Question

Simplify:
$4\frac{4}{5}÷\left\{2\frac{1}{5}-\frac{1}{2}\left(1\frac{1}{4}-\overline{\frac{1}{4}-\frac{1}{5}}\right)\right\}$

Answer 1

Given expression:
$$\begin{gathered} =4\frac{4}{5}÷\left\{2\frac{1}{5}-\frac{1}{2}\left(1\frac{1}{4}-\overline{\overline{\frac{1}{4}}-\frac{1}{5}}\right)\right\} \\ =\frac{24}{5}÷\left\{\frac{11}{5}-\frac{1}{2}\left(\frac{5}{4}-\overline{\overline{\frac{1}{4}}-\frac{1}{5}}\right)\right\} \\ =\frac{24}{5}÷\left\{\frac{11}{5}-\frac{1}{2}\left(\frac{5}{4}-\frac{1}{20}\right)\right\}\left(\mathrm{Removing}\mathrm{bar}\right) \\ =\frac{24}{5}÷\left\{\frac{11}{5}-\frac{1}{2}\left(\frac{25-1}{20}\right)\right\} \\ =\frac{24}{5}÷\left\{\frac{11}{5}-\frac{1}{2}\times \frac{24}{20}\right\}\left(\mathrm{Removing}\mathrm{parentheses}\right) \\ =\frac{24}{5}÷\left\{\frac{11}{5}-\frac{12}{20}\right\}\left(\mathrm{Removing}\text{'}\times \text{'}\right) \\ =\frac{24}{5}÷\left\{\frac{44-12}{20}\right\} \\ =\frac{24}{5}÷\frac{32}{20}\left(\mathrm{Removing}\mathrm{braces}\right) \\ =\frac{24}{5}\times \frac{20}{32}(\mathrm{Removing}\text{'}÷\text{'}) \\ =\frac{3}{4}\times 4=3 \end{gathered}$$