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6 divided by 2(1+2)=?

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This was shared on my facebook. Apparently a lot of people get the answer wrong. I'm almost sure the answer is 9. Can anyone confirm this or tell me otherwise?

 

tia.

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Order of operations, BEDMAS.

 

Therefore,

6/2(3)

=6/6

=1

 

But order of operations says you do multiplication and division left to right, right? So you would do 6/2 before 2(3).

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I was taught that brackets are first, so therefore, you have to eliminate the 3 in the bracket before the division.

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Depends. It isn't possible to see how it is supposed to be written. Is it 6 over 2(2+1)? or 6 division symbol 2(2+1)? If the first, then you solve the bottom then divide to get 1. If the second, then you add to get 3, then work from left to right to get 9. Impossible to tell which way it is supposed to be written from the problem you gave.

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This was shared on my facebook. Apparently a lot of people get the answer wrong. I'm almost sure the answer is 9. Can anyone confirm this or tell me otherwise?

 

tia.

 

i haven't read the responses yet, but i get "1".

 

1+2 = 3

 

3 x 2 = 6

 

6 divided 6 = 1

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It's 9. I saw this on FB too and even shared it on my wall to see what people thought. There were quite a few that said 1 but I still think 9.

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The answer is one. Any time you have a number beside the parentheses, you are going to use the distributive property. This problem requires that you distribute the 2 to what is in the parentheses. You must do this before going left to right. If it was set up 2x(1+2), I might assume the problem should be worked the other way. Usually, when you set up a problem 2(1+2), it is assumed that you distribute first. It could have been made clearer, though.

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If it has the words 'divided by' and everything else in the OP is the same, the answer is 1 because you've separated the terms. They've made a distinction by using numbers, words, and symbols. If it has only symbols, the answer is 9. This according to my dh (who has the math degree).

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Sorry. I couldn't find a division symbol on my keyboard. It is 6 division symbol 2 (1+2). I solved the parenthesis first. Then do division and/or multiplication working from from left to right. Therefor, I get this:

 

6 division symbol 2 (1+2)

6 division symbol 2 (3)

Then working from left to right:

6 div. 2 = 3

Then you have:

3 (3) which equals 3 times 3 = 9

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I think it would be helpful to make the problem mean something. The 2(1+2) implies that you have 2 of 1+2. Maybe you have 2 bowls of fruit. Each bowl has 1 apple and 2 oranges. There are 6 pieces of fruit. I have a difficult time coming up with anything any other way.

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At first glance, I said 1 because I multiplied before dividing (probably because it said the words "divided by" rather than showing the symbol...which was probably the intention). This is why I make my kids do the work on paper even if it makes sense in their heads. If I had written it down, I would have done it this way:

 

6/2 (2+1) = X

6/2 * (3) = X

3 * 3 = 9

 

Although 6 over the result of 2(2+1) = 1 is also correct the way the original problem is written.

 

But yeah, I think it's deliberately ambiguous and designed to trip people up, which says more about the designer of the problem than about anyone attempting to solve it :tongue_smilie:

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This was shared on my facebook. Apparently a lot of people get the answer wrong. I'm almost sure the answer is 9. Can anyone confirm this or tell me otherwise?

 

tia.

 

The answer is 1.

 

order of operations is:

brackets

exponents

multiplication/division

addition/subtraction

 

So you solve in brackets first (3)

Then multiply 2x3=6

6/6=1

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If it has the words 'divided by' and everything else in the OP is the same, the answer is 1 because you've separated the terms. They've made a distinction by using numbers, words, and symbols. If it has only symbols, the answer is 9. This according to my dh (who has the math degree).

 

 

That's what I was going by, as well.

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Order of operations, BEDMAS.

 

Therefore,

6/2(3)

=6/6

=1

 

BEDMAS and then solve left to right. Only things within parentheses take precedence, not multiplication due to parentheses touching an adjacent number.

 

Therefore,

6/2(3)

=3(3)

=9

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Although I could suggest writing an essay about how it makes you feel when you discovered you got the right/wrong answer, and how it changed your life.

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Order of operations: Please excuse my dear aunt Sally. PEMDAS. PE: You first calculate numbers with exponents and what is inside parenthesis. MD: Then moving from left to right, do the multiplication and division. AS: Finally moving from left to right, do the addition and subtraction. Order of operations problems are generally presented all on one line..

 

6 / 2 ( 2 + 1 )

 

Parenthesis and exponents: 6 / 2 ( 3 )

 

Multiplication and division: 3 ( 3 ) = 9

 

There is no addition or subtraction left to do.

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Order of operations: Please excuse my dear aunt Sally. PEMDAS. PE: You first calculate numbers with exponents and what is inside parenthesis. MD: Then moving from left to right, do the multiplication and division. AS: Finally moving from left to right, do the addition and subtraction. Order of operations problems are generally presented all on one line..

 

6 / 2 ( 2 + 1 )

 

Parenthesis and exponents: 6 / 2 ( 3 )

 

Multiplication and division: 3 ( 3 ) = 9

 

There is no addition or subtraction left to do.

 

Ah, this is why I was not a math major. I didn't go left to right.

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Once you solved what was in the brackets (2+1) the brackets are irrelevent. So the problem could then be written 6/2*3 which would be 9.

