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#1

48?2(9+3) = ?

Archive: 81 posts


http://i51.tinypic.com/8z1u08.jpg

Okay, this "thing" has gotten way out of hand. Not only is it all over the internet, but people (even mathematicians) are arguing about the answer to this problem. People even claim their calculators give them mixed results.

Right now, the two possible answers are 2 or 288. However, I know this site has a lot of smart people, so I'm pretty confident we'll all agree on an answer quickly.

So, what's the answer?
2011-04-10 04:10:00

Author:
CyberSora
Posts: 5551


5







...

I mean 2.
2011-04-10 04:14:00

Author:
Silver39
Posts: 1703


288. You have to do the numbers in the parentheses first.
48/2 x 12
Then you do the problem from left to right
24 x 12
288

Why are people arguing about it, it seems so obvious ._.
2011-04-10 04:15:00

Author:
Testudini
Posts: 3262


5







...

I mean 2.


288. You have to do the numbers in the parentheses first.
48/2 x 12
Then you do the problem from left to right
24 x 12
288

Why are people arguing about it, it seems so obvious ._.

Oh. My. God.
2011-04-10 04:16:00

Author:
CyberSora
Posts: 5551


288. You have to do the numbers in the parentheses first.
48/2 x 12
Then you do the problem from left to right
24 x 12
288

Why are people arguing about it, it seems so obvious ._.
This. Basic order of operations people.
2011-04-10 04:17:00

Author:
Patronus21
Posts: 266


Well....it IS basic algebra....? Is there something I'm missing here?2011-04-10 04:17:00

Author:
Laharl
Posts: 152


Because some, like me.

Combined 12 and 2 because you have to take care of the parenthese first right?

48/2(12)

12 is in parentheses.
2011-04-10 04:18:00

Author:
Silver39
Posts: 1703


Oh. My. God.

I had the same reaction

The only way you could get two is if you did the problem completely wrong. You have to do the parentheses first, then multiply, THEN divide, which is not how you do math at all and means you need to go back to school if you think the answer is 2...



Because some, like me.

Combined 12 and 2 because you have to take care of the parenthese first right?

48/2(12)

12 is in parentheses.

Read my explanation.
You do parentheses first (I know there's something else you do first, but can't remember what it's called right now)
Then you do multiplication and division, left to right
Then you do addition and subtraction, left to right
2011-04-10 04:19:00

Author:
Testudini
Posts: 3262


So close to finding answer... so close.

/facepalm
2011-04-10 04:19:00

Author:
CyberSora
Posts: 5551


Yeah, I'm exactly the same as UltimateClay. Did it the same way, got the same answer, confused as to why it's confusing.

/5 x sniped
2011-04-10 04:19:00

Author:
SR20DETDOG
Posts: 2431


CS, if your really taking my answer seriously, I think you should consider my horrible average grade in Algebra last year of 90.2011-04-10 04:22:00

Author:
Silver39
Posts: 1703


This is why people are arguing.

"2" version:

48/2(9+3)
48/2(12) <- Multiply the parentheses, because it's a must.
48/24
2

"288" version:

48/2(9+3)
48/2x12 <-They remove parentheses
24x12
288

Basically, nobody's winning here. ;_;
2011-04-10 04:23:00

Author:
CyberSora
Posts: 5551


This is why people are arguing.

"2" version:

48/2(9+3)
48/2(12) <- Multiply the parentheses, because it's a must.
48/24
2

"288" version:

48/2(9+3)
48/2x12 <-They remove parentheses
24x12
288

Basically, nobody's winning here. ;_;

But the 2 way is wrong, because they're doing the RIGHT side first, instead of the left.
2011-04-10 04:25:00

Author:
Testudini
Posts: 3262


You can't change the parentheses into a multiplication symbol? That's the purpose of the parentheses.

Left to right, AFTER the parentheses.
2011-04-10 04:25:00

Author:
Silver39
Posts: 1703


sigh. Basic order of operations people, you do what's INSIDE the brackets first, not anything beside them. It's 288.2011-04-10 04:26:00

Author:
Merc
Posts: 2135


You can't change the parentheses into a multiplication symbol? That's the purpose of the parentheses.

Left to right, AFTER the parentheses.

x(y+z) means you multiply x times the sum of y+z. Doesn't change when you change the variables to numbers. Or did I totally misread that?

And yes, left to right after you solve the problem(s) IN the parentheses.
2011-04-10 04:29:00

Author:
Testudini
Posts: 3262


I'm sure this is some sort of trolling post, but...

Think about it like this:

http://latex.codecogs.com/gif.latex?frac{48}{2%289+3%29}

Or hell, even like this:

http://latex.codecogs.com/gif.latex?frac{48}{2}%289+3%29
2011-04-10 04:33:00

Author:
comphermc
Posts: 5338


I'm sure this is some sort of trolling post, but...

Think about it like this:

http://latex.codecogs.com/gif.latex?frac{48}{2%289+3%29}

Or hell, even like this:

http://latex.codecogs.com/gif.latex?frac{48}{2}%289+3%29

Thank you!

Now, if only we can convince half of the internet now. -_-
2011-04-10 04:34:00

Author:
CyberSora
Posts: 5551


48/2(9+3) Parenthese first so add 9 and 3.
48/2(12) Parentheses is still there so it has more priority.
48/24 Parentheses gone, free to multiple and divide as you must.
2 That's how I read it.

