# 48÷2(9+3) = ??

## What is the answer?

• ### 2

Votes: 261 51.2%
• ### 288

Votes: 249 48.8%

• Total voters
510

#### RyanRF

##### Professional
Amusing thread.

288

But I work as a math tutor, and I do admit that the way the expression is written can be misleading for some.

Funny how Matlab has it's own order of operations

#### Readers

##### Professional
Amusing thread.

288

But I work as a math tutor, and I do admit that the way the expression is written can be misleading for some.

Funny how Matlab has it's own order of operations

Dude, read my post, which is only second one above yours, he is using a alpha/beta version of 2011b which won't be out for another half year or so.

#### BreakPoint

##### Bionic Poster
be sure???
What are you talking about?
Do you know the difference between the rule and assumption.
This is the rule.
What you're talking about is: a/(bc) = a/(b*c) = a/b(1/c) = a/b*(1/c)

48÷2(9+3) = 48/2(9+3) = the first equation on top above.

48(9+3)÷2 = 48(9+3)/2 = the second equation on the bottom above.

Get it now? The / sign is how people type the horizontal divide line on a computer keyboard as it's much easier than trying to type a horizontal divide line with numbers and variables above and below that line with a computer keyboard.

#### BreakPoint

##### Bionic Poster
That's what you get for use an unreleased software, 2011a is just out and u are using 2011b?? My 2009b tells me it's 288 which is correct.
So you're saying that his updated software with more bug fixes is wrong while your out-dated software without the bug fixes is correct? How do you know they didn't fix this problem with the new software when they realized that answer should be 2 and not 288?

#### subz

##### Rookie
here is info on associative law:
http://en.wikipedia.org/wiki/Associativity

And about the equation: 48÷2(9+3)
This is not a nice way to write an equation. better options:
(48÷2)(9+3) is 288 and 48÷(2(9+3)) is 2. Most people usually have to make up their own equations or solve problems using algebra where these trivila issues dont come up
I think its the fault of the person writing the equation !

#### dr325i

##### G.O.A.T.
And exactly how many engineering textbooks have you studied? I thought so.

What you're saying is that 48(9+3)÷2 = 48÷2(9+3), which is not true. One has (9+3) above the horizontal divide line and the other has (9+3) below the horizontal divide line.
Ah, you got me on that one...

15 years ago I got my MSEE, and before that my BSEE.
In the High School I studied stuff that in America you will NEVER see (Russian Math Books). Since then, I have written more engineering articles than the number of books you've read...

You are assuming things again (just like the "*" thing) and it is getting you nowhere and you get embarrassed with every post...

Get off this forum since 30k posts just drained your little brain... Learn the basics...PUNK

#### dr325i

##### G.O.A.T.

48÷2(9+3) = 48/2(9+3) = the first equation on top above.

48(9+3)÷2 = 48(9+3)/2 = the second equation on the bottom above.

Get it now? The / sign is how people type the horizontal divide line on a computer keyboard as it's much easier than trying to type a horizontal divide line with numbers and variables above and below that line with a computer keyboard.
you ABSOLUTELY have no idea what you're talking about...

#### dr325i

##### G.O.A.T.
here is info on associative law:
http://en.wikipedia.org/wiki/Associativity

And about the equation: 48÷2(9+3)
This is not a nice way to write an equation. better options:
(48÷2)(9+3) is 288 and 48÷(2(9+3)) is 2. Most people usually have to make up their own equations or solve problems using algebra where these trivila issues dont come up
I think its the fault of the person writing the equation !
It does not matter if it is written nicely or not. Math is tricky, but you have to follow the rules, simple as that, left to right, parenth first, then mult/division, then addition/subtraction.
48/2(9+3) is simple:
Parenthesis first gives you 48/2*12.
Left to right gives you 24*12 = 288

There are no assumptions in Math except in some cases where you have to prove them (like Mathematical induction method, etc)

Again, my 9 year old got this the first time, the guy with 30k useless posts is still debating if it is "*" or no "*" and so on...

#### equinox

##### Hall of Fame
Wow, the fact this question even needs to be asked shows decline of american education system.

This level of maths is taught before highschool.

Btw the answer is 2!

NOT!!!

#### cucio

##### Legend
The basic problem here is agreement on the rules of binary operation precedence. A expression like "a ^ b / c + d" has three binary operators, and its result is undefined unless there are implicit precedence rules. There are six possible sequences in which you can perform those three operations.

Some possible solutions to the problem of which operation goes first are:

1) No rules at all. The expression as notated above is meaningless and all the operations must be explicitly parenthesized (e.g., the lisp programming language.)

