Question

Simplify:
$7\frac{1}{2}-\left[2\frac{1}{4}÷\left\{1\frac{1}{4}-\frac{1}{2}\left(\frac{3}{2}-\overline{\frac{1}{3}-\frac{1}{6}}\right)\right\}\right]$

Answer 1

Given expression:
$$\begin{gathered} =7\frac{1}{2}-\left[2\frac{1}{4}÷\left\{1\frac{1}{4}-\frac{1}{2}\left(\frac{3}{2}-\overline{\overline{\frac{1}{3}}-\frac{1}{6}}\right)\right\}\right] \\ =\frac{15}{2}-\left[\frac{9}{4}÷\left\{\frac{5}{4}-\frac{1}{2}\left(\frac{3}{2}-\overline{\overline{\frac{1}{3}}-\frac{1}{6}}\right)\right\}\right] \\ =\frac{15}{2}-\left[\frac{9}{4}÷\left\{\frac{5}{4}-\frac{1}{2}\left(\frac{3}{2}-\frac{1}{6}\right)\right\}\right]\left(\mathrm{Removing}\mathrm{bar}\right) \\ =\frac{15}{2}-\left[\frac{9}{4}÷\left\{\frac{5}{4}-\frac{1}{2}\left(\frac{9-1}{6}\right)\right\}\right] \\ =\frac{15}{2}-\left[\frac{9}{4}÷\left\{\frac{5}{4}-\frac{1}{2}\times \frac{4}{3}\right\}\right]\left(\mathrm{Removing}\mathrm{parentheses}\right) \\ =\frac{15}{2}-\left[\frac{9}{4}÷\left\{\frac{5}{4}-\frac{2}{3}\right\}\right]\left(\mathrm{Removing}\text{'}\times \text{'}\right) \\ =\frac{15}{2}-\left[\frac{9}{4}÷\left\{\frac{15-8}{12}\right\}\right]\left(\mathrm{Removing}\mathrm{braces}\right) \\ =\frac{15}{2}-\left[\frac{9}{4}÷\frac{7}{12}\right] \\ =\frac{15}{2}-\left[\frac{9}{4}\times \frac{12}{7}\right](\mathrm{Removing}\text{'}÷\text{'}) \\ =\frac{15}{2}-\frac{27}{7}\left(\mathrm{Removing}\mathrm{square}\mathrm{brackets}\right) \\ =\frac{105-54}{14}=\frac{51}{14}=3\frac{9}{14} \end{gathered}$$