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Author Topic: Because I find the controversy surrounding this sadistically amusing
DDDaysh
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And because I'm curious about the general mathematical literacy of Hatrack...

6÷2(1+2)=? Solve

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Stone_Wolf_
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quote:
Rule 1: First perform any calculations inside parentheses.
Rule 2: Next perform all multiplications and divisions, working from left to right.
Rule 3: Lastly, perform all additions and subtractions, working from left to right.

Source.

6÷2(1+2)=?
6÷2(3)=?
3(3)= 9

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mr_porteiro_head
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This has already been thorougly hashed out:

http://www.hatrack.com/cgi-bin/ubbmain/ultimatebb.cgi?ubb=get_topic;f=2;t=058122

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Samprimary
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The hashing out of it has been amusing because some people have adopted the militaristically inflexible view that the answer to the last one is two.
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Lyrhawn
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I got into an epic almost hour long discussion over this with a half dozen people the other day. Getting them to understand the order of operations was nearly impossible, and two of them were engineers!

It was nice though. I never get to be smarter at math when my engineer friends are involved.

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DDDaysh
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Ah, I'm sorry, I didn't see that one! Thanks Porteiro.
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Wingracer
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This one is much easier than the other one. Anything other than 9 makes no sense what so ever.
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Lyrhawn
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It's exactly the same as the other one. The question hinges on whether Anything(Anything) is different than Anything X Anything. Does the parentheses give that multiplication operation precedence? If it does, the answer is 1.
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Wingracer
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The other one was less clear, at least to me. I agree that both are fundamentally the same but for whatever reason, this one is so easy there should be no controversy, the other one was easier to make a mistake.

And according to everything I have ever been taught or read or heard of, parenthesis only give precedence to operations WITHIN them. They have nothing to with things outside them, otherwise those operations would be IN them.

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scholarette
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I think where confusion comes in is that when you write in fraction form with numerator and denominator, you basically get the parentheses for free.

3+2
______
4+5

is the same as (3+2)/(4+5).

However, this whole conversation makes me feel like we live in a very math illiterate society which makes me sad.

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Lyrhawn
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I can do simple math. I can do all the math I can imagine needing to do to get through the day and my life.

You don't want me building bridges though.

I do wish I'd taken Statistics, but, that's probably a lot more work than I'm willing to invest.

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DDDaysh
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quote:
Originally posted by scholarette:
I think where confusion comes in is that when you write in fraction form with numerator and denominator, you basically get the parentheses for free.

3+2
______
4+5

is the same as (3+2)/(4+5).

However, this whole conversation makes me feel like we live in a very math illiterate society which makes me sad.

But what you wrote is fundamentally different than 3+2/4+5, and that's what seems to confuse people. I know, it makes me sad too, but even some of my math friends are arguing the other way - hence the sadistic part!
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Wingracer
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quote:
Originally posted by Lyrhawn:

I do wish I'd taken Statistics, but, that's probably a lot more work than I'm willing to invest.

It's never too late to start. Sounds like I am much the same as you except my hobbies do sometime require a bit more math than the average person would probably use. I have recently read some books on statistics, probability, game theory, etc. and find it quite fascinating.
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fugu13
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Get a copy of The Cartoon Guide to Statistics. Read that, trying to do the little exercises they talk about while going along.

If you do, you've gone through the equivalent of some of the best non-math major undergraduate statistics courses out there, and had a lot of fun doing it.

Further reading: Innumeracy and A Mathematician Reads the Newspaper.

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Lyrhawn
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Thanks fugu, I'm going to check those out.
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Wingracer
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I think I will too.
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Stephan
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quote:
Originally posted by Lyrhawn:
I can do simple math. I can do all the math I can imagine needing to do to get through the day and my life.

You don't want me building bridges though.

I do wish I'd taken Statistics, but, that's probably a lot more work than I'm willing to invest.

I took two statistics courses in college. Got A's in them both. I found it incredibly easy, especially since both teachers made all of the tests open book. Never had to memorize any formulas. I was shocked by how bad many of my classmates were doing in it.

I think I struggled in calculus because the teacher made us memorize formulas, and memorization is a huge weakness for me.

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Tresopax
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The controvesy here is not over order of operations. The controversy is over notation.

The question is whether there is an implied parenethesis around BC in the expression "A÷BC" created by the fact that no multiplication symbol was used. As someone mentioned, the reason it might be implied is because that might be interpretted as the electronic text equivalent of
A
----
BC

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Selran
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quote:
Originally posted by Tresopax:
The controvesy here is not over order of operations. The controversy is over notation.

The question is whether there is an implied parenethesis around BC in the expression "A÷BC" created by the fact that no multiplication symbol was used. As someone mentioned, the reason it might be implied is because that might be interpretted as the electronic text equivalent of
A
----
BC

Exactly, I was tough never to use the ÷ symbol, and to always express any division as a fraction. I think these threads demonstrate why.
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Lisa
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quote:
Originally posted by DDDaysh:
And because I'm curious about the general mathematical literacy of Hatrack...

6÷2(1+2)=? Solve

The answer is 1. Because 2(1+2) is not the same as 2 × (1 + 2). The side-by-side notation groups it. So we do 1+2=3. 2×3=6. And 6 divided by 6 is 1.
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Xavier
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quote:
Because 2(1+2) is not the same as 2 × (1 + 2).
Do you have any sources on this?
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fugu13
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It's just something she decided was the truth. Juxtaposition is nothing but another notation for multiplication, with no implicit grouping.
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theCrowsWife
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My calculator agrees with Lisa.
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rivka
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Many calculators get order of operations wrong. This is a limitation of programming small devices, not of OoO.
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just_me
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2(1+2) is the same as 2 × (1 + 2)

Calculators are NOT a good way to judge. rivka is right - many calculators don't follow the proper OoO

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aspectre
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So y'alls arguin' that 6÷2a = 3a ?
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The White Whale
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quote:
Originally posted by Lisa:
Because 2(1+2) is not the same as 2 × (1 + 2).

Yeah, that's wrong.
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The Rabbit
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quote:
Originally posted by aspectre:
So y'alls arguin' that 6÷2a = 3a ?

Yes!!

Are you maintaining the following

6/2*a=6/2a=6÷2*a=6÷2a

is not correct.

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Allomancer
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quote:
Originally posted by theCrowsWife:
My calculator agrees with Lisa.

That's funny. My calculator says the answer is 9. Of course you can just avoid the whole issue by adding another set of parentheses.
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DDDaysh
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I've tried two different graphing calculators and they were right, but the little regular one on my coworkers desk got it wrong. The windows calculator actually got it correct, though I remember it didn't do order of operations correctly a few years back.
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scholarette
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If you translate into English "six divided by two A" is different from "six divided by two times a." When people see 6/2A, they are translating it incorrectly to English and then doing the math based on that. If you think of the equation as six divided by two times A, I think everyone would get the question right.
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Juxtapose
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The order of operations here (as it exists now) is pretty clear. The answer is 9.

I do think Lisa's point is somewhat valid though. The fact that a significant portion of people see the juxtaposed numbers as grouped, and therefore with a higher precedence in the OoO, is a good reason to think that the rules should reflect that. This is after all a convention of language. If convention is communicating something other than what is intended, it's not good communication.

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theCrowsWife
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quote:
Originally posted by rivka:
Many calculators get order of operations wrong. This is a limitation of programming small devices, not of OoO.

I suspect it is more likely a choice made by the programmers of the calculator, rather than a limitation on the calculator itself. Anyhow, as Tresopax put it, the issue is not really with order of operations, but with the notation.
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