解:先判断各绝对值内式子的正负性,去掉绝对值符号:
因为$\dfrac{1}{5}<\dfrac{150}{557},$所以$\left|\dfrac{1}{5}-\dfrac{150}{557}\right|=\dfrac{150}{557}-\dfrac{1}{5};$
因为$\dfrac{150}{557}<\dfrac{1}{2},$所以$\left|\dfrac{150}{557}-\dfrac{1}{2}\right|=\dfrac{1}{2}-\dfrac{150}{557};$
$\left|-\dfrac{1}{2}\right|=\dfrac{1}{2}。$
将上述结果代入原式:
$\begin{aligned}&\mathrm{原式}\\=&(\dfrac{150}{557}-\dfrac{1}{5})+(\dfrac{1}{2}-\dfrac{150}{557})-\dfrac{1}{2}\\=&\dfrac{150}{557}-\dfrac{1}{5}+\dfrac{1}{2}-\dfrac{150}{557}-\dfrac{1}{2}\\=&-\dfrac{1}{5}\end{aligned}$