6÷2(1+2)=?

Originally posted by _BoneZ_

Originally posted by prolific
it's still 6÷2(3) or otherwise know as 6÷2x3 = 9.
The only way to get one is if you do multiplication first which is an invalid move.

Because you work from left to right, just as you read from left to right.

Thus 6÷2(1+2)= 6÷2(3)= 3(3)= 9


It really doesn't get more simple than that. Well, besides:

6÷2(1+2)=

is the same as:

(6÷2)(1+2)=

Yes that is correct. He is working from right to left which violates the rules.
This thread scares me and makes me want to .

6/2(3) is not the same as 6/2*3

6 / x(1+2) = 1
That becomes 6 = x(1+2)
which is 6 = x+2x
which is 6 = 3x
meaning x = 2.
Therefore 6/2(1+2)= 1 NOT 9

Following PEMDAS, you always multiply before you divide

Originally posted by Itop1
6/2(3) is not the same as 6/2*3

Those are exactly the same and you will get the same answer if you work from left to right as you're supposed to. Both equations above will give you 9 if you work from left to right.

But by claiming that they're not the same shows that your math education is lacking. We're done here (for real this time).

Originally posted by Itop1
Following PEMDAS, you always multiply before you divide

Incorrect. You do whichever one comes first.

Example:

2*2/2*2 = 4

Note / does not equal fraction, instead means divide like the earlier symbol.

6÷2(1+2)=9

6/2 = 3
1+2 = 3
3*(3) =9

/hangs self due to the simplicity of this problem causing so many headaches here...

The answer is 9. How to explain this..
You cannot read it as a fraction with this type of problem. You cannot place the 2(1+2) underneath the 6 to be solved separately. The division symbol must remain just that you cannot juggle between it and the bar this changes the order of operations. This is a no no and shouldn't be done. You have to solve it as it is read.

(After solving the what inside the P)
SIX divided by TWO times THREE since the multiplication and division can both be used we simply solve the problem from left to right giving the answer NINE.


Also my TI-83 would like to disagree with your calculator.

PEDMAS, BODMAS AND BEDMAS

Im going to bed, after some paracetimol

I got 63.7.

reply to post by Itop1


I take offense to that, sir.

This thread is making me chuckle.. reminds me of theoretical english mechanics (proper use of words and context... bizzare stuff).

We had a challenge like this in High School years ago. Ultimately the dicision was made that both arguments *might* be valid. The teacher explained that this is a good reason why you should always use parenthesis to be exact about what you are trying to express.

BTW, in my opinion based on what I learned in algebra:

6 ÷ 2(1+2) = 6 ÷ 2(3) = 6 ÷ 6 = 1

Reason being is that ALL paretheticals MUST be resolved before division happens. In the case of 6 ÷ 2(3), there is STILL a parenthetical in place (just because you reduced the inside doesn't mean it is gone).

Course, it can be argued that once you reduce the inside of the parenthetical, it's just multiplication.. *shrug*

So, kinda of interesting that so many people are getting so fired up about this.. is it on the TAAKS or AIMS tests? www.abovetopsecret.com...

Originally posted by rogerstigers
This thread is making me chuckle.. reminds me of theoretical english mechanics (proper use of words and context... bizzare stuff).

We had a challenge like this in High School years ago. Ultimately the dicision was made that both arguments *might* be valid. The teacher explained that this is a good reason why you should always use parenthesis to be exact about what you are trying to express.

BTW, in my opinion based on what I learned in algebra:

6 ÷ 2(1+2) = 6 ÷ 2(3) = 6 ÷ 6 = 1

Reason being is that ALL paretheticals MUST be resolved before division happens. In the case of 6 ÷ 2(3), there is STILL a parenthetical in place (just because you reduced the inside doesn't mean it is gone).

Course, it can be argued that once you reduce the inside of the parenthetical, it's just division.. *shrug*

So, kinda of interesting that so many people are getting so fired up about this.. is it on the TAAKS or AIMS tests? www.abovetopsecret.com...

If this was in my school GCSE then i probably got it wrong, although it would be a bit cruel to put this equation in the test....

The way you did it is the same way as i learned in school

I am lousy at math, but...

People get all mathsnobby about this, while OP makes a good point. By the time the point is made, people have mathsnobbered all over themselfs and its really gross how quickly snobber starts to trickle in some corners of ye Internets.

Now, I am just a country dummie, and all that, but I know I reads my adult mangas from right to left. But I reads my American comics code comics from left to right. Point is, they should not censor that stuff, because its personal preference.

However I was taught that PEMDAS is not directional. When the hell did you ever need left or right as concepts to do math? It's too random because what if someone has multi layers to their equation? What if left and right do not apply or shall you always do math in 2d space? I think OPs thread is excellent if for no other reason than to clear out your snob glands.

Now I don't do much math and I am dumb. However, I have read Wolfram's book and I think that the reason OP's equation when typed into Wolfram Alpha truns out the way it does, is due to the way computer maths and calculator maths are done behind the scenes, as OP points out. His Casio gets 1, but the Computer based math calcs (even wolfram's) gets 9.

OP makes a good point which if we can clear the snobber from the thread, we might see: It is that computers make you dumber.

