Simplify the following expression.
$4 ÷[2 + 2 ÷ \begin{Bmatrix}2 + 2 ÷ (2 + \frac{2}{3})\end{Bmatrix}]$
Answer & explanation
Correct answer: option 3
$4 ÷[2 + 2 ÷ \begin{Bmatrix}2 + 2 ÷ (2 + \frac{2}{3})\end{Bmatrix}]$
= $4 ÷[2 + 2 ÷ \begin{Bmatrix}2 + 2 ÷ (\frac{8}{3})\end{Bmatrix}]$
= $4 ÷[2 + 2 ÷ \frac{11}{4}$]
= $4 ÷[2 + \frac{8}{11}]$
= $4 ÷[\frac{30}{11}]$
= $\frac{22}{15}$