EDIT: CS, those two end up with different outcomes too.
2011-04-10 04:37:00

Author:
Silver39
Posts: 1703


48/2(9+3) Parenthese first so add 9 and 3.
48/2(12) Parentheses is still there so it has more priority.
48/24 Parentheses gone, free to multiple and divide as you must.
2 That's how I read it.

EDIT: CS, those two end up with different outcomes too.

That means your multiply 2 by 12. So you must do the problem left to right.

EDIT: Read the post totally wrong. I'm tired, so I apologize.
2011-04-10 04:40:00

Author:
Testudini
Posts: 3262


Oh so it's 48/212

Since the parentheses goes away.
2011-04-10 04:41:00

Author:
Silver39
Posts: 1703


http://www.sherdog.net/forums/f7/48-2-9-3-500-1000-educated-people-got-answer-wrong-worldwide-1623165/
-and-
http://knowyourmeme.com/memes/48293

There's more sites debating about this (especially 4chan), but I'm too lazy to go find them.
2011-04-10 04:42:00

Author:
CyberSora
Posts: 5551


http://www.sherdog.net/forums/f7/48-2-9-3-500-1000-educated-people-got-answer-wrong-worldwide-1623165/
-and-
http://knowyourmeme.com/memes/48293

There's more sites debating about this (especially 4chan), but I'm too lazy to go find them.
My god, that first thread you linked has gone on for 51 pages...The internet blows anything out of proportion!
2011-04-10 04:51:00

Author:
TheZimInvader
Posts: 3149


I know this may be different, but I've always learn you use the Distributive Property to distribute the numbers if a number multiplies an equation in parentheses. Like this:

1. 48?2(9+3)

- Starting Expression

2. 48?18+6

- When you distribute, you multiply 2 x 9 and then 2 x 3. This gives you 18 and 6 and the parentheses are lost from the Distributive Property

3. 2.67+6

- Now, following the basic order of operations, you first divide 48 by 18. This gives you ≈ 2.67. The real answer continues (=2.6666666666666.....).

4. 8.67

- Finally, I end up with 8.67 by adding 6. Because the Distributive Property always comes before the basic order of operations, it seems this is the most logical answer (in my opinion).
2011-04-10 05:26:00

Author:
Night Angel
Posts: 1214


I learned
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction In my math class(P.E.M.D.A.S). It's the order you do things in...
2011-04-10 05:40:00

Author:
sackboy7789
Posts: 280


Let's say 48?2(9+3)=2 then how would it be written so that it equals 288? 48?2x(9+3)? The "x" is redundant in that situation.

Surely for it to equal 2 it would have to be written 48?(2(9+3))
2011-04-10 05:44:00

Author:
SR20DETDOG
Posts: 2431


*grabs popcorn*

This has got to be the greatest, and most relevant debate in the history of the internet.

Definitley not blown out of proportion at all.

But srsly, why is this such a big deal?
2011-04-10 05:51:00

Author:
Merc
Posts: 2135


Mathematicians are arguing about this? I guess the qualifications for being a mathematician are pretty low-standard nowadays.

It's 288.
2011-04-10 06:06:00

Author:
Frinklebumper
Posts: 941


No, no, no, no.... You see. What you do is this.

Step 1. Write down 48/2(9+3)=x

Step 2. Stare at it.

Step 3. Grab SCIENTIFIC calculator (Or calculator on windows) and plug problem into calculator.

Step 4. Celebrate.

If you want to do it on paper, here's what you do.

Step 1. Write down problem.

Step 2. Read this. http://i1108.photobucket.com/albums/h419/00Cryogen/tumblr_lek6z59EWZ1qegwr2o1_500-1.jpg

Step 3. Repeat step 2 five times.

Step 4. Realize, the cake was a lie.

Step 5. Grab calculator.

Step 6. Break calculator.

Step 7. Realize you just broke a $130 dollar piece of equipment.

Step 8. ???

Step 9. Profit.
2011-04-10 06:11:00

Author:
Devious_Oatmeal
Posts: 1799


But srsly, why is this such a big deal?

Because people on the internet are wrong, and we can't have that!
2011-04-10 06:12:00

Author:
SR20DETDOG
Posts: 2431


Because people on the internet are wrong, and we can't have that!

Touch?. ___
2011-04-10 06:17:00

Author:
Merc
Posts: 2135


48/2(9+3)
-
48/2(12)
-
24(12) or 48/24
-
288 or 2

I'm going to go with 288 as equations are simply solved left to right. Remember that with PEMDAS, multiplication & division are equal and do not go ahead of one another.
2011-04-10 06:21:00

Author:
warlord_evil
Posts: 4193


48/2(9+3)
-
48/2(12)
-
24(12) or 48/24
-
288 or 2

I'm going to go with 288 as equations are simply solved left to right. Remember that with PEMDAS, multiplication & division are equal and do not go ahead of one another.


I don't know.... Can we really trust a Warlord named Evil? That has bad written all over it.

But in all seriousness - I'm just gonna grab some popcorn and join Merc - this is really being blown out of proportion. While we're at it. Let's discuss which came first, the chicken or the egg?

Also, why do y'all have to bring pandas into this. What did they ever do to you?
2011-04-10 06:25:00

Author:
Devious_Oatmeal
Posts: 1799


*Leaves LBPC for a while.*
*Come back to see this.*

Really? I thought we covered this problem already.