2) Strict positional order, for instance left to right. I have seen this in certain specific cases, mostly associated to simplified software parsers (programming exercises or quick proof-of-concept tests.) Also (reverse) Polish notation, but we are talking infix here.

3) GEMAL. This is very convenient for writing things like polynomials, linear equations, or dot products, which is what most of basic calculus and algebra is about. As far as I know this is the international standard, the one you find in most programming languages, software tools and scientific papers.

4) GEMAL-ish half-baked rules, like implicit multiplication having extra precedence or that weird thing with the division symbol BP keeps beetching about (how do you solve the "a / b / c" situation then? selective application of left to right?) I had never found these anywhere, so I would be very confused if I found them in a scientific paper. I am utterly surprised that some scientific calculators support it, since it complicates the expression parsing notably and introduces ambiguity with GEMAL.

As you see, the more expressive and concise you want to make the notation, the more complicated gets to learn and apply it (more rules and special cases.)

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#### cucio

##### Legend
I am curious... how do these old calculators handle, for instance, "5 ^ 2 (3)" Does the implicit multiplication take precedence over the exponential?

#### jonnythan

##### Professional
I am curious... how do these old calculators handle, for instance, "5 ^ 2 (3)" Does the implicit multiplication take precedence over the exponential?
No. Exponents come first in the order of operations.

Answer is 75.

#### jonnythan

##### Professional
And exactly how many engineering textbooks have you studied? I thought so.

What you're saying is that 48(9+3)÷2 = 48÷2(9+3), which is not true. One has (9+3) above the horizontal divide line and the other has (9+3) below the horizontal divide line.
I've studied plenty of them, and most of my friends are actual working engineers. They all agree with me.

I don't know why you keep talking about enumerated and denominators. It males no sense.

#### Bartelby

##### Bionic Poster
I think we've reached the breaking point.

#### subz

##### Rookie
ALL scientific litearture expresses equations in a much nicer way, so this thread is only suited for people who are interested in elementary maths ...

#### sureshs

##### Bionic Poster
People of an older generation assume a 2 line fraction whenever they see a /

#### BobFL

##### Hall of Fame
Math of this level is a non-negotiable. It is amazing how far some people can go to prove unprovable.

Btw, BP why don't you switch to Poincare conjecture although Mr. Григории Перельман has a few words to say about it.

#### baek57

##### Professional
There's a difference between 48÷2(12) and 48÷2*12 no?

48÷2(9+3) add inside the parentheses
48÷2(12) distribute the 2 inside the parentheses
48÷(24) = 2

or you can distribute the 2 first

48÷2(9+3) distribute
48÷(18+6) add
48÷(24) = 2

vs

48÷2*(9+3) add inside parentheses
48÷2*(12) divide
24*(12) = 288

or you can divide first

48÷2*(9+3) divide
24*(9+3) add
24*(12) = 288

Then the confusion seems to come from the parentheses vs multiplication sign. If there's no difference, then the answer is 288, as you just go left to right. If there is a difference, then the answer is 2, as you distribute the parentheses first.

Anyways I think the answer is 2. But I can see both ways and won't argue against 288 either.

#### LameTennisPlayer

##### Professional
Well my answer has and will probably be 288 as I was taught Bedmas. No preference to division/multiplication or addition over subtraction.

if you turn the equation

48/2(9+3) and make an algebraic expression it would be

a/b(c+d)=x

step 1. Brackets- (c+d)=e

x= a/b x e

left to right
a/b first then multiply by e....giving 288 when u substitute the numbers back.

Thats how I see it anyway.

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#### dr325i

##### G.O.A.T.
There's a difference between 48÷2(12) and 48÷2*12 no?

.
Here we go again...
Dont you know the basic rule: a*b = ab
So, why is there a difference???

Of course, a/bc != a/(bc), and some here believe that those two are equal.

#### Readers

##### Professional

48÷2(9+3) = 48/2(9+3) = the first equation on top above.

48(9+3)÷2 = 48(9+3)/2 = the second equation on the bottom above.

Get it now? The / sign is how people type the horizontal divide line on a computer keyboard as it's much easier than trying to type a horizontal divide line with numbers and variables above and below that line with a computer keyboard.

You are soooooo wrong on this.

48÷2(9+3) = 48/2(9+3)=48(9+3)÷2 = 48(9+3)/2 =the second equation

48/(2(9+3)) = the first equation.

