6÷2(1+2)=?

Originally posted by canselmi
There is the rule called the Distributive Property. You may not remember it because it was taught back in elementary school, but believe me, it's real.
6÷2(1+2)=x
6÷(2+4)=x
6÷6=x
1=x

You're right, primary school was a little while back. My bachelor's degree in science (with honours), however, was not.

Read my post from a page or so back.

My Bachelor's degree in Science (with honors as well) was not long ago either, about 6 years.

2(1+2) is one term.
So you have the first term: 6
Divided by the second term: 2(1+2)

Originally posted by canselmi
My Bachelor's degree in Science (with honors as well) was not long ago either, about 6 years.

2(1+2) is one term.
So you have the first term: 6
Divided by the second term: 2(1+2)

This argument is pointless. I have countless friends with mathematics degrees, some with post-graduate qualifications, all of whom say that the answer is 9. The 6, 2 and (2+1) are their own entities and you treat them from left to right, following the addition of the terms within the bracket. You get:

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

Since division and multiplication have the same precedence when considering the order of operations, you go from left to right and the answer is 9.

Argue it all you want, I give up on trying to explain it. Try physics forums if you want more proof. There's at least 2 or 3 threads I know of that go into it in some detail.

It is definitely 9.

2nd line

Let's let 1=x; and we'll set the equation equal to 9

Can you tell me what I'm doing wrong in the following?

6÷2(1+2)=?
6÷2(x+2)=9
6÷(2x+4)=9 --->Distributive Property
6=9*(2x+4) --->Multiply both sides by (2x+4)
6÷9=2x+4 --->Divide both sides by 9
.6667=2x+4 --->Change into decimal (for clarity)
.6667-4=2x --->Subtract 4 from both sides
-3.333=2x
-3.333÷2=x
-1.667=x

But we know that x=1, so therefore the equation doesn't =9.
I know I won't change your mind, but can you tell me what I'm doing wrong?

Originally posted by canselmi
Let's let 1=x; and we'll set the equation equal to 9

Can you tell me what I'm doing wrong in the following?

6÷2(1+2)=?
6÷2(x+2)=9
6÷(2x+4)=9 --->Distributive Property
6=9*(2x+4) --->Multiply both sides by (2x+4)
6÷9=2x+4 --->Divide both sides by 9
.6667=2x+4 --->Change into decimal (for clarity)
.6667-4=2x --->Subtract 4 from both sides
-3.333=2x
-3.333÷2=x
-1.667=x

But we know that x=1, so therefore the equation doesn't =9.
I know I won't change your mind, but can you tell me what I'm doing wrong?

Your proof is useless because you are applying your maths incorrectly.

I posted an explanation about it two pages back. In the middle of writing a research proposal right now (and it's 4.20 in the morning where I am), so I can't really be bothered finding it.

hi guys ... had to stop back by and see what transpired and i too cannot believe this thread has gone on sooooooo long. however, since 2 posters asked for my response specifically ... ASeeker and Megamind ... this is for you.

Again, the only answer is 1 as the expression is written ... without arguing semantics or laws, let's try some basic logic (which is where algebra is based)

So, i have $6 dollars in my hand.
I have to distribute my dollars to a group of people and i'd like to know how much each receives.
2 adults are traveling with children and each will get an equal amount.
so, we have 6 (dollars) divided by 2 adults times (their children - 1+2)
or 6/2(1+2) ... given the above goal of EQUAL distribution to all parties, would ANY of you please justify or even show me the way to the secret stash of cash that i'll need to give $9 to each party.

btw, if you can locate that stash of cash, please share.
and, just because one holds a degree does not indicate the holder possesses usable knowledge, shame on you for assuming such nonsense.

Classic example: A delivery truck approaches a mountain underpass which is lower than the height of the truck. All 3 passengers (who are have engineering degrees) get out of the truck and begin evaluating the problem. As they are discussing their options for increasing the entrance to the underpass, a small child on a bicycle approaches and asks "what's the problem?"

The engineers describe their dilemma and openly offer suggestions for a solution ... about that same time, the child smiles at each engineer and shakes his head. When asked "what are you smiling about?", the child replies, all those degrees, yet none of you consider letting a bit of air out of the tires, ironic indeed.

This obvious solution is much like the algebra expression presented, it IS all in how you look at it. But the answer doesn't change ... it is still 1 and only 1.

ps: thank you SkyEvolved for the link you included ... hope those confused actually read it.

I stopped by also.

[atsimg]http://files.abovetopsecret.com/images/member/d1eca1619752.jpg[/atsimg]

The equation is ambiguous. Therefore the answer can be both.
I thought we cleared that up.

Originally posted by snowspirit
6÷2(1+2)=?

Order of operations: BEDMAS

Brackets
Exponents
Division
Multiplication
Addition
Subtraction

1+2=3
2x3=6
6/6=1

edit on 1-5-2011 by snowspirit because: spelling

I always thought it was PEMDAS

I really feel silly for doing this but everything made sense to me so I punched it into the old calculator and came up with this:



I don't know though...maybe the calculator is wrong?

I would put 9 on a test though if I were to have to awnser because I could not make the calculator come up with 1!

reply to post by Honor93


Over a month later and your still wrong .... answer is 9!

reply to post by Itop1

Originally posted by snowspirit 6÷2(1+2)=? Order of operations: BEDMAS Brackets Exponents Division Multiplication Addition Subtraction 1+2=3 2x3=6 6/6=1

someone else wrote:

if division is before multiplication in operation order wouldn't it be 1+2=3 6/2=3 3x3=9?

