From a rope of length $20\dfrac{1}{2}$ m, a piece of length $3\dfrac{5}{8}$ m is cut off. Find the length of the remaining rope.

Total length of rope = $20\dfrac{1}{2}$ m.

Length of piece cut off = $3\dfrac{5}{8}$ m.

Length of remaining rope = $20\dfrac{1}{2} - 3\dfrac{5}{8}$

LCM of 2 and 8 = 8.

$\Rightarrow \dfrac{41}{2} - \dfrac{29}{8}\\[1em] \Rightarrow \dfrac{41 \times 4}{2 \times 4} - \dfrac{29}{8}\\[1em] \Rightarrow \dfrac{164}{8} - \dfrac{29}{8}\\[1em] \Rightarrow \dfrac{164 - 29}{8}\\[1em] \Rightarrow \dfrac{135}{8}\\[1em] \Rightarrow 16\dfrac{7}{8} \text{ m}$

Hence, the length of the remaining rope = $16\dfrac{7}{8}$ m.