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How is the above equation equal to 9 with order of operations? Does this calculator not take into account the fact that a 2 positioned next to a () is automatically multiplication?

6/2(2+1) = 9 or 1?  I am getting "1"

 Dec 13, 2016
 #1
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(6 (2 + 1))/(2) = (6 (2 + 1))/2:
(6 (2 + 1))/2

6/2 = (2×3)/2 = 3:
3 (2 + 1)

2 + 1 = 3:
3×3

3×3 = 9:
Answer: |9

 Dec 13, 2016
 #2
avatar+9665 
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6/2(2+1)

= 3(2+1)

= 3(3)

= 9

 Dec 13, 2016
 #4
avatar+14985 
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Place brackets, MaxWrong!

 

then

 

(6/2)(2+1)

= 3(2+1)

= 3(3)

= 9

 

\(\large\frac{6}{2}\times{(2+1)} =9\)

 

\(6/2(2+1)=\large\frac{6}{2\times(2+1)}=1\)

 

Greeting asinus :- )  laugh  !

asinus  Dec 13, 2016
 #3
avatar+14985 
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6/2(2+1) = 9 or 1? I am getting "1"

  

\(\large \frac{6}{2(2+1)}=\frac{6}{4+2}=1\) 

 

laugh  !

 Dec 13, 2016
 #5
avatar+14985 
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MaxWong, excuse me! I've mistyped. Sorry! crying

asinus  Dec 13, 2016
 #6
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So, I am the one originally asking the question, and I am still getting two answers of 9 or 1. 

If order of operations is correct, is it not true that the parenthesis are added first, and then, that answer is automatically multiplied by the number adjacent to it?

 

 

6/ 2(2+1) =

6/ (2 x (2+1)) =

6/ (2 x (3)) =

6/ (6) =

1

 

Is it not true the division would be last in this case, due to the parenthesis and multiplication, which would preeced the function of division?  I understand that in other cases, say, if there were no parenthesis, then the addition would be second to last in order of ops, but that is not the case here, and, the addition inside the parenthesis would come first... PEMDAS?

Parenthesis (which in this cases, houses a sum of numbers), then multiplication, then division... or am I wrong ... has something changed?

  Thanks!

 Dec 13, 2016
 #7
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If you want to avoid any ambiguities such as in this case, then ALWAYS use brackets to make it crystal clear what your intention is. That way, you will not get any arguments. Fair?.

 Dec 13, 2016
 #8
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@Guest

 

In this case, someone posted the problem on social media, so we are trying to clear up what is accurate.  Since I don't have access to the person who posted the problem initially (plus we can't always trust other people's answers), would you not agree that the brackets indicate multiplication, which, in this case, would cause the 3 (from 2+1) to be multiplied by 2 adjacent to it?  Or, is it possible there are two answers, because this equation is ambiguous?  I have always learned that (x)(y) = xy, or that x(y) is xy.  So, from this I have deduced that the division comes last.  I want to settle this once and for all!  Thanks! :)

 Dec 13, 2016
edited by Guest  Dec 13, 2016
 #9
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Here is your problem as originally posed. I entered it in Wolfram/Alpha Computing Engine, which is just about the final arbiter in Math!. Here is the result:

http://www.wolframalpha.com/input/?i=6%2F2(2%2B1)+%3D%3F

Just copy and paste in the address of your Browser.

 Dec 13, 2016
 #10
avatar+14985 
0

\(\large a/2b=\frac{a}{2b}\)

 

so

 

\(\large 6/2(2+1)=\frac{6}{2(2-1)}\)

asinus  Dec 13, 2016

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