Anyhoo, I can understand why everybody's been getting this wrong (kind of).

They're multiplying with parentheses, as shown: 2(12) = 24. Because the basic math rule states you need to multiply when the parentheses is near a number, people automatically think they need to multiply to get rid of the parentheses. However, the division part gets in the way with that, so people who're going for the left-to-right way are saying the others are wrong.

Yeah. I'm just as confused myself. This question is like Troll God material.
2011-04-10 06:35:00

Author:
CyberSora
Posts: 5551


36/3(2+2)

Solve that bro.

BONUS QUESTION:
75/5(3+2)

That should keep em busy for awhile. Now to take over LBPC.
2011-04-10 06:43:00

Author:
Silver39
Posts: 1703


I really like this one. It involves nothing more than addition to confuse.

Add the numbers together as you go, starting from the top working your way down.
If you're gonna post the answer, put it in a spoiler, this only works if you don't already know the answer.
http://www.futilitycloset.com/wp-content/uploads/2008/01/2008-01-03-priming-effect.png
2011-04-10 06:52:00

Author:
SR20DETDOG
Posts: 2431


Yeah, that one is great, fooled me the first time too. Oh the lulz.2011-04-10 06:54:00

Author:
Merc
Posts: 2135


I'm going to give a direct answer to that one: 4100?2011-04-10 07:25:00

Author:
Laharl
Posts: 152


I'm going to give a direct answer to that one: 4100?

WHAT!?!?! WHY... DON'T YOU KNOW??? It's 42... DUH.
2011-04-10 07:32:00

Author:
Devious_Oatmeal
Posts: 1799


WHAT!?!?! WHY... DON'T YOU KNOW??? It's 42... DUH.
Someone likes Hitchhikers Guide to the Galaxy

And I'm probably wrong anyways. I'm terrible at math.
2011-04-10 07:35:00

Author:
Laharl
Posts: 152


36/3(2+2)


Oooh I love maths!
48.


BONUS QUESTION:
75/5(3+2)


75!! Can I have a cookie now?
2011-04-10 07:40:00

Author:
Jovuto
Posts: 2345


Someone likes Hitchhikers Guide to the Galaxy

And I'm probably wrong anyways. I'm terrible at math.


Nah, you're right. It's

4100
I think the joke is they're suppose to get 5000.

It worked on my little brother just now.
2011-04-10 07:42:00

Author:
Devious_Oatmeal
Posts: 1799


The answer is 2. I've hired a professional mathematician to engineer a word problem pertaining to the problem at hand. By applying a practical application to the problem, we have demonstrated that the answer must be reasonable within the given context thus the answer could reasonably only be 2.

Jack purchases 9 apples. Then he purchases three more. Joe has twice as many apples as Jack. John has 48 apples. The number that Jim has is equal to the number that John has divided by the number that Joe has. Find the number of apples that Jim has.

As you can see from the word problem, the answer is 2.

The number of apples that Jack has is 9 + 3.
The number of apples that Joe has is twice as many as the number of apples that Jack has, thus 2(9 + 3).
The number of apples that John has is 48.
The number of apples that Jim has is equal to the number that John has divided by the number that Joe has. Since John has 48 and Joe has 2(9 + 3), this is expressed as 48 ? 2(9 + 3), which is 48 ? 2 ? 12, which is 24 ? 12, which is 288.

Obviously, this answer is not reasonable as Jim cannot have a greater number of apples when his total is divided by that of John and Joe.

Therefore the correct solution is:

The number of apples that Jack has is 9 + 3.
The number of apples that Joe has is twice as many as the number of apples that Jack has, thus 2(9 + 3), which is 2 ? 12, which is 24.
The number of apples that John has is 48.
The number of apples that Jim has is equal to the number that John has divided by the number that Joe has. Since John has 48 and Joe has 24, this is expressed as 48 ? 24, which is 2.

Therefore, Jim has 2 apples, not 288 apples.
2011-04-10 07:46:00

Author:
Enlong3
Posts: 357


AHA!!! You didn't take into account the REAL story of the apples.

So...

Jack has 9 apples, he then gets 3 more. John takes 48 apples, then divides them so they both get an equal cut. But then John sees Jack got 12 more apples than him, so he takes more to even out the total. But then that greedy Jack keeps taking apples so he has more than John. John then calls the others over, Jim and Joe. They talk it over and pull out a bat, chain, and brass knuckle. Jack sees this and goes, "OH ****!!!". He grabs a shopping cart and throws all his apples into it. He then pushes it towards checkout, but... WHAT'S THIS?!?!? A security officer is standing right in front of him. Jack points to the others and the cop immediately heads towards them. They scatter. Jack, seeing an opening, shoots out the front door.

Moral of the story? What kind of freakin apples were those to begin with? I want some of THOSE apples.

But seriously:

Jack has 48 bags. He needs to separate them so him and Joe have the same number of bags.

Joe has 9 "apples", then gets 3 more because he realizes the bags can hold more than 9.

So... Jack separates the bags then Joe puts 12 "apples" into each bag. They now have enough for the month long road trip. Each getting 24 bags to themselves.

See... You're not the only one that can hire a lawyer...
2011-04-10 08:15:00

Author:
Devious_Oatmeal
Posts: 1799


FACE.DESK.FACE.DESK.