According to BEDMAS or PEDMAS you do the brackets or parentheses first. (1+2)= 3 then the exponent which is 2. SO 2x3=6 then division which is 6÷6=1. That was my answer but just looking at the equation without thinking about it too hard I can see that to an awful lot of people, 9 seems easy and perfect but it is neither in order or correct.

Originally posted by MollyStewart
reply to post by Itop1

 

Originally posted by snowspirit 6÷2(1+2)=? Order of operations: BEDMAS Brackets Exponents Division Multiplication Addition Subtraction 1+2=3 2x3=6 6/6=1

someone else wrote:

if division is before multiplication in operation order wouldn't it be 1+2=3 6/2=3 3x3=9?

According to BEDMAS or PEDMAS you do the brackets or parentheses first. (1+2)= 3 then the exponent which is 2. SO 2x3=6 then division which is 6÷6=1. That was my answer but just looking at the equation without thinking about it too hard I can see that to an awful lot of people, 9 seems easy and perfect but it is neither in order or correct.

I'm sorry, I don't see any exponentials in that equation. Try again.

reply to post by MegaMind

well, golllleeee gee here it is nearly 1.5 months later and you still haven't directed me to that "stash of cash" you insist exists. (me thinks you are being a bit selfish)

But what i find even more amazing is the fact that your own signature line must serve as nothing more than whitewash ... "the ability to repeat catch-phrases, cant terms, familiar propositions, gives the conceit of learning and coats the mind with varnish waterproof to new ideas."

math needs no new ideas ... it works fine just as it is.
ps: the ability to accept facts as presented leads to a wisdom far surpassing the entrapment of ideology.

I love this post! Knowledge gap and language gaps are amazing.

Do we divide first or multiply first? Do we go left to right? Do we trust calculators? lol.

There will be problems with this based on what order of operations you use. PEMDAS and the like are great, but the farther you get in math the more they drill that you should simplify first and then do orders.

If you simplify this it is 1. If you do not it is 9. If you trust calculators it can be either answer. It is sloppy notation in a way when seen in this context.

So a little look:
PEMDAS:
6÷2(1+2)=
Simplify:
6÷2(3)=
The only answer at this point is one.

Now PEMDAS without simplifying from left to right:
6÷2(1+2)=
6/2=3
3(1+2)=3(3)=9

So the question is do we do left to right or actually use order of operations? All systems agree that parentheses/brackets come first no matter what, so left to right does not matter in this equation. We must simplify first. We have to based on all systems.
So 6÷2(1+2)=6/2(3)

We can all agree so far no doubt. Now the problem is do we multiply or divide first? Well to me this is written as 6 over 2(3) where 1 is the answer. This is very obvious to me.

Now if we do left to right from 6/2(3) we get 9. BUT! Look closely. What is weird with that 3? It is still in parentheses! That means we should go right to left to simplify the parenthesis farther. The 2(3) must be done first before the 6/2. The 2 is modifying the equation of (1+2), so it is part of the parenthesis equation. It must be done under all systems.

If you want 9 as an answer then write the equation as:
(6÷2)(1+2)=

Now both sets of parentheses modify each other. Logic! I love it.

Anyways I don't feel like bragging or proving my point farther, but I will just say I have had a lot of math in my life.

Edit: PEMDAS and BEDMAS are very curious. We are taught that */ have equal importance, but different countries teach that multiplication should come first and others teach division coming first but we all agree on +- (either way I feel we must simplify fully first giving 1 as the answer).

Obviously this will cause a little division in the results

6
------------
2(1+2)

I would have solved it this way.

Which is 1

Then I used an algebra problem site which agreed with that answer. 1

Originally posted by Honor93
reply to post by MegaMind

 

well, golllleeee gee here it is nearly 1.5 months later and you still haven't directed me to that "stash of cash" you insist exists. (me thinks you are being a bit selfish)

But what i find even more amazing is the fact that your own signature line must serve as nothing more than whitewash ... "the ability to repeat catch-phrases, cant terms, familiar propositions, gives the conceit of learning and coats the mind with varnish waterproof to new ideas."

math needs no new ideas ... it works fine just as it is.
ps: the ability to accept facts as presented leads to a wisdom far surpassing the entrapment of ideology.

No matter how much time will pass unless you change your mind to the correct way of thinking you will be forever wrong.

Rules are well established to answer such a problem of interpretation. They are widely accepted and agreed upon so that they yield the same answer. It is more than a repeating of catch phrases or cant terms, it is repeating a rule that is accepted so that we may all arrive at the same answer. Like any language we must agree on definitions in order to communicate. You refuse to accept this. That's your problem - and it makes you wrong!!

6 over 2(1+2) = 6/6...1 2 becomes part of the equation on the sub level.

Are we still going on about this?

How long must we beat the dead horse.

We've already establised, 10 pages ago I might add, that the equation is ambiguous.

Even a string theorists agrees, in a youtube video when asked the question, that both answers are valid.

The way the question is written ambiguously.

BTW my cousin who's a physicist also agrees with the answer of 9.

reply to post by grey580


If he agrees with 9 then he's wrong, because you just stated it's ambiguous. It can be either, so you can't rightly side with 1 or 9. You must accept that the equation is faulty in its presentation.