To find out how many boxes of cereal Jake will eat in a month, we will first determine his rate of cereal consumption.
Jake eats \( \frac{1}{4} \) of a box of cereal in \( \frac{1}{8} \) of a month. We can calculate how much he would eat in a whole month by scaling up from his consumption in \( \frac{1}{8} \) of a month to a full month.
To do this, we need to find out how many \( \frac{1}{8} \) months fit into 1 month:
\[ 1 \text{ month} \div \frac{1}{8} \text{ month} = 8 \]
Now, since Jake eats \( \frac{1}{4} \) of a box during each \( \frac{1}{8} \) month, over 8 such intervals (which represent a whole month), he will eat:
\[ 8 \times \frac{1}{4} = 2 \text{ boxes} \]
Therefore, if Jake continues at this rate, he will eat 2 boxes of cereal in a month.