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I don't think the issue is orders of operations at all. It is that 2(1+2) is always interpreted as one expression. It is as good as (2(1+2)). Otherwise it would be denoted 2x(1+2). This has always been my experience. Does that make sense? What I'm trying to say is that if the answer was 9, it would have been written as 6 divided by 2 times (1+2). 6 divided by 2(1+2) is generally interpreted as 6 divided by (2(1+2)) or 6 divided by (2+4). Am I the only one who has come across this? I'm sure there is some official rule somewhere. It is starting to bother me. :)

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I don't think the issue is orders of operations at all. It is that 2(1+2) is always interpreted as one expression. It is as good as (2(1+2)). Otherwise it would be denoted 2x(1+2). This has always been my experience. Does that make sense? What I'm trying to say is that if the answer was 9, it would have been written as 6 divided by 2 times (1+2). 6 divided by 2(1+2) is generally interpreted as 6 divided by (2(1+2)) or 6 divided by (2+4). Am I the only one who has come across this? I'm sure there is some official rule somewhere. It is starting to bother me. :)

 

That is what I thought too. I thought 2(1+2) was one expression.

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I just think that (2(1+2)) is implied from 2(1+2). It has been my experience, anyway. You could also work it this way and get 7. 6 divided by 2(1+2)= 6 divided by 2 + 4= 3+ 4= 7. But this, again is wrong because the parentheses are still implied and should be 6 divided by (2+4) which is, again, 1. :). The way the expression is written implies 6 divided by 2 of (1+2) not 6 divided by 2 times 3.

 

Sometimes there is more than just pemdas.

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I'm with the syntax error folks; I ended up with 1 initially but 9 also makes sense to me

 

6/2(1+2)

 

change the first 2 to x

6/x(1+2)

 

Option "1":

6/x(1+2)

6/(x+2x)

[but x=2 so]

6/(2+4)

6/6

1

 

Option "9":

6/x(1+2)

(6(1+2))/x

(6+12)/x

[but x=2 so]

18/2

9

 

My natural inclination is to read it as the whole of 2(1+2) is in the denominator, especially when I stick in x for the 2. But it's really not clear where they intended (1+2) to land, which as a PP pointed out, it's a mathematical error on the part of the initial writer of the problem.

 

:)

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Funny and gives an answer:

http://www.askamathe...ation-business/

 

Didn't think math could make me LOL- then again, I've not had much sleep.

 

Oh that was funny to read--all the discussion in the comments among a variety of mathematically minded folks. And shows that there is some inherent ambiguity in this particular problem and therefor a reasonable case can be made for more than one answer--9, or 1, or 7. Take your pick...it's a good thing that in real life problems aren't just a series of numbers and symbols but represent real situations, and hopefully the person setting up the problem based on a real situation will take care to set it up in a way that unambiguously represents that situation.

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I saw this on fb too, and I'm with the 1 people. The way I was taught, you'd distribute the two first, then go left to right.

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I'm siding in with the 9 people (must admit that initially I jumped to 1 due to the english writing). I agree that once the operation within the brackets is done, there is no operation within brackets to be done. in essence the brackets disappear and division/multiplication are done left to right.

 

Definitely in how the problem is written though: 6 / 2(1+2) or 6/(2(1+2))

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I'm siding in with the 9 people (must admit that initially I jumped to 1 due to the english writing). I agree that once the operation within the brackets is done, there is no operation within brackets to be done. in essence the brackets disappear and division/multiplication are done left to right.

 

Definitely in how the problem is written though: 6 / 2(1+2) or 6/(2(1+2))

 

In Algebra and above, whatever is below the division sign (the denominator of a fraction) is done first, as if in brackets, but no brackets are needed.

 

6

---------- = 1

2(1+2)

 

When the problem says 6 divided by 2(1+2), I do see that as 6 divided by the whole expression, as if it were in the denominator of a fraction. The fact that the expression is written algebraically (without the "times" sign) strengthens that assumption.

 

I agree that if it were written as a simple arithmetic problem, it should be 6 divided by 2 times (1+2), which would result in 6/2*(1+2) = 9

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The three would still be in parentheses after 1 + 2 is done first due to order of operations. The parentheses must be eliminated before the division can take place. Therefore, the 2 must be distributed to the three. This gives an answer of six and then it is six/six.

 

Most people are skipping that fact that parentheses was NOT eliminated simply by doing the addition. That answer would still be inside the () 2(3) must be solved before the simple division outside of (). Essentially, 2(1+2) is all one unit or expression. It is a simple issue of order of operations, but it is easy to overlook that fact that after adding the two numbers, the answer is still in ().

 

Dh has a bachelor's in mathematics and agrees with me. The answer is one.

 

Faith

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I'm no math major...I said one.

 

DH said 9.

 

However, when I set the problems up as 6/2(1+2) as a fractional equation (which is a valid manner of interpreting that problem), he came up with 1.

 

I guess I just don't read 6/2(1+2) as the same as 6/2*(1+2). I don't recall any problems in any of the Pre-Algebra, or Algebra programs we've got here that have set anything up like the OP problem 6/2(1+2) where my answer would have been incorrect (we have Foerster's, TT, and AoPS). But, I could check ;)

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I agree with FaithManor. The reality is, you will never see this problem in a 5th or 6th grade textbook where they want you to apply pemdas. It would be clarified with a x sign. In algebra and above, you would just assume it was one expression because people use this notation as shorthand to imply parentheses. It is more about convention or common usage than order or operations, and our kids will not have to worry about this in real life. In an algebra class this would have been set up as 6 over 2(1+2), which would be simplified 3 over (1+2) which is one.

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Think about this. How would you solve 6 divided by 2x = 1? Would you solve it 3x = 1, x =1/3? No. It would be 2x = 6, x = 3. Just like you have 2 xs, you have 2--1+2s. It is the same concept. 2(1+2) goes together like 2x. At the algebra level, it is just implied.

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