How many pieces of length $3\dfrac{5}{7}$m each can be cut from a wall paper 52 m long?

Given:

Piece length = $3\dfrac{5}{7}$ m = $\dfrac{26}{7}$ m $\hspace{1.5cm}\text{[Converting mixed to improper fraction]}$

Total length = 52 m

Number of pieces = ?

Number of pieces = (Total length) ÷ (Piece length)

Substituting the values in above, we get:

Number of pieces = 52 m ÷ $\dfrac{26}{7}$ m

$\begin{array}{ll} = \Big(\dfrac{52}{1} \times \dfrac{7}{26}\Big) & [\text{Reciprocal of } \dfrac{26}{7} \text{ is } \dfrac{7}{26}] \\ = \Big(\dfrac{2}{1} \times \dfrac{7}{1}\Big) & \text{[Simplifying 52 and 26 ⇒ Divide by 26]} \\ = \Big(\dfrac{2 \times 7}{1 \times 1}\Big) \\ = \dfrac{14}{1} \\ = 14 \end{array}$

∴ Number of pieces = 14