First, we need to round each number to the nearest whole number.
For \( 11 \frac{1}{2} \):
- \( \frac{1}{2} \) is equal to 0.5, which means \( 11 \frac{1}{2} \) is approximately 12 when rounded to the nearest whole number.
For \( 2 \frac{5}{7} \):
- \( \frac{5}{7} \) is approximately 0.714, which means \( 2 \frac{5}{7} \) is approximately 3 when rounded to the nearest whole number.
Now we subtract the rounded values: \[ 12 - 3 = 9 \]
Therefore, the approximate difference is 9.