Solve the following proportion for x 6/7 = 48/x

The answer is:  " x = 56 " .
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Given :  " 6/7 = 48/x ;  Solve for "x" ;

Method 1):   "Cross multiply" ;

6x = 7 * 48 ;

6x = 336 ;

Divide each side by "6" ;  as follows:
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 6x / 6 = 336 / 6 ;
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to get:
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   x = 56 .
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Method 2):   Given:  " 6/7 = 48/x " ; Solve for "x" ;
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  Cross-multiply:
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                    6x = 7 * 48 ;
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  Now, divide EACH SIDE of the equation by "6" ;  
    to isolate "x" on one side of the equation; 
 & to solve for "x" ;
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                      6x = 7 * 48 ;
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Divide EACH side of the equation by "6" :
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→    =   ;
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On the "left-hand side" of the equation, the "6 's " cancel out to "1" ; 

{since:  (6÷6=1) ; & we are left with "x" on the left-hand side of the equation} ;

On the "right-hand side" of the equation; the "48" in the denominator

  cancels out to an "8" ; and the "6" cancels to a "1" ; 

{since: (48÷6=8); & (6÷6=1) ; and the denominator gets "eliminated"; 

{since the denominator is equal to "1" ;

    & any value (including the numerator),  divided by "1" (the denominator),

  is equal to that same value (the numerator);

so there is no need for the "denominator".
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We can rewrite the equation as:

        x = 7 * 8 ; and solve;  →   7 * 8 = 56 ;

          →  x = 56 .
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Method 3):  Given:  " 6/7 = 48/x " ; Solve for "x" ;
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    →  6/7 = 48/x ;  

   → Comparing the "numerators" ;  " [ 6 * (what value?)  = 48 ?] " ??

                                                      → [ (48 ÷ 6 = (what value?) ] ??
                                         
                                                      →   48 ÷ 6 = 8 /

→ So:  "6/7" = (6*8) / (7*8) = 48/56 = 48/ x ??  ;
   
                                                          → x = 56 .
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