#### Readers

##### Professional
There's a difference between 48÷2(12) and 48÷2*12 no?

48÷2(9+3) add inside the parentheses
48÷2(12) distribute the 2 inside the parentheses
48÷(24) = 2

or you can distribute the 2 first

48÷2(9+3) distribute
48÷(18+6) add
48÷(24) = 2

Anyways I think the answer is 2. But I can see both ways and won't argue against 288 either.
Please understand you CANNOT do it from right to left, that's the wrong order.

The 2 is NOT inside the parentheses.

#### Readers

##### Professional
So you're saying that his updated software with more bug fixes is wrong while your out-dated software without the bug fixes is correct? How do you know they didn't fix this problem with the new software when they realized that answer should be 2 and not 288?

Can u read?

The most up to date version of the software is 2011a, somehow he is using 2011b, which shouldn't be out until this fall.

#### MegacedU

##### Professional
WOW, out of everything, my score really got the most of the attention.
Again, I ask you HOW did you do it?!

I truly do not understand how you got through the Calc 3 not understanding the basics?! How did you go through the difeq or complex integrals? No way you can solve those without understanding a simple division and multiplication.

Again, I NEVER called you a "strikingly dumb" as you claim (to enforse your argument), I am just wondering how you write a book without knowing the alphabet?
I think the real question here is, how did you manage to make it through Harvard or whatever Ivy you claim to have attended without being able to spell a BASIC word?! The equation is expressed in an ambiguous manner. The way that I solved that equation wasn't erroneous and I'm not saying that the other way is.

Additionally, no one asked for your opinion on how I look, so keep it to yourself. Kthx.

#### rfprse

##### Professional
This next example displays an issue that almost never arises but, when it does, there seems to be no end to the arguing.

Simplify 16 ÷ 2[8 – 3(4 – 2)] + 1.
16 ÷ 2[8 – 3(4 – 2)] + 1
= 16 ÷ 2[8 – 3(2)] + 1
= 16 ÷ 2[8 – 6] + 1
= 16 ÷ 2[2] + 1 (**)
= 16 ÷ 4 + 1
= 4 + 1
= 5

The confusing part in the above calculation is how "16 divided by 2[2] + 1" (in the line marked with the double-star) becomes "16 divided by 4 + 1", instead of "8 times by 2 + 1". That's because, even though multiplication and division are at the same level (so the left-to-right rule should apply), parentheses outrank division, so the first 2 goes with the [2], rather than with the "16 divided by". That is, multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication. Typesetting the entire problem in a graphing calculator verifies this hierarchy:

Note that different software will process this differently; even different models of Texas Instruments graphing calculators will process this differently. In cases of ambiguity, be very careful of your parentheses, and make your meaning clear. The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. But not all software is programmed this way, and sometimes teachers view things differently. If in doubt, ask!

(And please do not send me an e-mail either asking for or else proffering a definitive verdict on this issue. As far as I know, there is no such final verdict. And telling me to do this your way will not solve the issue!)
This is the convention I am used to.
As long as people can see that there is another convention they are not used to, it's hard to see what the fuss is about. It has nothing to do with even the 'real' order of operation, which many people seems to think what is at stake but a way to save writing a painful number of '(' ')' and checking if one got the number of ')' right to get a well-formed formula.

^^^^^great post.

#### Readers

##### Professional
This is the convention I am used to.
As long as people can see that there is another convention they are not used to, it's hard to see what the fuss is about. It has nothing to do with even the 'real' order of operation, which many people seems to think what is at stake but a way to save writing a painful number of '(' ')' and checking if one got the number of ')' right to get a well-formed formula.
If you think that way, the the way you wrote it is wrong. It HAS to be INSIDE (), to work, next to () means nothing.

#### TripleB

##### Hall of Fame
You mean Please Excuse My Dear Aunt Sally failed me?

Math never was my strong subject.

:-|
No...your teacher failed you. When using 'Please Excuse My Dear Aunt Sally' your teacher should have explained that Multiplication and Division are of equal importance (not completed in the order they go in the saying) and should be worked left to right! (same with Addition and Subtraction)

As a 7th grade Math teacher I have a lot of students come in thinking you work these problems in the order of the saying.

TripleB

#### Readers

##### Professional
4) GEMAL-ish half-baked rules, like implicit multiplication having extra precedence or that weird thing with the division symbol BP keeps beetching about (how do you solve the "a / b / c" situation then? selective application of left to right?) I had never found these anywhere, so I would be very confused if I found them in a scientific paper. I am utterly surprised that some scientific calculators support it, since it complicates the expression parsing notably and introduces ambiguity with GEMAL.
The rule used to get the right answer, 288, can solve a/b/c just fine. Now on the other hand, seeing how some got 2...

