6÷2(1+2)=? SOLVED by the Professor of Mathematics at California State University [video]

worfram's result:

6÷2(1+2)=1

false

Ahhh, another young Jedi who needs some training:

[link to cstl.syr.edu]

Maybe you will learn something. Oh wait, you will just ignore it, because you are too proud to swallow your pride, like the rest.

1

Your own link has proven you wrong.

The order of operations tells us a step-by-step method for evaluating expressions:

Evaluate all expressions within parentheses and other grouping symbols.
(See page 20 for a discussion of this step.)
Evaluate all expressions involving exponents. (See page 12 for a discussion
of this step.)
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.)

One trick to help remember the correct order of operations is to think of the acronym PE[MD][AS]. This stands for Parentheses, Exponents, [Multiplication and Division], [Addition and Subtraction].

What is so complicated about it?

6÷2(1+2)=?

Order of operations:

Parenthesis solved: 6÷2*3

Exponents solved: none

MD/DM solved: 6÷2*3 becomes 3*3 becomes 9

AS/SA solved: none

Answer: 9

The order of operations can be P-E-MD-AS, P-E-MD-SA, P-E-DM-AS, P-E-DM-SA.... They are all equally correct since the MD/DM followed then by the AS/SA parts have no hierarchical precedence between one another, respectively, and thus are implemented in the order they occur in the equation from left to right.


Obviously you are all falling for a very old trick; sophisticated trolling is employed by higher educated posters to confuse the other posters who aren't capable of solving it themselves, as well as the ones who are able to solve the problem yet are still dumb enough to take the trolls seriously up until (or even if) they get to the point where they can determine that they are being intentionally deceived.

When you use the first order of operations (P) to get you to 6÷2*3 you obviously then have to do the division of 6÷2 first before you can multiply, you can't just make it 6÷6 without first doing the first problem in the order of operations, because that would be mathematically incorrect.

If you're unable to see that you're being trolled after I'm explaining this to you, I feel sorry for you.

As for the trolls...can't you find something better to do with your time?

It's ambiguous and should be parenthesised appropriately as per the 2nd email update.

Caper admits... 6*.5(2+1)=9 so what about this....

[link to www.wolframalpha.com]

How grouping works:

100mm ÷ 10cm = ?

Parentheses not required, but perhaps useful for a math apprentice.

Easiest way to see the light is derive both equations from scratch, using factoring (the reverse of distribution).

6 ÷ 6 = 1
6 ÷ (4+2) = 1
6 ÷ 2(2+1)= 1 Extra Parentheses not required since we know the 2 was the GCF of 4+2. You can put them in, but it is redundant, just as (6) ÷ (6) = (1) is redundant.
Also, 2x = x2 by commutative Law of multiplication. So when we factor 2 from 4+2, we can put the 2 before or after the ( ) like this:
4+2 = 2(2+1)
4+2 = (2+1)2
THEREFORE:
6 ÷ (4+2)
= 6 ÷ 2(2+1)
or 6 ÷ (2+1)2

3 * 3 = 9
(6/2)3 = 9 Here, we NEED ( ) because we cannot write 6/23
(6/2)(2+1) = 9

There you have it. Another way:
6 + 3 = 9
(6/2)2 + (6/2)1 = 9; We can't write 6/22 + 6/21
(6/2)(2+1) = 9

There are the 2 proofs of the equations in debate.

The trolls are arguing that...
6÷2(3) is not the same as 6÷2*3= Seriously, that is what they are arguing. I shit you not.



There is still only one correct answer 9. No matter how confused someone is (OP, scientist or otherwise), there still only one answer.

Your own link has proven you wrong.

Nice one. I already proved wolfram doesn't know how to substitute values for variables.

If I gave you 6÷2n = 3/n, then told you n=2+1; it is mathematically invalid to say 9 = 1

This is what wolfram does. Wolfram is proven useless to solve this equation correctly.

[link to i46.tinypic.com]


.

Agreed, but this thread is evidence enough that the formula as written is confusing. It is a very simple equation but it's causing alll manner of debate, where the addtion of a couple of brackets could remove all doubt.

