Question : Simplify:
$5 \frac{1}{3}-\left\{4 \frac{1}{3}+\left(3 \frac{1}{3} \div \overline{2 \frac{1}{3}-\frac{1}{3}}\right)\right\}$
Option 1: $\frac{2}{3}$
Option 2: $\frac{1}{3}$
Option 3: $-\frac{1}{3}$
Option 4: $-\frac{2}{3}$
Correct Answer: $-\frac{2}{3}$
Solution :
$5 \frac{1}{3}-\left\{4 \frac{1}{3}+\left(3 \frac{1}{3} \div \overline{2 \frac{1}{3}-\frac{1}{3}}\right)\right\}$
$=\frac{16}{3}-\left\{ \frac{13}{3}+\left( \frac{10}{3} \div \overline{\frac{7}{3}-\frac{1}{3}}\right)\right\}$
$=\frac{16}{3}-\left\{ \frac{13}{3}+\left( \frac{10}{3} \div 2\right)\right\}$
$=\frac{16}{3}-\left\{ \frac{13}{3}+( \frac{5}{3})\right\}$
$=-\frac{2}{3}$
Hence, the correct answer is $-\frac{2}{3}$.
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