#### BreakPoint

##### Bionic Poster
Ah, you got me on that one...

15 years ago I got my MSEE, and before that my BSEE.
In the High School I studied stuff that in America you will NEVER see (Russian Math Books). Since then, I have written more engineering articles than the number of books you've read...

You are assuming things again (just like the "*" thing) and it is getting you nowhere and you get embarrassed with every post...

Get off this forum since 30k posts just drained your little brain... Learn the basics...PUNK
Then you ought to know that in engineering books, when bc is in the denominator, they will often write it a/bc. Thus, your claim that c CAN ONLY BE in the numerator in a/bc is preposterous. Either that or you got your BSEE and MSEE from some mail order correspondence school. :???:

#### BreakPoint

##### Bionic Poster
It does not matter if it is written nicely or not. Math is tricky, but you have to follow the rules, simple as that, left to right, parenth first, then mult/division, then addition/subtraction.
48/2(9+3) is simple:
Parenthesis first gives you 48/2*12.
Left to right gives you 24*12 = 288

There are no assumptions in Math except in some cases where you have to prove them (like Mathematical induction method, etc)

Again, my 9 year old got this the first time, the guy with 30k useless posts is still debating if it is "*" or no "*" and so on...
You have yet to explain why the 12 MUST be in the numerator and CAN NEVER be in the denominator!

Massive FAIL!!!!!

Oh, and 48/2(9+3) gives you 48/2(12), NOT 48/2*12.

48/2*(9+3) gives you 48/2*12

There are inherent implications by leaving out the * when typing out equations on a computer keyboard, rather than by hand.

#### tennisnoob3

##### Professional
What the heck is a "lower Ivy"????

Oh yeah, you must mean one of those schools you had zero chance to get into? OK, I see.

Oh, and what does either "Standford" or Stanford have to do with Ivy schools? Oh, yeah, nothing! :???:
lower ivy= cornell, and some argue brown/penn, basically not hyp. they are much less competitive than hyp.

your lack of intelligence shows you can't grasp simple concepts. Asking if you went to "standford" was putting you on the same level as fedace, this is called an insult.

for reference, you brought up Ivy league school with my mentioning of standford", thanks for acknowledging your lack of relevance.

Care to explain what a halfway decent school is then? or at least where you went to schoo?

#### dr325i

##### G.O.A.T.
I think the real question here is, how did you manage to make it through Harvard or whatever Ivy you claim to have attended without being able to spell a BASIC word?! The equation is expressed in an ambiguous manner. The way that I solved that equation wasn't erroneous and I'm not saying that the other way is.

Additionally, no one asked for your opinion on how I look, so keep it to yourself. Kthx.
You continue to amaze me...
And I guarantee you will fail in your law career...

1) Point me WHERE I claimed I went to Harvard or any Ivy school
2) The way you solved the equation is erroneous if you got anything else than 288 as the result. This is not your Law stuff, this is math, science -- proven things rule here, not the assumptions or "nicely written" equations. The rule is clear and simple, there is no priority of division over multiplication and vice versa, therefore, you go from let to right. Simple as that. And there is a reason why this problem is given to the 3rd graders and not at the College level.
3) English is not my native language, occassional misspell or a grammar error is just fine.
4) I never said anything about your looks. I just said that the looks are subjective thing which is completely true statement. Does not say anything about your looks.

Amazing...

#### BreakPoint

##### Bionic Poster
Here we go again...
Dont you know the basic rule: a*b = ab
So, why is there a difference???

Of course, a/bc != a/(bc), and some here believe that those two are equal.
Yet, you seem to think a/bc = ac/b. Those two are NOT equal!

#### dr325i

##### G.O.A.T.
You have yet to explain why the 12 MUST be in the numerator and CAN NEVER be in the denominator!

Massive FAIL!!!!!

Oh, and 48/2(9+3) gives you 48/2(12), NOT 48/2*12.

48/2*(9+3) gives you 48/2*12

There are inherent implications by leaving out the * when typing out equations on a computer keyboard, rather than by hand.
I am finished with you...
Go to your Math teachers and punch them in the face...

#### BreakPoint

##### Bionic Poster
You are soooooo wrong on this.

48÷2(9+3) = 48/2(9+3)=48(9+3)÷2 = 48(9+3)/2 =the second equation

48/(2(9+3)) = the first equation.
How the heck did the (9+3) end up in your numerator when it started out in the denominator in the original equation? Please explain that one!

