Question : The value of $1 \frac{2}{5}-\left[3 \frac{3}{4} \div\left\{1 \frac{1}{4} \div \frac{1}{2}\left(1 \frac{1}{2} \times 3 \frac{1}{3} \div 1 \frac{1}{3}\right)\right\}\right]$ is:
Option 1: 3
Option 2: 0
Option 3: 2
Option 4: 1
Correct Answer: 1
Solution :
Given: $1 \frac{2}{5}-\left[3 \frac{3}{4} \div\left\{1 \frac{1}{4} \div \frac{1}{2}\left(1 \frac{1}{2} \times 3 \frac{1}{3} \div 1 \frac{1}{3}\right)\right\}\right]$
$=\frac{7}{5}-[\frac{15}{4} \div{\{\frac{5}{4} \div \frac{1}{2}(\frac{3}{2} \times \frac{10}{3} \div \frac{4}{3})}\}]$
$=\frac{7}{5}-[\frac{15}{4} \div{\{\frac{5}{4} \div \frac{1}{2}(\frac{3}{2} \times \frac{10}{3} \times \frac{3}{4})}\}]$
$= \frac{7}{5}-[\frac{15}{4} \div{\{\frac{5}{4} \div \frac{1}{2}\times\frac{15}{4}}\}]$
$= \frac{7}{5}-[\frac{15}{4} \div{\{\frac{5}{2} × \frac{15}{4}}\}]$
$= \frac{7}{5}-[\frac{15}{4} \div\frac{75}{8}]$
$= \frac{7}{5}-\frac{2}{5}$
$= \frac{5}{5}$
$= 1$
Hence, the correct answer is 1.
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