Also take a look at that:

6÷2(1+2)=9 >>>> [link to s20.postimage.org]

then this one:

3÷1(1+2)=9 >>>> [link to s20.postimage.org]

You cant take apart a complete equation and sub in that way. You are changing the order of operation by doing that.

Holy shit you people are dumb.

This is honestly like 6th grade math.

Only Caper and DUCM are still trolling.

Hopefully I can resist this nonsense now.

How grouping works:

100mm ÷ 10cm = ?

Parentheses not required, but perhaps useful for a math apprentice.

Easiest way to see the light is derive both equations from scratch, using factoring (the reverse of distribution).

6 ÷ 6 = 1
6 ÷ (4+2) = 1
6 ÷ 2(2+1)= 1 Extra Parentheses not required since we know the 2 was the GCF of 4+2. You can put them in, but it is redundant, just as (6) ÷ (6) = (1) is redundant.
Also, 2x = x2 by commutative Law of multiplication. So when we factor 2 from 4+2, we can put the 2 before or after the ( ) like this:
4+2 = 2(2+1)
4+2 = (2+1)2
THEREFORE:
6 ÷ (4+2)
= 6 ÷ 2(2+1)
or 6 ÷ (2+1)2

3 * 3 = 9
(6/2)3 = 9 Here, we NEED ( ) because we cannot write 6/23
(6/2)(2+1) = 9

There you have it. Another way:
6 + 3 = 9
(6/2)2 + (6/2)1 = 9; We can't write 6/22 + 6/21
(6/2)(2+1) = 9

There are the 2 proofs of the equations in debate.

then this one:

3÷1(1+2)=9 >>>> [link to s20.postimage.org]

That is THE most retarded answer I have ever seen. If you believe that, then no bloody wonder you getting 9 as a response.

"Redundancy Law"

A coefficient of 1 does NOT need to be written. It is ALWAYS implied. a = 1a . Also the Identity Law. You CAN write though, but because of the math LAW stated, it cannot change the outcome of the answer.

Please tell me you see what is wrong with this! I thank you for posting, because I can actually use that as yet ANOTHER way to prove 1 is the answer, as a matter of fact !!

3÷1(1+2)=9 What kind of special math is this??

'1' as a coefficient can be omitted.
that means, according to you:

3÷1(1+2)= 3÷(1+2)
9 = 1

In reality though,
3÷1(1+2)= 3÷(1+2)
1 = 1

Thank you for showing everyone this "proof" and good night. Nothing more to be said here after that one.

Hopefully this will end this debate.

The other OP removed this video from his thread as the answers differed.

This is from a math professor and a very well respected one at that.

***UPDATE***

I received this e-mail from Dr. Stein about 20 minutes ago


Russell,

I just researched this in several places, AND I'M WRONG!!! I'd appreciate it if you posted this answer. Here's a nice explanation.

[link to chilimath.com]

While the acronym PEMDAS is correct, the problem comes with the confusion about how M and D are treated.

I have always thought that it meant that M (multiplication) is to precede D (division). On reading several sources, M and D are treated at the same level of hierarchy, and are to be done left to right.

In other words, 6/2 x 3 really is 9, because M and D are at the same hierarchy level, and so M no longer PRECEDES D, but should be done left to right. The division is encountered first in reading 6/2 x 3, and so is done first.

Jim


***2nd e-mail update***

Hi Russell,

One of the things that I've always believed is that one should admit to one's mistakes. I just made one, and the important thing is to get it right.

Most mathematicians are aware of the possibility of error in such a situation (I'm willing to bet I'm not the only mathematician who would make this mistake). As a result, they will usually parenthesize to avoid potential misinterpretation. For instance, I would write the problem as either

6 / (2(1+2)) if I wanted the answer to be 1

or

(6/2) (1+2) if I wanted the answer to be 9

I sincerely hope this is the last time you reply.

You are right, the 1 can be omitted. But that just means you remove the ÷, (the item between the 1 and 3), but that still leaves multiplication there. If you drop the "useless" 1, then you drop the item in between. Not the one after. DUH!!

I can't believe you wasted this professors time with that question...

Why don't we just email the English lit professor what their thoughts on green eggs and ham are...

And email a top geologist on advice on how to make one of those baking soda volcano models...