A cord of length $126\dfrac{1}{2}$ m has been cut into 46 pieces of equal length. What is the length of each piece?

Given, total length of cord = $126\dfrac{1}{2}$ m

Number of pieces = 46

Let x be the length of each piece.

By formula,

Total length = Number of pieces x length of each piece

$\Rightarrow 46 \times x = 126\dfrac{1}{2}\\[1em] \Rightarrow 46 \times x = \dfrac{253}{2} \\[1em] \Rightarrow x = \dfrac{253}{2} ÷ 46\\[1em] \Rightarrow x = \dfrac{253}{2} \times \dfrac{1}{46} \\[1em] \Rightarrow x = \dfrac{253}{46} \times \dfrac{1}{2} \\[1em] \Rightarrow x = \dfrac{253}{92} \\[1em] \Rightarrow x = \dfrac{23 \times 11}{23 \times 4} \\[1em] \Rightarrow x = \dfrac{11}{4} \\[1em] \Rightarrow x = 2\dfrac{3}{4}.$

Hence, the length of each piece = $2\dfrac{3}{4}$ m.