To find Jake's rate of reading in books per month, we first need to convert the time he took to read the books into months.
Jake read 19 books in \( \frac{19}{6} \) months.
Now, we can calculate his reading rate by dividing the number of books by the number of months:
\[ \text{Rate} = \frac{\text{Number of books}}{\text{Number of months}} = \frac{19}{\frac{19}{6}} \]
To divide by a fraction, we multiply by its reciprocal:
\[ \text{Rate} = 19 \times \frac{6}{19} = 6 \]
Therefore, Jake's rate of reading is 6 books per month.