First, let's round each number to the nearest whole number.
For 11, the nearest whole number is \(11\).
For 1.257, the nearest whole number is \(1\).
For 2.567, the nearest whole number is \(3\).
Now, we can perform the subtraction using the rounded numbers:
\[ 11 + 1 - 3 \]
Calculating the expression:
\[ 11 + 1 = 12 \] \[ 12 - 3 = 9 \]
So, the approximate difference is \(9\).