48÷2(9+3) =

[bloop]

Also I added a poll.

[HarlequinForest]

There's no consensus in the math community about whether implied multiplication takes precedence over regular multiplication or not.  Think about that before you try to argue that there is a "right" answer, because there isn't.

Yes there is.

And that answer is 288.

So to answer your question, I think both answers can be considered
right - which means, of course, that the question itself is wrong.

Some mathematicians hold that multiplication by juxtaposition (omitting the x sign, ex. 2(4+3) ) is a symbol of grouping. No fixed convention exists.

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!)

[Dimitrius]

I think he was just joking HF...

[rumborak]

It's just bad syntax. So, "no definite answer" from me.

rumborak

[Fiery Winds]

Implied multiplication being of higher precedence is more an exception rather than the rule, especially in the math classes I've been in as a student and teacher.  If you want to deviate from the standard Order of Operations, use parenthesis, that's why they're there. 

Quick overview of Order of Operations:

Level 1: Parenthesis   {}[]()
Level 2: Exponents  x², sqrt(), log_xy
Level 3: Multiplication and Division  x, *, /
Level 4: Addition and Subtraction +, -

Each operation on the same level has equal precedence, so you don't always do multiplication first, or addition first.  Left to right precedence when dealing with operations residing on the same level.

[yorost]

It's just bad syntax. So, "no definite answer" from me.

rumborak

If you know how what you're writing for interprets it you're fine.   ...but yeah, it can't be said enough to not skip out on parens when writing code or expressions.  Even if you know how it is interpreted someone else reading your code in the future might get confused.  Exponents, negations, and functions are also big ones where it is often good to just be clear with your parens.

[rumborak]

IMHO, the "÷" sign ios something that is best left in 5th grade and below. Same thing with the forward-slash to indicate division.

rumborak

[mizzl]

IMHO, the "÷" sign ios something that is best left in 5th grade and below. Same thing with the forward-slash to indicate division.

rumborak

This. Real men use fractions.

[Fiery Winds]

IMHO, the "÷" sign ios something that is best left in 5th grade and below. Same thing with the forward-slash to indicate division.

rumborak

I dislike those signs as well, but they are a necessity when communicating via text.

[rumborak]

IMHO, the "÷" sign ios something that is best left in 5th grade and below. Same thing with the forward-slash to indicate division.

rumborak

I dislike those signs as well, but they are a necessity when communicating via text.

The forward-slash, yes (e.g. "5/(3+1)"), but the "÷" sign should IMHO never be used outside of the plain "X divided by Y".

rumborak

[rumborak]

IMHO, the "÷" sign ios something that is best left in 5th grade and below. Same thing with the forward-slash to indicate division.

rumborak

This. Real men use fractions.

Speaking of which, one of those "cultural differences" between Europeans and Americans is that Europeans love decimal writing, whereas Americans seem to hate it. There's the "5 and 3/16th of an inch" and the "$3 7/10" as the gas price, where I'm looking at it, thinking "wouldn't it have been easier to just write $3.70?".

rumborak

[mizzl]

IMHO, the "÷" sign ios something that is best left in 5th grade and below. Same thing with the forward-slash to indicate division.

rumborak

This. Real men use fractions.

Speaking of which, one of those "cultural differences" between Europeans and Americans is that Europeans love decimal writing, whereas Americans seem to hate it. There's the "5 and 3/16th of an inch" and the "$3 7/10" as the gas price, where I'm looking at it, thinking "wouldn't it have been easier to just write $3.70?".

rumborak

Really? I absolutely despise decimal writing. It's so imprecise!

[yorost]

Never seen $3 7/10 at a gas station in the US or Canada.  Are you sure you aren't seeing fractions of a cent?  I do see a lot of $3.45 9/10, but never fractions of dolars.

[bloop]

IMHO, the "÷" sign ios something that is best left in 5th grade and below. Same thing with the forward-slash to indicate division.

rumborak

It's not as if  the ÷ is ambiguous, as it's the same as /. However I understand what you mean, and if the original equation was in the form of a fraction there wouldn't be anything debatable about it.

For 2.

For 288.

[rumborak]

Never seen $3 7/10 at a gas station in the US or Canada.  Are you sure you aren't seeing fractions of a cent?  I do see a lot of $3.45 9/10, but never fractions of dolars.

Yeah, sorry, bad example on my part

Yes, it's fractions of a cent. But, what's wrong with "$3.452"? I mean, would people really be that confused by it?

rumborak

[orcus116]

Honestly, yes. Only because Americans are so used to seeing two decimal places so adding another one would completely shatter certain peoples minds.