288. Just because you see 2(12) does not mean you have to multiply the two first. The point of parenthesis taking precedence is that you do what is INSIDE it first. Notice the two is on the outside, thus it is equivalent to 2*12. I'm not feeding this topic anymore after this. Have better things to do, like my vector calculus homework.
2011-04-10 08:21:00

Author:
Patronus21
Posts: 266


fEeD uS!!!!! wE lIvE oFf yOuR cRuShEd hOpE fOr hUmAnItY.... aLl wE kNoW iS sImPle qUaNtUm pHySiCs... bUt vEcToRs aRe fUn tOo..... GrRrRRrRRrrrrrrRrrrRRRRR.

(Btw folks, my last post was just to say, a word problem isn't necessary, and doesn't prove anything. If you follow the basics of math, you'd know the answer)
2011-04-10 08:53:00

Author:
Devious_Oatmeal
Posts: 1799


The calculator built into my computer says 4. O_o Google says 288 though (http://www.google.co.uk/#hl=en&xhr=t&q=48/2(9%2B3)&cp=9&pf=p&sclient=psy&aq=f&aqi=&aql=&oq=48/2(9%2B3)&pbx=1&fp=e807647f54fc789f). Some random calculator online said NaN, so that calculator just fails. I dunno what to believe!

http://img407.imageshack.us/img407/8205/kbmindblown2.gif
2011-04-10 09:04:00

Author:
Doopz
Posts: 5592


Both times it was put in wrong.

You have to press ONLY THESE, IN THIS ORDER:

48

/

(

2

)

(

9

+

3

)

If you don't do it this way, you need to take a class in proper calculator etiquette. You must type what the problem says. The only time you can add parentheses is on only 1 number.

(48)/(2)((9)+(3))

lol

But seriously, so I don't add to the confusion. Write it like this:

48/2*(9+3)
2011-04-10 09:19:00

Author:
Devious_Oatmeal
Posts: 1799


I'm not an idiot, I know how to use a calculator. That's what I put in.2011-04-10 09:23:00

Author:
Doopz
Posts: 5592


I got 80085.2011-04-10 09:27:00

Author:
Rabid-Coot
Posts: 6728


217 if you go from left to right without doing the '( )' first.
288 if you go from left to right but first you do the '( )'.
0.5 if you go from right to left.

That are the three solutions I found...
2011-04-10 09:30:00

Author:
yoda97yoda
Posts: 121


Ahem, problem solved:

For instance, we have the two expressions:

1) 48 ? 2 • (9+3)
2) 48 • 2 ? (9+3)

Applying reciprocal method:

1) http://latex.codecogs.com/gif.latex?frac{48}1 ? http://latex.codecogs.com/gif.latex?frac{2%289+3%29}1

http://latex.codecogs.com/gif.latex?frac{48}1 • http://latex.codecogs.com/gif.latex?frac{1}%20{2%289+3%29}

http://latex.codecogs.com/gif.latex?frac{48}1 • http://latex.codecogs.com/gif.latex?frac{1}%20{2%2812%29}

http://latex.codecogs.com/gif.latex?frac{48}1 • http://latex.codecogs.com/gif.latex?frac{1}%20{24}

http://latex.codecogs.com/gif.latex?frac{48}%20{24}

http://latex.codecogs.com/gif.latex?frac{2}%20{1}

Applying order of operations:

1) 48 ? 2 • (9+3)
48 ? 2 • 12
48 ? 24
2

Applying reciprocal method:

2) http://latex.codecogs.com/gif.latex?frac{48%20%282%29}%20{1} ? http://latex.codecogs.com/gif.latex?frac{%289+3%29}%20{1}

http://latex.codecogs.com/gif.latex?frac{48%20%282%29}%20{1} • http://latex.codecogs.com/gif.latex?frac{1}%20{%289+3%29}

http://latex.codecogs.com/gif.latex?frac{48%20%282%29}%20{1} • http://latex.codecogs.com/gif.latex?frac{1}%20{12}

http://latex.codecogs.com/gif.latex?frac{96}%20{1}• http://latex.codecogs.com/gif.latex?frac{1}%20{12}

http://latex.codecogs.com/gif.latex?frac{96}%20{12}

http://latex.codecogs.com/gif.latex?frac{8}%20{1}

Applying order of operations:

2) 48 • 2 ? (9+3)
48 • 2 ? 12
96 ? 12
8

Solution? When applying the order of operations, multiply before dividing.
2011-04-10 10:22:00

Author:
Enlong3
Posts: 357


Can we please leave algebra out of LBP it is SO CONFUSING!!!!!!!!2011-04-10 12:05:00

Author:
craigmond
Posts: 2426


48 and 2(9+3) are two separate terms. The 2 only affects what's in the brrackets. So you can't say 48?2x12, because BODMAS would suggest that 2 divides 48, when in actual fact it should multiply the 12. More on that later, but ...


I'm sure this is some sort of trolling post, but...

