How many pieces, each of length $2\dfrac{3}{4}$m, can be cut from a rope of length 66 m ?

Given:

Total length of rope = 66 m

Length of each piece = $2\dfrac{3}{4}$ m = $\dfrac{11}{4}$ m

Number of pieces = ?

Number of pieces = (Total length ÷ length of each piece)

Substituting the values in above, we get:

Number of pieces = 66 m ÷ $\dfrac{11}{4}$ m

$= \dfrac{66}{1} \times \dfrac{4}{11} \quad \left[\text{Reciprocal of }\dfrac{11}{4} \text{ is } \dfrac{4}{11}\right] \\[1em] = \dfrac{6}{1} \times \dfrac{4}{1} \quad \text{[Dividing 66 by 11]} \\[1em] = \dfrac{6 \times 4}{1 \times 1} \\[1em] = \dfrac{24}{1} = 24$

Hence, 24 pieces can be cut from the rope.