Subtract 1/6a+3 from 1/3a−5 a. −1/6a+8 b. 1/6a−8 c. −1/6a−2 d. 1/6a−2

The answer is:   [B]:  " ⅙ a − 8 " .

Note:

  (⅓ a  −  5)  −  (⅙ a  +  3) = 
 
       (⅓ a  −  5)  −  1 (⅙ a  +  3)


Note the "distributive property" of multiplication:a(b + c) = ab + ac ;
a(b – c) = ab – ac .So, let us examine the following portion of our expression:

             "  − 1 (⅙ a  +  3)  "  ; 

                    − 1 (⅙ a  +  3) ;

                      =  (-1 * ⅙ a)  +  (-1 * 3)  ;

                      = (-1/1 * ⅙ a)  + (-1 * 3) ;

                      =  -⅙ a + (-3) ;  →  {Note: "Adding a negative" is the same                                                                     thing as "adding a positive".}. 

                      =  -⅙ a – 3 ; 

So, we can rewrite the original equation:

     " (⅓ a  −  5)  −  (⅙ a  +  3) "  ;

as:   →  " ⅓ a  −  5  −  ⅙ a  –  3 " ; 

Change the " (⅓ a)" to "(²/₆ a)" ;  {since "1/3 = (1*2)/ (3*2) = 2/6" } ;

And since we want the TWO (2) "fraction values" in the expression to having "matching denominators" ;

Rewrite as:

           →  " ²/₆ a  −  5  −  ⅙ a  –  3 " ; 

Now, combine the "like terms" ; 

→   ²/₆ a  −  ⅙ a = (2-1)/6  a =  ⅙ a 

→   −5 − 3 = -8 ; 

So we can rewrite the expression as:

→    " ⅙ a − 8 "  ;  which is:  "Answer choice:  [B]:  " ⅙ a − 8 " .

    

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