Think about it like this:

http://latex.codecogs.com/gif.latex?frac{48}{2%289+3%29}

As the 2(9+3) is one term at the start, 48 divides the whole of this expression. So, we simplify down to this:

http://latex.codecogs.com/gif.latex?frac{48}{2%2812%29}

http://latex.codecogs.com/gif.latex?frac{48}{24}

http://latex.codecogs.com/gif.latex?frac{2}{1}

http://latex.codecogs.com/gif.latex?{2}

There's a difference between 48?2x12 and 48?2(12), which is where the biggest discrepancies arise I think. In the left one, BODMAS states that division occurs before multiplication, so the answer is 288. But that's not our situation - we have the right expression. 2(12) is a single term - it means that "2 is multiplied by 12, and no other number". Brackets come first, so that becomes 24 before dividing by 48.
2011-04-10 12:12:00

Author:
Holguin86
Posts: 875


How then would you re-write 48?2(9+3) so that it would equal 288? (not a rhetorical question)2011-04-10 12:51:00

Author:
SR20DETDOG
Posts: 2431


I have always been taught that you don't go left to right in every problem, you only follow "PEMDAS"

Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

So I am a supporter of 2. Of course, that is just how I was taught...

48/2(9+3)
48/2(12)
48/24
2

Since I have been taught this all my life, it puzzles me why someone would say, "288" or any other number for that matter, but that's just because I have grown accustomed to this method. This doesn't necessarily mean that I couldn't be convinced that I am wrong. To be honest, I don't have any great confidence in my education.
2011-04-10 13:06:00

Author:
Unknown User


This is algebra. So you generally use the order of operations PEMDAS. (Well...that's what I was taught)

so 48/2(9+3) would be 2 because:

1. Parenthesis
2. Exponent
3. Multiplication
4. Division
5. Addition
6. Subtraction

So you do what's in the parenthesis first. (9+3) = 12

So the equation will be 48/2(12)

you skip exponents because there aren't any, then you do multiplication

48/24

then you divide

48/24 = 2

I guess no one here learned PEMDAS in grade school?
2011-04-10 13:09:00

Author:
comishguy67
Posts: 849


How then would you re-write 48?2(9+3) so that it would equal 288? (not a rhetorical question)

(48?2)(9+3)
2011-04-10 13:16:00

Author:
Syroc
Posts: 3193


I guess no one here learned PEMDAS in grade school?

I've always been taught it as BIDMAS

Brackets
Indices
Division
Multiplication
Addition
Subtraction

Which I guess would explain why there's so much confusion here, because following those rules you do, 9+3 = 12. 48?2 = 24, then 12x24 = 288.

It's simply that we've all been taught different rules, so either 2 or 288 are correct, depending on what rules you were taught.
2011-04-10 13:30:00

Author:
Doopz
Posts: 5592


(48?2)(9+3)
Of course, not sure why that didn't occur earlier, oh well.
2011-04-10 13:49:00

Author:
SR20DETDOG
Posts: 2431


I got 288 too.2011-04-10 14:11:00

Author:
Cactii
Posts: 426


There's a difference between 48?2x12 and 48?2(12), which is where the biggest discrepancies arise I think.

No, there's not a difference at all. A number smooshed against a parenthesis implies multiplication. Multiplication doesn't change because it looks a little different.

I'm surprised nobody caught my little tongue-in-cheek post back there:


I'm sure this is some sort of trolling post, but...

Think about it like this:

http://latex.codecogs.com/gif.latex?frac{48}{2%289+3%29} <--- This is just idiocy!!

Or hell, even like this:

http://latex.codecogs.com/gif.latex?frac{48}{2}%289+3%29

This was just restating what everyone else is already saying to rile everyone up. Instead, they thought I was picking a side. Heh.

Well, I will pick a side now, since you guys obviously didn't learn anything in your algebra classes...

Most of you are spot in with your assessment of PEMDAS (or BEMDAS), which is an acronym to remember that when doing mathematics, we perform calculations in the order of parenthesis (bracket), exponents, multiplication, division, addition, subtraction. The problem with this is that multiplication/division and addition/subtraction are completely interchangeable when you write it as line text. For example, consider the expression:

http://latex.codecogs.com/gif.latex?30div5times%202

I think you are able to see that this the answer is 3. Some of you might argue that this has the same inherent problem as the problem addressed in this thread, since multiplying the 5 and 2 first will result in the same answer. This is not because multiplication comes first, but because multiplication is commutative (you can rearrange the order of multiplication). To show this, we just look at division as multiplication by the reciprocal, and apply commutativity as we please:

http://latex.codecogs.com/gif.latex?30div5%20times%202=left{begin{matri x}%20frac{1}{5}times2times30=3%20frac{1}{5} times30times2=3%2030times%20frac{1}{5}%20tim es%202%20=3%2030times2timesfrac{1}{5}=3%202 timesfrac{1}{5}times30=3%202times20timesfr ac{1}{5}=3%20end{matrix}right.

Clearly it doesn't matter what order we multiply in. This is called commutativity.

Let's apply the same logic to the stated problem:

http://latex.codecogs.com/gif.latex?48div2left%20(%209+3%20right%20)=48t imesfrac{1}{2}left%20(%209+3%20right%20)=48tim esfrac{1}{2}left%20(%2012%20right%20)=48times6 =288

Most of you are hung up on the parenthesis from the original problem, saying that we need to multiply the 2 to what's inside the parenthesis. No. You clearly don't understand what it means to say that we take order of operations priority on the parenthesis... it means that everything inside the parenthesis is done first. This does not mean that we need to apply external operations on the parenthesis first, unless said operation is next in the order.

Note that the wikipedia page on Order of Operations (http://en.wikipedia.org/wiki/Order_of_operations) clearly states the brackets (or parenthesis) part of the acronym applies to what is inside. I thought that was clear.

---

I consider the argument over. If you're trolling... well done. If you still don't get it... too bad. That's how it works, and it's not up for debate.

