The product of three numbers is $7\dfrac{1}{2}$. If two of them are $1\dfrac{1}{7}$ and $3\dfrac{3}{4}$, find the third number.

Given, product of three numbers = $7\dfrac{1}{2}$

Two numbers = $1\dfrac{1}{7}$ and $3\dfrac{3}{4}$

Let the other number be x.

$\Rightarrow 1\dfrac{1}{7} \times 3\dfrac{3}{4} \times x = 7\dfrac{1}{2}\\[1em] \Rightarrow \dfrac{8}{7} \times \dfrac{15}{4} \times x = \dfrac{15}{2}\\[1em] \Rightarrow \dfrac{8 \times 15}{7 \times 4} \times x = \dfrac{15}{2}\\[1em] \Rightarrow \dfrac{120}{28} \times x = \dfrac{15}{2}\\[1em] \Rightarrow x = \dfrac{15 \times 28}{2 \times 120}\\[1em] \Rightarrow x = \dfrac{420}{240}\\[1em] \Rightarrow x = \dfrac{7}{4}\\[1em] \Rightarrow x = 1\dfrac{3}{4}.$

Hence, the third number = $1\dfrac{3}{4}$.