper Fractions**:
- \( 13 \frac{1}{2} = \frac{27}{2} \) (since \( 13 \times 2 + 1 = 27 \))
- \( 4 \frac{1}{2} = \frac{9}{2} \) (since \( 4 \times 2 + 1 = 9 \))

So, the expression becomes:
\[ \frac{27}{2} - \left[\frac{9}{2} - \{3 - (2 - \frac{1}{2})\}\right] \]

2. **Evaluate the Innermost Bracket**:
- Calculate \( 2 - \frac{1}{2} = \frac{4}{2} - \frac{1}{2} = \frac{3}{2} \)

Now substitute this back into the expression:
\[ \frac{27}{2} - \left[\frac{9}{2} - \{3 - \frac{3}{2}\}\right] \]

3. **Evaluate the Next Bracket**:
- Calculate \( 3 - \frac{3}{2} = \frac{6}{2} - \frac{3}{2} = \frac{3}{2} \)

Now substitute this back into the expression:
\[ \frac{27}{2} - \left[\frac{9}{2} - \frac{3}{2}\right] \]

4. **Simplify the Expression Inside the Brackets**:
- Calculate \( \frac{9}{2} - \frac{3}{2} = \frac{6}{2} = 3 \)

Now substitute this back into the expression:
\[ \frac{27}{2} - 3 \]

5. **Convert 3 to a Fraction**:
- Convert \( 3 \) to a fraction: \( 3 = \frac{6}{2} \)

Now the expression becomes:
\[ \frac{27}{2} - \frac{6}{2} = \frac{27 - 6}{2} = \frac{21}{2} \]

6. **Final Result**:
- The final answer in improper fraction form is \( \frac{21}{2} \).
- If needed in mixed number form, it can be expressed as \( 10 \frac{1}{2} \).