To determine how far the caterpillar can crawl in 1 minute, we start with the given rate: the caterpillar crawls \( \frac{1}{2} \) of an inch in \( \frac{1}{4} \) of a minute.
First, we need to find the rate per minute. Since \( \frac{1}{4} \) of a minute is a quarter, we can multiply the distance crawled by how many quarters there are in a minute (which is 4):
\[ \text{Distance in 1 minute} = \frac{1}{2} \text{ inch} \times 4 = 2 \text{ inches} \]
Therefore, the caterpillar can crawl 2 inches in one minute.