\frac{1}{2}-\frac{3}{4}\left(11+5\right)+\frac{1}{4}
To simplify this expression, we can start by simplifying the terms within the parentheses first:
$\frac{1}{2}-\frac{3}{4}(11+5)+\frac{1}{4}=\frac{1}{2}-\frac{3}{4}(16)+\frac{1}{4}$
Next, we simplify the multiplication inside the parentheses:
$\frac{1}{2}-\frac{3(16)}{4}+\frac{1}{4}=\frac{1}{2}-\frac{48}{4}+\frac{1}{4}$
Now, we simplify the subtraction and addition of the fractions:
$\frac{1}{2}-\frac{48}{4}+\frac{1}{4}=\frac{1}{2}-12+\frac{1}{4}$
Next, we need to write the fractions with a common denominator of 4:
$\frac{1}{2}-12+\frac{1}{4}=\frac{2}{4}-\frac{48}{4}+\frac{1}{4}$
Now, we can combine the numerators:
$\frac{2}{4}-\frac{48}{4}+\frac{1}{4}=\frac{2-48+1}{4}$
Finally, we combine the numerators and simplify the expression:
$\frac{2-48+1}{4}=\frac{-45}{4}$
Therefore, $\frac{1}{2}-\frac{3}{4}(11+5)+\frac{1}{4}=\frac{-45}{4}$.