Mom cake remainder

Mom baked cakes. She set aside a third of them for her father. She left the rest on the table. Rick came and ate a third of the cakes that were on the table. What fraction of all the cakes was left on the table? Write the result in fractions.

Final Answer:

x =  4/9

Step-by-step explanation:

$$\begin{gathered} o=1-\frac{1}{3}=\frac{1\cdot 3}{3}-\frac{1}{3}=\frac{3}{3}-\frac{1}{3}=\frac{3-1}{3}=\frac{2}{3}\doteq 0.6667 \\ r=\frac{1}{3}\cdot o=\frac{1}{3}\cdot \frac{2}{3}=\frac{1\cdot 2}{3\cdot 3}=\frac{2}{9}\doteq 0.2222 \\ x=o-r=\frac{2}{3}-\frac{2}{9}=\frac{6}{9}-\frac{2}{9}=\frac{6-2}{9}=\frac{4}{9}=0.4444 \end{gathered}$$

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