Question
Simplify: $2 \frac{3}{4}-\left[3 \frac{1}{8} \div\left\{5-\left(4 \frac{2}{3}-\frac{11}{12}\right)\right\}\right]$
✓
Answer
$\begin{aligned} & 2 \frac{3}{4}-\left[3 \frac{1}{8} \div\left\{5-\left(4 \frac{2}{3}-\frac{11}{12}\right)\right\}\right] \\ & =\frac{11}{4}-\left[\frac{25}{8} \div\left\{5-\left(\frac{14}{3}-\frac{11}{12}\right)\right\}\right] \\ & =\frac{11}{4}-\left[\frac{25}{8} \div\left\{5-\left(\frac{56-11}{12}\right)\right\}\right] \\ & =\frac{11}{4}-\left[\frac{25}{8} \div\left\{5-\frac{45}{12}\right\}\right] \\ & =\frac{11}{4}-\left[\frac{25}{8} \div\left\{\frac{60-45}{12}\right\}\right] \\ & =\frac{11}{4}-\left[\frac{25}{8} \div \frac{15}{12}\right]=\frac{11}{4}-\left[\frac{25}{8} \times \frac{12}{15}\right] \\ & =\frac{11}{4}-\frac{5}{2}=\frac{11-10}{4}=\frac{1}{4}\end{aligned}$
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