To simplify the equation \( \frac{1}{2} (24d + e) \), we start by distributing \( \frac{1}{2} \) to both terms inside the parentheses:
\[ \frac{1}{2} (24d + e) = \frac{1}{2} \cdot 24d + \frac{1}{2} \cdot e \]
Calculating each term:
\[ \frac{1}{2} \cdot 24d = 12d \]
and
\[ \frac{1}{2} \cdot e = \frac{1}{2}e \]
Now, putting it all together, we have:
\[ \frac{1}{2} (24d + e) = 12d + \frac{1}{2} e \]
This means:
- The first blank for \( [__]d \) is 12.
- The second blank for \( [__] \) (numerator) is 1.
- The third blank for \( [__] \) (denominator) is 2.
Therefore, the completed expression is:
\[ \frac{1}{2} (24d + e) = 12d + \frac{1}{2} e \]
This leads us to the answer:
12d + 1/2e, or filling in the blanks:
12, 1, 2.