Question

Simplify:

\[4\frac{1}{10} - \left[ 2\frac{1}{2} - \left\{ \frac{5}{6} - \left( \frac{2}{5} + \frac{3}{10} - \frac{4}{15} \right) \right\} \right]\]

Answer 1

Given expression:

\[= 4\frac{1}{10} - \left[ 2\frac{1}{2} - \left\{ \frac{5}{6} - \left( \frac{2}{5} + \frac{3}{10} - \frac{4}{15} \right) \right\} \right] \]
\[ = \frac{41}{10} - \left[ \frac{5}{2} - \left\{ \frac{5}{6} - \left( \frac{2}{5} + \frac{3}{10} - \frac{4}{15} \right) \right\} \right] \]
\[ = \frac{41}{10} - \left[ \frac{5}{2} - \left\{ \frac{5}{6} - \left( \frac{12 + 9 - 8}{30} \right) \right\} \right] \]
\[ = \frac{41}{10} - \left[ \frac{5}{2} - \left\{ \frac{5}{6} - \frac{13}{30} \right\} \right] \left(\text{Removing parentheses }\right)\]
\[ = \frac{41}{10} - \left[ \frac{5}{2} - \left\{ \frac{25 - 13}{30} \right\} \right] \]
\[ = \frac{41}{10} - \left[ \frac{5}{2} - \frac{12}{30} \right] \left( \text{Removing braces }\right)\]
\[ = \frac{41}{10} - \left[ \frac{75 - 12}{30} \right] \]
\[ = \frac{41}{10} - \frac{63}{30} (\text{Removing square brackets})\]
\[ = \frac{123 - 63}{30} = \frac{60}{30} = 2 \]