Why don't you use the distributive property when calculating 6/2(1+2)

Question

This equation i an example, for the concept is the same regardless of the numberS:

 

6/2(1+2)

 

If following the order of operations, the equation calculates like this:

 

6/2(1+2)

6/2(3)

you can now implicitly remove the parenthesis and write the equation as:

6/2*3

division and multiplicati are considered equal so you would sold left to right:

3*3

9

 

However, if using the distributive property the equation calculates as follows:

 

6/2(1+2)

6/(2+4)

6/6

1

 

Now my question is, where is the delineation between the two? In what context or real world situation would 9 be the correct answer and in what context ot real world situation would 1 be the correct answer?

 

 

Answer 1

To begin, you do not follow the order of operations.

6/2(1 + 2)

6/2(3)       parenthesis

3(3)          multiplication/division from left to right

9

 

Now perhaps you meant (though did not properly signify)

 

(6/2)(1 + 2)

6/2 + 12/2       distribute

3 + 6

9

 

Answer 2

6/2(1+2)       means    6/2*(1+2)      [the "*" is implied; this is important!]

 

You performed PEMDAS correctly and obtained the answer 9.

 

Using the Distributive Property before performing PEMDAS produces:

       6/2*1 + 6/2*2     [ a*(b+c) = a*b + a*c ]

  Then, using PEMDAS,

        3*1 + 3*2

          3 + 6

             9

Answer 3

Great question. Here is an article that discusses in detail.

 

https://www.theproblemsite.com/ask/2016/12/vinculum-and-bodmas

 

The key is that the line separating the numerator from the denominator of a fraction (called the vinculum) is itself a grouping symbol. 

 

So this problem could be interpreted as:

 

    6

---------

2(1+2)

 

You could divide numerator and denominator by 2 to get:    

 

      3

-----------

   (1+2)

 

Either way the answer is 1 when the "/" is interpreted as a vinculum.

 

However if you did use 6 ÷ 2 (1+2), then the division does take precedence over the multiplication.