Math: 6÷2(1+2) = ?

"These mnemonics may be misleading when written this way, especially if the user is not aware that multiplication and division are of equal precedence, as are addition and subtraction."


It's 9

6/2(1+2)

[link to en.wikipedia.org]

"Today, parentheses or brackets are used to explicitly denote precedence by grouping parts of an expression that should be evaluated first."

"The order of operations used throughout mathematics, science, technology and many computer programming languages is expressed here:
exponents and roots
multiplication and division
addition and subtraction"

"Mnemonics are often used to help students remember the rules, but the rules taught by the use of acronyms can be misleading. In the United States the acronym PEMDAS is common."
"These mnemonics may be misleading when written this way, especially if the user is not aware that multiplication and division are of equal precedence, as are addition and subtraction."

It's parenthesis first, then follow the standards for order of operations from left to right

6/2(1+2)
Parenthesis first: 1+2 =3
Multiplication and division are of equal precedence, but since division is farthest to the left in this problem, division comes next:
6/2=3

3x3 = 9
The answer is 9

Actually. I have proven the interpretation, time and time again. But of course, it is impossible to show the entire internet. Read back about 10-12 pages.

I used to be a 9er. Now I am a die hard 1er...

Casper_26 knows his shit...

you don't need the brackets for the division part, order of operations is from left to right, multiplication and division have equal precedence, but division comes first (farthest to the left) in this problem

Brackets first, then multiplication and division from left to right, then addition and subtraction

the answer is 9

This is all WIN ... if people actually opened books, or even online PDFs, they would see. But they argue based on what they remember instead of what is true...

YES!!!! (and a chest hug of my fists)!

you are a little late to the discussion if you remotely think that this is about order of operations. Everyone here knows the OoO. The problem is 90% of the readers don't know what to apply the OoO to. The 2 can't be torn away from the ( ). That is the final result. Now you just need to figure out why...

Speak of the devil (Caper though I wrote Casper)

haha, you need to start a thread on the evidence. You taught me and I thank you for it.

It is quite clear the answer is 1. There are NO laws of mathematics that you work left from right. Confirmed by two PhDs in mathematics... my buddy of course but that is hearsay, but also by the Berkely professor in the video I posted.

Besides that, you have the obelisk, which clearly does not mean divide by this next number, which is what my calculator does, but it groups numbers into a numerator and denominator.

Then, you have a/1a = 1...

Then you have every single math problem done in algebra and calc class using variables ever done. This is what really started to let the light in on me and opened my mind. Why the fuck would I do these problems differently than I would do the problem in the OP?

yea yea bidmas stuff

I asked my friend to come in here and explain to people why he believes it is 1 and he said "no, I have better things to do"... lulz.

Fucking asshole.

Right now I am reading up on the distributive property. Hopefully I will learn exactly how parentheses work. Because, apparently I don't know even though I thought I did...

There are NO laws of mathematics that you work left from right.

Wasn't mathematics introduced by Arabs? I think they write right to left, like the Jews. Curious where the left to right rule in PEDMAS came from.

Wasn't mathematics introduced by Arabs? I think they write right to left, like the Jews. Curious where the left to right rule in PEDMAS came from.


Interesting... the Babylonians were the first to use algebra... but most of the methods and work done in algebra was done during the Islamic Golden Age... the word algebra itself comes from Arabic...

However I am no expert but yes I find this insight interesting. THanks.

wow, this page came alive with some rudimentary stuff. The equation has nothing to do with mnemonics here. Nothing to do with Order of Operations. We all know multiplication and Division are on the same level, as well as add and subtract. Even a step back from that, we don't even have to go left to right if we switch all division to inverse mult. and subt. to adding a negative number.
How do we READ the question? You are not a robot or software. The division symbol is a grouping symbol. Everything on the left divided by everything on the right. You know, Dividend; Divisor; Quotient. Now you will say that is untrue, and you must go left to right, and follow order of ops.
Ask yourself what is a ÷ a ?
Now ask, what is 1a ÷ 1a ?
1a ÷ 1a is not 1 * a ÷ 1 * a.
a ÷ a = 1a ÷ 1a
(a) ÷ (a) = (1a) ÷ (1a)
6 ÷ 2a = (6) ÷ (2a) = 3/a

a = 2+1
6 ÷ 2a = 3/a
6 ÷ 2(2+1) = 3/(2+1)
= 1

Read this if you still disagree and try to keep up: [link to cstl.syr.edu]

I can see why people think it is 9 because the problem would never actually be written like this. It is one and here is why...