Compher - out!

Edit: Wolfram'd for good measure (http://www.wolframalpha.com/input/?i=48%2F2%289%2B3%29)
2011-04-10 14:57:00

Author:
comphermc
Posts: 5338


Sooooooooooo Comph Y U NO LOCK?

EDIT: /looks at comph's post below
Oooooooh, My mistake.
2011-04-10 15:14:00

Author:
KILLA_TODDZILLA
Posts: 653


My name's not blue, mate.2011-04-10 15:17:00

Author:
comphermc
Posts: 5338


Finally, a proper explanation from a maths teacher. Thanks for clearing that up. 2011-04-10 15:36:00

Author:
Holguin86
Posts: 875


... People actually think the answer is 2?

And that there is a huge internet war over this?

...

Come on humanity, please, for the love of god, I NEEDED that little bit of faith I had >_<

God...

For the lvoe of god people, when you do the stuff inside paranthesis... THEY GO AWAY.

Is 2 inside the paranthesis? No? THEN WHY THE **** ARE YOU ACTING LIKE THEY ARE.

For the love of god, people, when you see paranthesis, you do what's INSIDE them. There is no operation in 12. Hence, when you do the operation, there is nothing there but the value.

48/1 / 2...

48 *.5 * 12

My god, is the internet actually in open debate over what happens when you do the operation in paranthesis? You do what's INSIDE. INSIDE. That's what they're for.

... God. And I know I'm overreacting, but the mere thought that people are in open debate over the most simple of mathmatical properties (as opposed to anything else) makes me sick >_<
2011-04-10 15:54:00

Author:
RockSauron
Posts: 10882


Ah, math... 3208 solutions but only one answer.

48/2(9+3)=48/2(12)=12*48/2=12*24=24*12 ≠ 48/(2(9+3))=48/(18+6)=48/(2(12)=48/24 (≠24/48)

0
2011-04-10 15:56:00

Author:
Syroc
Posts: 3193


Well, Comph answer seems to be quite definitive but I think this is kind of a Sybillin stuff.
It's just made up to be ambiguos and unsolvable with a unique answer.

In Italy (actually Latin) we have a nice story.
Before leaving for a war, a warrior goes to the sybil to know if he will be back.
The sybil answers:

IBIS REDIBIS NON MORIERIS IN BELLO

Which translates in Italian as
ANDRAI TORNERAI NON MORIRAI IN BATTAGLIA
which translates into English as
(assume the future tense for all the sentence, this things doesn't work well in English )
YOU'LL GO BE BACK NOT DIE IN THE BATTLE

As you see there's not a coma so the sentence can be read both as

YOU'LL GO, BE BACK, NOT DIE IN BATTLE
and as
YOU'LL GO, BE BACK NOT, DIE IN BATTLE

As you see, just moving the coma has 2 opposites outcomes.

So actually I think that no answer can totally eliminate the other since the inappropriate system of visualization the math is intentionally confusing, because even if Comph's explanation of "the visualization" of that math is the most logic, it still remains just an interpretation, because we may never now if the parentesis is placed as the divisor together with the 2 or not.
2011-04-10 15:58:00

Author:
OmegaSlayer
Posts: 5112


... People actually think the answer is 2?

And that there is a huge internet war over this?

...

Come on humanity, please, for the love of god, I NEEDED that little bit of faith I had >_<

God...

For the lvoe of god people, when you do the stuff inside paranthesis... THEY GO AWAY.

Is 2 inside the paranthesis? No? THEN WHY THE **** ARE YOU ACTING LIKE THEY ARE.

For the love of god, people, when you see paranthesis, you do what's INSIDE them. There is no operation in 12. Hence, when you do the operation, there is nothing there but the value.

48/1 / 2...

48 *.5 * 12

My god, is the internet actually in open debate over what happens when you do the operation in paranthesis? You do what's INSIDE. INSIDE. That's what they're for.

... God. And I know I'm overreacting, but the mere thought that people are in open debate over the most simple of mathmatical properties (as opposed to anything else) makes me sick >_<

ROTFL!

Maybe it's because math is my Achilles heel, but I just don't get why anyone would care about this. Is the answer going to solve any other problems other then the equation?
2011-04-10 16:07:00

Author:
KILLA_TODDZILLA
Posts: 653


You guys are still debating over this? No one's locked the thread yet? whatever.

*fills bowl with more popcorn*
2011-04-10 16:13:00

Author:
Merc
Posts: 2135


Again the point is like Comph said, it's just some kind of trolling to have fun with something that, again, is PURPOSEDLY AMBIGUOUS.
What I noticed is that everyone that tried to solve the problem had to interpret the equation before solving it.
So the ? has become / , and the "space" between the brackets and the 2 has become a * or a x.
Anyway nice little funny joke

@Merc...I arrived late, got some problem with that? ... LOL
2011-04-10 16:14:00

Author:
OmegaSlayer
Posts: 5112


So actually I think that no answer can totally eliminate the other since the inappropriate system of visualization the math is intentionally confusing, because even if Comph's explanation of "the visualization" of that math is the most logic, it still remains just an interpretation, because we may never now if the parenthesis is placed as the divisor together with the 2 or not.

I think the thing you're not thinking of is "What is mathemetics?"

