Question

Subtract 1/6a+3 from 1/3a−5

A. −1/6a+8
B. 1/6a−8
C. −1/6a−2
D. 1/6a−2

Answer 1

The answer is: [B]: " ⅙ a − 8 " .
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Note:
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(⅓ a − 5) − (⅙ a + 3) =

(⅓ a − 5) − 1 (⅙ a + 3)

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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:
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" − 1 (⅙ a + 3) " ;
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− 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 ;
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So, we can rewrite the original equation:

" (⅓ a − 5) − (⅙ a + 3) " ;
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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" ;
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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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