From a piece of wire $12\dfrac{3}{4}$ m long, a small piece of length $3\dfrac{5}{6}$ m has been cut off. What is the length of the remaining piece?

Given, total length of wire = $12\dfrac{3}{4}$ m

Piece of wire that has been cut off = $3\dfrac{5}{6}$ m

Remaining piece

$\Rightarrow 12\dfrac{3}{4} - 3\dfrac{5}{6}\\[1em] \Rightarrow \dfrac{51}{4} - \dfrac{23}{6}\\[1em]$

LCM of 4 and 6 = 12

$\Rightarrow \dfrac{51 \times 3}{4 \times 3} - \dfrac{23 \times 2}{6 \times 2}\\[1em] \Rightarrow \dfrac{153}{12} - \dfrac{46}{12}\\[1em] \Rightarrow \dfrac{153 - 46}{12}\\[1em] \Rightarrow \dfrac{107}{12}\\[1em] \Rightarrow 8\dfrac{11}{12}\\[1em]$

Hence, the length of the remaining piece = $8\dfrac{11}{12}$ m.