To add the fractions \( \frac{1}{4} \) and \( \frac{3}{2} \), we first need a common denominator. The least common denominator (LCD) for 4 and 2 is 4.
Next, we convert \( \frac{3}{2} \) to have a denominator of 4:
\[ \frac{3}{2} = \frac{3 \times 2}{2 \times 2} = \frac{6}{4} \]
Now we can add the fractions:
\[ \frac{1}{4} + \frac{6}{4} = \frac{1 + 6}{4} = \frac{7}{4} \]
Thus,
\[ \frac{1}{4} + \frac{3}{2} = \frac{7}{4} \]
This can also be written as a mixed number:
\[ 1 \frac{3}{4} \]
So the final answer is \( \frac{7}{4} \) or \( 1 \frac{3}{4} \).