The way calculators do math is totally different than the way binary PC processor does math. In essence, the electronic old school method is more sublime and skillful, because in the old days they really knew their schaznatt and since then we've gotten dumber and relied upon computers. In essence, when you utilize wolfram alpha, you do have to add the extra brackets, to get the PC calc to be as smart as the old school calc. So it's like giving the computer an extra handhold, because it's dumber than the old casio, which was programmed soley by math wizards of the 50s and 60s. When I learned how an electronic calculator actually does math, I found it very interesting. I am sure OP can tease us some more. AM I right OP?

Hehe, math is fun when you become a masochist!

Ive no idea to be honest, i asked a friend that is at cambridge and he said the answer could be 1 or 9..... the equation is flawed, so it turns out none of us were correct because the answer can be eather and it depends if you were tought BODMAS or PEDMAS at school...

Some people learn BODMAS and dont know what the hell PEDMAS is and vice versa...

I dont know, i was tought BODMAS at school not PEDMAS, but seems a lot of people here were tought PEDMAS and not BODMAS

First of all, this is a poorly written problem. The problem arising is that people are interpreting it in 2 different ways. If it were written in a textbook, it should be written in a way that makes the division more clear. However, the way that it is written, if you follow the order of operations, the answer is 9. Whether you are using BEDMAS or PEMDAS or whatever is irrelevant, they all state the same thing.

Parentheses: Simplify the argument inside the parentheses. The two on the outside is an implied multiplication, so techically it should be written like this:

6÷2*(1+2)

The arguments inside the parentheses reduce to 3:

6÷2*(3) = 6÷2(3) = 6÷2*3

Meh.. If you write them as fractions and cross multiply you still get 9. I would say the equation is just so sloppy and can be confusing that it would be best to just void it out altogether and rewrite it. Thanks for the math class flashbacks

reply to post by Itop1


the answer is 1. pemdas is being applied wrong in previous cases. Due to paranthesis the 2 must be distributed into the parenthesis first. 6/2(1+2) = 6/(2+4) = 6/6 = 1

it's easy to think of this as (6/2)(1+2) but that is wrong. the easiest way to see the real problem is 6/(2(1+2)), in this case 2(1+2) is treated as a singular entity not as 2 x (1+2). 2(1+2) = 2x3 or 2+4, depending on whether you distribute or not. but again, key part of this question is knowing that distribution comes prior to any solving of the parenthesis

Originally posted by lifeoflyman
reply to post by Itop1

 

the answer is 1. pemdas is being applied wrong in previous cases. Due to paranthesis the 2 must be distributed into the parenthesis first. 6/2(1+2) = 6/(2+4) = 6/6 = 1

it's easy to think of this as (6/2)(1+2) but that is wrong. the easiest way to see the real problem is 6/(2(1+2)), in this case 2(1+2) is treated as a singular entity not as 2 x (1+2). 2(1+2) = 2x3 or 2+4, depending on whether you distribute or not. but again, key part of this question is knowing that distribution comes prior to any solving of the parenthesis

I have to disagree here. The distributive property does not fall under the P in PEMDAS or B in BODMAS or whichever acronym you use. The distribution is just an implied multiplication. 6÷2(3) is the same as 6÷2*(3) is the same as 6÷2*3. Once you simplify the arguments inside the parentheses they can be dropped. The multiplication is implied by the parentheses, but it does not mean it comes before the division. To properly distribute this you would take the 6/2 >> 3 and distribute it into the parentheses. 3(1+2)=(3+6)=9. Distribution is NOT part of the parentheses/brackets portion of the order of operations. It is simply a rule of multiplication.

The correct answer is 9

Edit: Another way to look at it: Distribution is not a necessary operation at all. to solve 2(1+4) you can either distribute (2+8) or simplify the arguments in the parentheses and then multiply 2(5). Distribution is merely a property of multiplication that is being misused here.

MY last reply before i slepp...

2 options are available, both incorrect and equally just and here is my reason why.....


a)Standard bodmas/pemdas/etc variations which render 9

b)The previous again in which the 2 preceding the brackets 2(3) becomes included as a "bracket/parenthesis" multipli...cation, rendering it of higher importance than standard bodmas/variant left-to-right law, rendering 1

c)The idea that everything beyond the 6 becomes a denominator in its entirety, again rendering 1

d)The notion that the implied multiplication with the 2(3) of the solved parenthesis becomes of higher precedence than standard bodmas again, rendering 1. (Cited at purplemaths.com and also supported and contradicted elsewhere)

Standardised calculators and highly computational engines such as WolframAlpha and the like, will output conflicting answers when input with the sum, as is, verbatim.



The problem between the human "physically worked out" answers seems to lie with

1) Is everything after the 6 a denominator? (conflicting evidence for both cases, implied parenthesis or not)

2) Are non-variable singular integer multiplications in the "parentheses family" of the bodmas law, taking precedence beyond standard (D or M) ie: 2(3)

3) If 2 is false, do implied multiplications take precedence over overt ones. (Again, there is conflicting views and citations from apparently "viable" and "authorative" sources.)

Until there's a definite answer to the points proposed, or corrected notation, I don't believe this can be resolved in its entirety with a "right"

Comparing calculators and mathematical engines online will also achieve polarised results.

sorry for any spelling mistakes, im very tired, im off to bed

I always end up with 3x3=9.

I can't see any other way around it.