To find the number of fields planted with cabbage, we start by calculating \( \frac{1}{12} \) of the total number of fields, which is 32.
To do this calculation:
\[ \text{Number of cabbage fields} = \frac{1}{12} \times 32 \]
Calculating this step-by-step:
- Compute \( 32 \div 12 \):
\[ 32 \div 12 = \frac{32}{12} = \frac{8}{3} \]
So, we can conclude:
\[ \text{Number of cabbage fields} = \frac{8}{3} \]
This represents the number of fields planted with cabbage as a fraction. To express it as a mixed number, we calculate:
\[ \frac{8}{3} = 2 \frac{2}{3} \]
Thus, the final answer is:
\( \frac{8}{3} \) (or \( 2 \frac{2}{3} \) as a mixed number) fields of cabbage were planted.