I think people fail to make the distinction between the nature of mathematics and the way that we represent it. You were getting at an interesting point which I'll address in a moment, but the problem that this thread focuses on is not a discussion on the nature of mathematics, but on the way that we represent mathematics. In reality, there is no actual, real-world problem that is meant to be solved with the problem - it's merely a collection of symbols.

The discussion, then, is based around our interpretation of those symbols.

The funny thing is... it's not even a discussion. There is a set, pre-determined, formulaic way of interpreting mathematic symbols. There is no discussion about it. It only becomes a problem when people can't properly interpret the symbols. As it is written, the expression reduces to 288. If I wanted to use the same symbols written in a slightly different way so that it reduces to 2, I can:

http://latex.codecogs.com/gif.latex?frac{48}{2%289+3%29}

The problem is that this is not the same form, and is line equivalent to:

http://latex.codecogs.com/gif.latex?48div[2(9+3)]

Thus, it's a different representation altogether. It's not up for debate as to the interpretation because smarter men than you or I decided that this is how we are going to symbolically represent mathematical operations. It was done this way so that there will be no interpretation issues, as long as people are educated on how to interpret the forms.

Now, as for your example of a sentences interpretation based on where a comma is placed - you are exactly proving my point.

It's the notation, the symbols, and our interpretations that give meaning. If a comma is placed somewhere, it is done for a reason. It is up to the author to choose the representation that matches with the intended meaning. It becomes an issue only when the reader cannot correctly interpret the symbols or when the author chose the wrong representation.

Back to the math problem. This expression is equal to 288. If someone were to interpret it as 2, they are misreading the symbols per the formally-agreed-upon method of reading mathematics. If the author intended the expression to be equal to 2, they misrepresented it. The argument here is the former since there is no context provided for the expression - it's just symbols. If you are reducing the expression to 2, then you are at fault. You are not interpreting correctly.

I cannot stress this enough:

This is not a debate. The interpretation is clearly defined. If it doesn't make sense, your knowledge of mathematical symbol interpretation is lacking. I don't mean offense, but your lack of knowledge does not constitute a reason to argue that math is inherently contradictory. You just haven't figured it out yet.
2011-04-10 16:25:00

Author:
comphermc
Posts: 5338


Good God, what have I done!? 2011-04-10 16:26:00

Author:
CyberSora
Posts: 5551


288. You have to do the numbers in the parentheses first.
48/2 x 12
Then you do the problem from left to right
24 x 12
288

Why are people arguing about it, it seems so obvious ._.

I agree that this shouldn't be open for debate. Simple order of operations (http://www.mathgoodies.com/lessons/vol7/order_operations.html). This is basic mathematics. Not even high school level.


The funny thing is... it's not even a discussion. There is a set, pre-determined, formulaic way of interpreting mathematic symbols. There is no discussion about it.

QFT
2011-04-10 16:28:00

Author:
BlackWolfe
Posts: 299


BODMAS we call it at school (standing for Brackets, Order, Division, Multiplication, Addition, Subtraction). It's brackets first (12), then divison, so 48/2, then multiplication, so 24*12, which equals 288.

Thanks, now I can claim I did Maths revision
2011-04-10 16:28:00

Author:
kirbyman62
Posts: 1893


Heh. I'm done. I've said all I needed to say. See the bold.2011-04-10 16:30:00

Author:
comphermc
Posts: 5338


Well, I'm officially done with this. All I wanted was an answer and an explanation so people at KYM can drop this. I didn't want this to become an issue. :/

Going for a lock now.
2011-04-10 16:42:00

Author:
CyberSora
Posts: 5551


... People actually think the answer is 2?

And that there is a huge internet war over this?

...

Come on humanity, please, for the love of god, I NEEDED that little bit of faith I had >_<

God...

For the lvoe of god people, when you do the stuff inside paranthesis... THEY GO AWAY.

Is 2 inside the paranthesis? No? THEN WHY THE **** ARE YOU ACTING LIKE THEY ARE.

For the love of god, people, when you see paranthesis, you do what's INSIDE them. There is no operation in 12. Hence, when you do the operation, there is nothing there but the value.

48/1 / 2...

48 *.5 * 12

My god, is the internet actually in open debate over what happens when you do the operation in paranthesis? You do what's INSIDE. INSIDE. That's what they're for.

... God. And I know I'm overreacting, but the mere thought that people are in open debate over the most simple of mathmatical properties (as opposed to anything else) makes me sick >_<

I helped tick off Rock. I feel fulfilled.

(Also Done, because others said it too.) :3
2011-04-10 16:44:00

Author:
Silver39
Posts: 1703


"summarized as intersting stuff"

Actually I have no problem in saying that when I studied mathsand equations 16-17 years ago we wrote the stuff on paper, so there weren't other ways to read what was written.
Now, when I get in touch with something like that equation, I need to visualize it in a way that I actually know, because, like it's written there, with a system purposedly and universally decided as a computer visualization, it's not the stuff I know.
So, the point is that for who has studied maths some years ago, and didn't kept exercising, didn't kept up to date to the standard decided as a scientific codification and didn't degree, that visualization is puzzling.
Don't get mad Comph
2011-04-10 16:49:00

Author:
OmegaSlayer
Posts: 5112


Well, I'm officially done with this. All I wanted was an answer and an explanation so people at KYM can drop this. I didn't want this to become an issue. :/

Going for a lock now.