[rumborak]

What they do in Germany a lot is to have the third digit be slightly different:

[TimmyHiggy]

My conclusion: The person that wrote the question did a piss poor job of it. You will never see maths published with ambiguous notation ever, and if someone had asked you to do that you would ask them what they meant. And I'm with everyone else who said that you are better off writing divisions as fractions, the primary school notation is best phased out as quickly as possible!

[LieLowTheWantedMan]

It's 288.

[Jamesman42]

Hmm, that is tricky. So tricky because it looks like shoddy notation/writing rather than some arithmetic black hole. To explain, a THIRD possible answer is to distribute the 2 onto (9 + 3). So this is what happens:

48 ÷ 2(9 + 3)   [Given, with spaces added, which is allowed]
=48 ÷ 18 + 6    [Distribute the 2 onto the parentheses to get rid of them]
=8/3 + 6          [48/18 + 6]
=26/3



But here is my real answer. I believe it is 288, because 48/2 is happening outside of the parentheses, but still to each other. Like, instead of using that elementary division sign, you are allowed to replace it with the forward slash, to get 48/2(9+3). Now if we distribute this number like I did in my joke math up there, we get (48/2)*9 + (48/2)*3 = 216 + 72 = 288. Q.E.D.lol.

All that said, I'm gonna ask some people tomorrow about this. Math professors and math majors alike. They are my people.


EDIT: I think the answer would be 2 if the 2 in the problem were included solely with the (9 + 3)...but then that would be obvious.

[LearningToLive]

The answer is 2. What kind of moron would say that there is no definitive "correct answer"? 

[LieLowTheWantedMan]

The answer is 288.

At least the way I'm being taught in school.

[Jamesman42]

The answer is 2. What kind of moron would say that there is no definitive "correct answer"? 

And what kind of person comes onto a message board, calls some people a moron, gives an answer to a tricky question and does not back it up?

[Dimitrius]

The answer is 288.

At least the way I'm being taught in school.

Your school is obviously wrong.

[tri.ad]

The syntax doesn't make it clear, so there's no definitive answer to this imo.

[LearningToLive]

The answer is 2. What kind of moron would say that there is no definitive "correct answer"? 

And what kind of person comes onto a message board, calls some people a moron, gives an answer to a tricky question and does not back it up?

The kind of person that doesn't feel the need to repeat what several people have already said  

It's a mathematical equation. There is one answer to it.

[millahh]

The answer is 2. What kind of moron would say that there is no definitive "correct answer"? 

People who actually think about the question rather than being knee-jerk about the issue?

[millahh]

The answer is 2. What kind of moron would say that there is no definitive "correct answer"? 

And what kind of person comes onto a message board, calls some people a moron, gives an answer to a tricky question and does not back it up?

The kind of person that doesn't feel the need to repeat what several people have already said  

It's a mathematical equation. There is one answer to it.

There's one answer to a correctly written, unambiguous equation.

[yorost]

It's a mathematical equation. There is one answer to it.

You really missed the problem, didn't you?  Equations have to be parsed.

[LearningToLive]

/troll

[Jamesman42]

Alright alright...here is another way to look at this. Division and multiplication are in the same rank, and an expression must be read left to right when operations are of the same rank.

48 ÷ 2(9 + 3) [Given]

= 48 ÷ 2 x (9+3) [Multiplication sign added to further show it is multiplication]

= 48 ÷ 2 x (12) [Parentheses, dogg]

= 24 x 12 [Read it left to right] [Smart]

= 288



Edit: Equations need an equal sign.

[ScioPath]

In order for a problem to have a an answer, it first must be a problem. And this problem sucks at being a problem.

[LieLowTheWantedMan]

Alright alright...here is another way to look at this. Division and multiplication are in the same rank, and an expression must be read left to right when operations are of the same rank.

48 ÷ 2(9 + 3) [Given]

= 48 ÷ 2 x (9+3) [Multiplication sign added to further show it is multiplication]

= 48 ÷ 2 x (12) [Parentheses, dogg]

= 24 x 12 [Read it left to right] [Smart]

= 288

Exactly.

[Jamesman42]

In order for a problem to have a an answer, it first must be a problem. And this problem sucks at being a problem.

I guess the problem is that it sucks at being a problem...which is itself a problem, recursively becoming more and more problematic. Fibonacci headache.

[Implode]

It's just bad syntax. So, "no definite answer" from me.

rumborak

IMHO, the "÷" sign ios something that is best left in 5th grade and below. Same thing with the forward-slash to indicate division.

rumborak

I agree everything rumborak has said.