Question

Simplify:

\[4\frac{4}{5} \div \left\{ 2\frac{1}{5} - \frac{1}{2}\left( 1\frac{1}{4} - \overline{\frac{1}{4} - \frac{1}{5}} \right) \right\}\]

Answer 1

Given expression:

\[= 4\frac{4}{5} \div \left\{ 2\frac{1}{5} - \frac{1}{2}\left( 1\frac{1}{4} -\overline{ \frac{\overline{1}}{4} - \frac{1}{5}}\right) \right\}\]
\[ = \frac{24}{5} \div \left\{ \frac{11}{5} - \frac{1}{2}\left( \frac{5}{4} -\overline{ \frac{\overline{1}}{4} - \frac{1}{5}} \right) \right\} \]
\[ = \frac{24}{5} \div \left\{ \frac{11}{5} - \frac{1}{2}\left( \frac{5}{4} - \frac{1}{20} \right) \right\} \left(\text{ Removing bar }\right) \]
\[ = \frac{24}{5} \div \left\{ \frac{11}{5} - \frac{1}{2}\left( \frac{25 - 1}{20} \right) \right\} \]
\[ = \frac{24}{5} \div \left\{ \frac{11}{5} - \frac{1}{2} \times \frac{24}{20} \right\} \left(\text{ Removing parentheses} \right)\]
\[ = \frac{24}{5} \div \left\{ \frac{11}{5} - \frac{12}{20} \right\} \left(\text{ Removing }' \times ' \right) \]
\[ = \frac{24}{5} \div \left\{ \frac{44 - 12}{20} \right\} \]
\[ = \frac{24}{5} \div \frac{32}{20} \left(\text{ Removing braces }\right) \]
\[ = \frac{24}{5} \times \frac{20}{32} (\text{ Removing }' \div ')\]
\[ = \frac{3}{4} \times 4 = 3 \]