Locked by request.
2011-04-10 17:03:00

Author:
schm0
Posts: 1239


I know this may be different, but I've always learn you use the Distributive Property to distribute the numbers if a number multiplies an equation in parentheses.

The equivalence...

http://latex.codecogs.com/gif.latex?a(b+c)=ab+ac

...is valid, but the result should be parenthesized, so it's...

http://latex.codecogs.com/gif.latex?48div2(9+3)=48div(18+6)=48div24=2

Factorizing (the reverse of this) so...

(a AND b) OR (a AND c)

...becomes...

a AND (b OR c)

...is really useful in boolean algebra applied to digital electronics, as it saves you a logic gate.

<table border="1"> <tr><th>a</th><th>b</th><th>c</th><th>b+c</th><th>a(b+c)</th><th>ab</th><th>ac</th><th>ab+ac</th></tr> <tr><td style="background:#ff7f7f">0</td><td style="background:#ff7f7f">0</td><td style="background:#ff7f7f">0</td><td style="background:#ffff7f">0</td><td style="background:#7fff7f">0</td><td style="background:#ffff7f">0</td><td style="background:#ffff7f">0</td><td style="background:#7fff7f">0</td></tr> <tr><td style="background:#ff7f7f">0</td><td style="background:#ff7f7f">0</td><td style="background:#ff7f7f">1</td><td style="background:#ffff7f">1</td><td style="background:#7fff7f">0</td><td style="background:#ffff7f">0</td><td style="background:#ffff7f">0</td><td style="background:#7fff7f">0</td></tr> <tr><td style="background:#ff7f7f">0</td><td style="background:#ff7f7f">1</td><td style="background:#ff7f7f">0</td><td style="background:#ffff7f">1</td><td style="background:#7fff7f">0</td><td style="background:#ffff7f">0</td><td style="background:#ffff7f">0</td><td style="background:#7fff7f">0</td></tr> <tr><td style="background:#ff7f7f">0</td><td style="background:#ff7f7f">1</td><td style="background:#ff7f7f">1</td><td style="background:#ffff7f">1</td><td style="background:#7fff7f">0</td><td style="background:#ffff7f">0</td><td style="background:#ffff7f">0</td><td style="background:#7fff7f">0</td></tr> <tr><td style="background:#ff7f7f">1</td><td style="background:#ff7f7f">0</td><td style="background:#ff7f7f">0</td><td style="background:#ffff7f">0</td><td style="background:#7fff7f">0</td><td style="background:#ffff7f">0</td><td style="background:#ffff7f">0</td><td style="background:#7fff7f">0</td></tr> <tr><td style="background:#ff7f7f">1</td><td style="background:#ff7f7f">0</td><td style="background:#ff7f7f">1</td><td style="background:#ffff7f">1</td><td style="background:#7fff7f">1</td><td style="background:#ffff7f">0</td><td style="background:#ffff7f">1</td><td style="background:#7fff7f">1</td></tr> <tr><td style="background:#ff7f7f">1</td><td style="background:#ff7f7f">1</td><td style="background:#ff7f7f">0</td><td style="background:#ffff7f">1</td><td style="background:#7fff7f">1</td><td style="background:#ffff7f">1</td><td style="background:#ffff7f">0</td><td style="background:#7fff7f">1</td></tr> <tr><td style="background:#ff7f7f">1</td><td style="background:#ff7f7f">1</td><td style="background:#ff7f7f">1</td><td style="background:#ffff7f">1</td><td style="background:#7fff7f">1</td><td style="background:#ffff7f">1</td><td style="background:#ffff7f">1</td><td style="background:#7fff7f">1</td></tr> </table>

Note the two columns in green are identical - the yellow columns being intermediate results.




http://latex.codecogs.com/gif.latex?30div5%20times%202=left{begin{matri x}%20frac{1}{5}times2times30=3%20frac{1}{5} times30times2=3%2030times%20frac{1}{5}%20tim es%202%20=3%2030times2timesfrac{1}{5}=3%202 timesfrac{1}{5}times30=3%202times20timesfr ac{1}{5}=3%20end{matrix}right.

Excuse me, Mr. 'math teacher'. You're totally correct that...

http://latex.codecogs.com/gif.latex?30div5times2=30timesfrac{1}{5}times 2

...but I think you'll find that...

http://latex.codecogs.com/gif.latex?30timesfrac{1}{5}times2neq3

http://latex.codecogs.com/gif.latex?30timesfrac{1}{5}times2=12

As for the original question, I was unable to locate an authoritative source for the interpretation of this expression, so it's arguably ambiguous. However, based on common usage in textbooks, it seems to be the case that expressions of the form...

http://latex.codecogs.com/gif.latex?adiv%20btimes%20c

...are implied as meaning...

http://latex.codecogs.com/gif.latex?(adiv%20b)times%20c

...but expressions of the form...

http://latex.codecogs.com/gif.latex?adiv%20bc

...are implied as meaning...

http://latex.codecogs.com/gif.latex?adiv(btimes%20c)

...so I'd conclude that "2" is a better answer than "288", but either is valid.


P.S. I'd just like to point out that this correction was intended to educate, and was not part of an ongoing effort (https://lbpcentral.lbp-hub.com/index.php?t=26224-LBP-Scoring-System-Analysis-amp-Guide&p=455533&viewfull=1#post455533) to point out Comph's math errors for comedy value.
2011-04-10 17:36:00

Author:
Aya042
Posts: 2870


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