[tex](1 + 0.12 \div 12) { 12 \times 1 \div 2} - 1 \div 0.12 \div 12 = [/tex]

The answer is:
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" [tex]\frac{4829}{900} [/tex] ";  or, "5[tex] \frac{329}{900} [/tex]" ;
                                   or, write as:  "5.366" .
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Explanation:
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Given:  " (1 + 0.12 ÷ 12)12 * 1 ÷ 2− 1 ÷ 0.12 ÷ 12 = ? " ;
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First, start with the "parentheses" ;
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  "(1 + 0.12 ÷ 12) = ??

Start with the division:  " 0.12 ÷ 12 = 0.01 " .

  "(1 + 0.01)" = (1.01) .

We have:  "1.01 (12) 
Given:  " (1.01)12 * 1 ÷ 2 − 1 ÷ 0.12 ÷ 12 = ? " ;

So, 1.01 * 12 = 12 .12 .
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    " 12.12 * 1 ÷  2 − 1 ÷ 0.12 ÷ 12 = ? " ;

Note:  Using order of operations, treat this problem as:

     " [ (12.12 * 1) ÷  2 ]  −  [ (1 ÷ 0.12) ÷ 12 ] = ? " ;
 
→    ( 12.12 ÷ 2 )  −  (25/3) ÷ 12 ] = ? " ;

→    ( 6.06)  −  { (25/3) * 1/12) }  = ?

→    ( 6.06)  −  { ( 25* 1) / (3*12)  = ?
 
→    ( 6.06)  −  { ( 25* 1) / (3*12)  = ?  

→    ( 6.06)  −  (25/36) ;

→     6 [tex] \frac{6}{100} [/tex]  −  [tex] \frac{25}{36} [/tex]  ;

→  6 [tex] \frac{3}{50} [/tex]   −  [tex] \frac{25}{36} [/tex]  ;

Rewrite " 6 [tex] \frac{3}{50} [/tex] " ; as an improper fraction:  

 →   " 6 [tex] \frac{3}{50}[/tex] "  = "[ (50*6) + 3 ] / 50 = [tex] \frac{303}{50} [/tex] ;
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→  6 [tex] \frac{3}{50} [/tex]   −  [tex] \frac{25}{36} [/tex]  ;

  =  [tex] \frac{303}{50} [/tex]  −  [tex] \frac{25}{36} [/tex] ; 

  = [tex] \frac{(303*36)-(25*50)}{50*36} = \frac{10,908-1250}{1800}[/tex] ;

  =  [tex] \frac{9658}{1800}[/tex] ;  
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→ Divide EACH SIDE of the "fraction" by "2" ; to simplify:
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→   [tex] \frac{9658/2}{1800/2}[/tex] ;
=[tex]\frac{4829}{900} [/tex]  = 5[tex]\frac{329}{900} [/tex] ; or, write as:
                                               
                                       (5 + (329 ÷ 900)   =   →  5.3655555555555556 .
                                                                     → round to:  5.366 .
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