In order to find which rational number is between 0 and 1, let's convert them into their decimal form:
[tex]\begin{gathered} \text{negative one-half:} \\ -\frac{1}{2}=-0.5 \\ \\ \text{one}-\text{fourth:} \\ \frac{1}{4}=0.25 \\ \\ \text{three}-\text{halves:} \\ 3\cdot\frac{1}{2}=\frac{3}{2}=1.5 \\ \\ 1.75 \end{gathered}[/tex]Looking at the numbers in their decimal form, we can see that the number between 0 and 1 is one-fourth, therefore the correct option is the second one.