If it were in the numerator, why wasn't the original equation written as 48(9+3)÷2? Please explain that one as well.

#### Readers

##### Professional
I am finished with you...
Go to your Math teachers and punch them in the face...
LOL, look on the bright side, at least more people voted for 288...

#### BreakPoint

##### Bionic Poster
Can u read?

The most up to date version of the software is 2011a, somehow he is using 2011b, which shouldn't be out until this fall.
Yes, I can read. But you seem to think a 2009 version of a software is newer and more updated than a 2011 version of the same software.

#### MegacedU

##### Professional
You continue to amaze me...
And I guarantee you will fail in your law career...

1) Point me WHERE I claimed I went to Harvard or any Ivy school
2) The way you solved the equation is erroneous if you got anything else than 288 as the result. This is not your Law stuff, this is math, science -- proven things rule here, not the assumptions or "nicely written" equations. The rule is clear and simple, there is no priority of division over multiplication and vice versa, therefore, you go from let to right. Simple as that. And there is a reason why this problem is given to the 3rd graders and not at the College level.
3) English is not my native language, occassional misspell or a grammar error is just fine.
4) I never said anything about your looks. I just said that the looks are subjective thing which is completely true statement. Does not say anything about your looks.

Amazing...
Mathematics is not my native language, a different interpretation of an expression is just fine.

#### Readers

##### Professional
How the heck did the (9+3) end up in your numerator when it started out in the denominator in the original equation? Please explain that one!

If it were in the numerator, why wasn't the original equation written as 48(9+3)÷2? Please explain that one as well.
I am too lazy to upload pic. But think this way. The 2, and only 2 is the denominator, the (9+3) is on the right side of 48/2, make some sense?

Second, there are many way to write an equation as long as they follow the same rule.

Again, think about it, the rule we use can solve a/b/c. The "rule" you use cannot.

#### Readers

##### Professional
Yes, I can read. But you seem to think a 2009 version of a software is newer and more updated than a 2011 version of the same software.
Do you understand the idea of an unreleased, unfinsihed version? Yes? No?

#### F-T-S

##### Rookie
I see only two points of confusion:

Does the division sign ever represent separating the entire left and right of it into numerator, denominator?

Are parenthesis ever considered a more a preeminent binding than other multiplication signs?

#### Readers

##### Professional
Mathematics is not my native language, a different interpretation of an expression is just fine.
No, it's not, else it's not math.

#### Readers

##### Professional
I see only two points of confusion:

Does the division sign ever represent separating the entire left and right of it into numerator, denominator?

Are parenthesis ever considered a more a preeminent binding than other multiplication signs?
For the first point, it does not, else how u going to do a/b/c/d ????

Second, yes, but only when it's INSIDE the (), not next to it.

#### BreakPoint

##### Bionic Poster
lower ivy= cornell, and some argue brown/penn, basically not hyp. they are much less competitive than hyp.

your lack of intelligence shows you can't grasp simple concepts. Asking if you went to "standford" was putting you on the same level as fedace, this is called an insult.

for reference, you brought up Ivy league school with my mentioning of standford", thanks for acknowledging your lack of relevance.

Care to explain what a halfway decent school is then? or at least where you went to schoo?
Um...YOU brought up "Standford" when the topic was Ivy League schools. :???:

Not that I went there, but anyone who thinks Cornell Engineering is "much less competitive" than HYP never went through any of their programs.

Oh, and I'm sure getting into Brown is a piece of cake compared to the school you went to, right?

#### BreakPoint

##### Bionic Poster
I am finished with you...
Go to your Math teachers and punch them in the face...
Just as I thought. You can't explain your assertions. Why? Because they are erroneous. You can't explain why the (9+3) or 12 HAS TO BE in the numerator.

#### BreakPoint

##### Bionic Poster
I am too lazy to upload pic. But think this way. The 2, and only 2 is the denominator, the (9+3) is on the right side of 48/2, make some sense?

Second, there are many way to write an equation as long as they follow the same rule.

Again, think about it, the rule we use can solve a/b/c. The "rule" you use cannot.
No, it makes no sense. Being on the right side of 48/2 does not mean the (9+3) is in the numerator. But being to the right of / means the (9+3) is in the denominator, just like the 2 being on the right side of the / means it's in the denominator. There's no difference between the 2 and the (9+3) as far as which side of the / they are located.

#### BreakPoint

##### Bionic Poster
Do you understand the idea of an unreleased, unfinsihed version? Yes? No?
And do you understand that 2011 is newer than 2009 and contains fixes to bugs and errors that were found in the 2009 version?