Maria has a total of \( \frac{3}{4} \) of an hour for her math test, and there are 4 parts to the test. To find out how much time she has to spend on each part, we need to divide the total time by the number of parts.
The calculation can be set up as follows:
\[ \text{Time per part} = \frac{\text{Total time}}{\text{Number of parts}} = \frac{\frac{3}{4}}{4} \]
Dividing by 4 can be expressed as multiplying by the reciprocal of 4, which is \( \frac{1}{4} \):
\[ \text{Time per part} = \frac{3}{4} \times \frac{1}{4} \]
Now, we multiply the fractions:
\[ \text{Time per part} = \frac{3 \times 1}{4 \times 4} = \frac{3}{16} \]
Thus, Maria has \( \frac{3}{16} \) of an hour to spend on each part of the test. Therefore, the answer is:
\[ \boxed{\frac{3}{16}} \]