To solve the given mixed number addition problem, we need to first convert the mixed number to an improper fraction. Then, we add the two fractions together and simplify the result if possible.
Step 1: Convert the Mixed Number to an Improper Fraction
The mixed number \( 11 \frac{5}{12} \) can be converted to an improper fraction:
\[
11 \frac{5}{12} = 11 + \frac{5}{12} = \frac{11 \times 12 + 5}{12} = \frac{132 + 5}{12} = \frac{137}{12}
\]
Step 2: Add the Fractions
Now, add the improper fraction \(\frac{137}{12}\) to \(\frac{1}{12}\):
\[
\frac{137}{12} + \frac{1}{12} = \frac{137 + 1}{12} = \frac{138}{12}
\]