question_answer

Simplify: \[222-\left[ \frac{1}{3}\left\{ 42+(56-\overline{\text{8+}9})+108 \right\} \right]\]

Answer:

We have \[222-\left[ \frac{1}{3}\left\{ 42+\left( 56-\overline{8+9} \right) \right\}+108 \right]\] \[=222-\left[ \frac{1}{3}\left\{ 42+\left( 56-17 \right) \right\}+108 \right]\]  [Removing vinculum]                                                                                          \[=222-\left[ \frac{1}{3}\left\{ 42+39 \right\}+108 \right]\] [Removing parentheses] \[=222-\left[ \frac{81}{3}+108 \right]\]    [Removing braces]                                                                                               = 222 - [27 + 108] = 222 -135 =87