Fractions are the same as division for example.

1 ÷ 2 = .5
Or
1/2 = .5

So if you make this problem into a fraction, which is what you should do, then you get :

6
_________
2(2+1)

Because the 2 belongs with (2+1). You cannot separate it because it need to be distributed.

So you get 4+2 when you distribute

6 6
____ = ____ = 1

4+2 6

It's one!

^ my above post did not format properly but you get the idea


And also 2a = a + a

So sub (2+1) for a and 2(2+1) = (2+1) + (2+1)= 6

^ this

Hey dude, what's happening tonight? There are so many ways of showing the maths to say 1, and blindly using "left to right rule" is the only one that says 9. I actually got in touch with some computer & electrical engineers I graduated with, today, and everyone of them said 1. I am also glad you realize that equations are basically "collapsed" , and there is no "left to right" rule in the real order of operations. This left-to-right thing was introduced by teachers or something. I have a very interesting article for you, that I think you will find interesting. It isn't too long.
[link to www.google.ca (secure)]

Have a great weekend my man...

Last Edited by caper_26 on 01/19/2013 02:27 AM

Yea he nailed it, and yes it is rudimentary stuff but that is why we are having this problem. Clearly people, including myself, are not as well versed in the rudimentary things as we should be.

Now that PDF from Syracuse is great... problem is I am not sure how true the bold part of this statement is:

"Do the remaining multiplication and division, as you come to them, when working from left to right in the expression. (See below for a discussion of this step.)

Do the remaining addition and subtraction, as you come to them, when working from left to right in the expression. (See below for a discussion of this step.)"

haha! Thanks bro! This is just the thing I was getting at and literally as I posted my last post, was wishing I could read more about it!

haha thanks again for all your help you taught me a lot and helped me realize just how wrong I can be despite how adamantly I believe I am right.

131 pages just proves very succinctly why this country is lagging so far behind the world at math.

There are no examples showing any operators in front of the term being distributed, that I could find. If you do find one, please let me know. The reason the 6/2 doesn't get distributed is because it is not in parentheses.

(6/2)(2+1) = [(6/2)2 + (6/2)1]
But,
6/2(2+1) we have proven that 2(2+1) is in the denominator, so we have
6
2(2+1)

which is

6
(4+2)

= 1

We can proven the requirement of ( ) using the same Identity Law Proof, where there is no ( ), like in the a / 1a expression

g'night. Hopefully we can open some doors to some new people tomorrow. Cheers !

Its 1, durp

9

It is just a numbers game. The population of the US is rather large, and the ratio of those people to those who have internet access is quite large as well. There is a high percentage of people who are just "not GREAT at math". This question involves things that go beyond the basics. therefore, you are going to get a LOT of people who will solve this like they were taught in elementary school (left to right, with mult&div first). That is the large percentage of the pop. Then you get people who are well versed in all areas of maths, who are the minority, and show some math facts, and we get called idiot, since we are the "only" one showing that "new" way of doing it, something they never saw before, so they immediately discard it. Anyway, that is MY take on the whole thing, but I am not a philosopher by any means. I actually suck with words, which is why I went the route I did... numbers only!! Ciao.

I think they tell people this so they have some organization when doing math. But it misleads people into thinking it is a law and takes precedence.

For example left to right does not matter just order of operators:

10 × 10 + 10 × 10 = 100 no matter if you do right multiplication first or left

But division confuses because EVERYTHING beyond a division sign is included if it is grouped. The inclusion ends if another operator is present


6/3+(2+1) is 5 not 1 because it would be rewritten as

6
______
3 + 2 + 1

I can't get the format right on my posts lol

But I meant to post

6
__ + 2 + 1

3

Where did you find that infos?


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