Let \( x \) be the amount of food Kendall gives to her cat during the rest of the day (morning and afternoon). According to the information given, we can write the equation:
\[ x + \frac{12}{1} = \frac{45}{1} \]
To solve for \( x \), we need to isolate it on one side of the equation:
\[ x = \frac{45}{1} - \frac{12}{1} \]
Now, perform the subtraction:
\[ x = \frac{45 - 12}{1} \] \[ x = \frac{33}{1} \]
Thus, Kendall feeds her cat \( \frac{33}{1} \) cups of food for the rest of the day. In fraction form, the answer is
\[ \frac{33}{1} \] or simply \( 33 \).