Question : The value of $2 \frac{3}{5} \div\left[2 \frac{1}{3} \div\left\{4 \frac{1}{3}-\left(2 \frac{1}{2}+\frac{2}{3}\right)\right\}\right]$ is equal to:
Option 1: $1 \frac{3}{10}$
Option 2: $2 \frac{7}{10}$
Option 3: $2 \frac{3}{7}$
Option 4: $1 \frac{3}{7}$
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Correct Answer: $1 \frac{3}{10}$
Solution :
$2 \frac{3}{5} \div[2 \frac{1}{3} \div\{4 \frac{1}{3}-(2 \frac{1}{2}+\frac{2}{3})\}]$
$= 2 \frac{3}{5} \div[2 \frac{1}{3} \div\{4 \frac{1}{3}-(\frac{5}{2}+\frac{2}{3})\}]$
$= 2 \frac{3}{5} \div[2 \frac{1}{3} \div\{4 \frac{1}{3}-(\frac{15+4}{6})\}]$
$= 2 \frac{3}{5} \div[2 \frac{1}{3} \div\{\frac{13}{3}-\frac{19}{6}\}]$
$= 2 \frac{3}{5} \div[2 \frac{1}{3} \div\{\frac{26-19}{6}\}]$
$= 2 \frac{3}{5} \div[\frac{7}{3} \div\frac{7}{6}]$
$= 2 \frac{3}{5} \div[\frac{7}{3} \times\frac{6}{7}]$
$= \frac{13}{5} \div 2$
$= \frac{13}{5} \times \frac{1}{2}$
$= \frac{13}{10}$
$= 1\frac{3}{10}$
Hence, the correct answer is $1\frac{3}{10}$.
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