Question

Find the quotient (line over 42 is repeating)

Answer 1

 The correct answer is:  [C]:  " $\frac{21}{11}$ " . 
_____________________________________________________

Explanation:
_____________________________________________________

Let us begin by converting the:  
"0.42 (with the "repeating bar on the digits, "42") " ;  

into a fraction, as follows:
______________________________________________________
   Let  x = 0.42424242424242424242424242424242....

100x = 42.42424242424242424242424242424242....
______________________________________________________
    
         100x = 42.42424242424242424242424242424242....
    –         x =   0.42424242424242424242424242424242...
______________________________________________________
          99x = 42.000000000000000000000000000000.... ;

         →   99x = 42 ;  

Divide each side of the equation by " 99 " ;  
       to isolate "x" on one side of the equation; & to solve for "x" ; 
______________________________________________________
         →  99x / 99 = 42/99 = (42 ÷ 3) / (99 ÷ 3) = 14/ 33; 

         →  x = "$\frac{14}{33}$" .

So;  "0.42 (with a repeating bar over the digits, "42" ;

           is equal to:  "$\frac{14}{33}$" 
________________________________________________
 So, rewrite the question/problem being asked:
________________________________________________
  "Find the quotient:  
________________________________________________
   $\frac{14}{33}$  ÷ $\frac{2}{9}$  ;

=  $\frac{14}{33}$ * $\frac{9}{2}$  ;

Note:  The "14" cancels to a "7" ; and the "2" cancels to a "1" ; 
       →  {since:  " 14 ÷ 2 = 7 " ; and since:  " 2 ÷ 2 = 1 "} ;

Note : The "33" cancels to an "11" ; and the "9" cancels to a "3" ;
        →  {since:  " 33 ÷ 3 = 11 " ; and since:  " 9 ÷ 3 = 3 "} ;

And we can rewrite the problem as:
____________________________________________________
 
 " $\frac{7}{11}$  * $\frac{3}{1}$ "  ;

  =  $\frac{(7*3)}{(11*1}$   =  $\frac{21}{11}$ ; 

            → which is:  Answer choice:  [C]:  " $\frac{21}{11}$ " .
____________________________________________________