Question

Simplify:

\[1\frac{5}{6} + \left[ 2\frac{2}{3} - \left\{ 3\frac{3}{4} \left( 3\frac{4}{5} \div 9\frac{1}{2} \right) \right\} \right]\]

Answer 1

Given expression:

\[= 1\frac{5}{6} + \left[ 2\frac{2}{3} - \left\{ 3\frac{3}{4} \left( 3\frac{4}{5} \div 9\frac{1}{2} \right) \right\} \right] \]
\[ = \frac{11}{6} + \left[ \frac{8}{3} - \left\{ \frac{15}{4} \left( \frac{19}{5} \div \frac{19}{2} \right) \right\} \right] \]
\[ = \frac{11}{6} + \left[ \frac{8}{3} - \left\{ \frac{15}{4} \left( \frac{19}{5} \times \frac{2}{19} \right) \right\} \right] \]
\[ = \frac{11}{6} + \left[ \frac{8}{3} - \left\{ \frac{15}{4} \times \frac{2}{5} \right\} \right] \left(\text{ Removing parentheses }\right)\]
\[ = \frac{11}{6} + \left[ \frac{8}{3} - \frac{3}{2} \right] \left( \text{Removing braces} \right) \]
\[ = \frac{11}{6} + \left[ \frac{16 - 9}{6} \right] \]
\[ = \frac{11}{6} + \frac{7}{6} (\text{Removing square brackets})\]
\[ = \frac{18}{6} = 3 \]