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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: $-\frac{2}{3}$


Team Careers360 24th Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

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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