Cake part remaining

We divide the cake into 11 equal parts and eat 2 of them. Then we divide each part of the cake that is left into two more parts and eat another 2 of them. Which part of the cake did we not eat?

Final Answer:

x =  0.2727

Step-by-step explanation:

$$\begin{gathered} a=1-\frac{2}{11}=\frac{1\cdot 11}{11}-\frac{2}{11}=\frac{11}{11}-\frac{2}{11}=\frac{11-2}{11}=\frac{9}{11}\doteq 0.8182 \\ b=a-\frac{1}{11}=\frac{9}{11}-\frac{1}{11}=\frac{9-1}{11}=\frac{8}{11}\doteq 0.7273 \\ x=1-b=1-\frac{8}{11}=\frac{1\cdot 11}{11}-\frac{8}{11}=\frac{11}{11}-\frac{8}{11}=\frac{11-8}{11}=\frac{3}{11}=0.2727 \end{gathered}$$

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