To find the length of the sandwich that did not have pepperoni on it, we first need to determine the length of the sandwich that did have pepperoni.
The length of the sandwich is \( \frac{11}{12} \) of a foot, and Henry put pepperoni on three-fourths of the sandwich. We can calculate the length of the sandwich with pepperoni by multiplying \( \frac{11}{12} \) by \( \frac{3}{4} \):
\[ \text{Length with pepperoni} = \frac{11}{12} \times \frac{3}{4} \]
To perform the multiplication:
\[ = \frac{11 \times 3}{12 \times 4} = \frac{33}{48} \]
Next, we will find the length of the sandwich that did not have pepperoni on it by subtracting the length with pepperoni from the total length of the sandwich:
\[ \text{Length without pepperoni} = \text{Total length} - \text{Length with pepperoni} \] \[ = \frac{11}{12} - \frac{33}{48} \]
To perform this subtraction, we need a common denominator. The least common multiple of 12 and 48 is 48. We will convert \( \frac{11}{12} \) to have the denominator 48:
\[ \frac{11}{12} = \frac{11 \times 4}{12 \times 4} = \frac{44}{48} \]
Now we can substitute back into the equation:
\[ \text{Length without pepperoni} = \frac{44}{48} - \frac{33}{48} = \frac{44 - 33}{48} = \frac{11}{48} \]
Thus, the length of the sandwich that did not have pepperoni on it is:
\[ \boxed{\frac{11}{48}} \text{ of a foot} \]
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