Solve this simple math problem: 48/2(9+3)

[balamw]

I assume any time I see a division symbol that it takes the place of a bar in traditional handwriting.

Would you also make the same assumption if we had a consistent way of entering

?

That is how those of us in the 288 camp are interpreting "/" because that is how it has become to be used in all of the tools we use daily.

B

 

[KnightWRX]

Wrong. As I posted, the expression as typed here is ambiguous because its interpretation depends on the conventions used. It has nothing to do with understanding or not mathematics. Both 2 and 288 are correct answers, according to the conventions you used.

Any answer could be right if you use the wrong conventions. There's only 1 right convention and only 1 right answer here though.

 

[iStudentUK]

Step back a bit. Someone in your group would actually send you an expression that was full of constant numbers rather than reducing that to the answer?

As s a physicist by training I hate it when the meaning is bled out of an expression, by rote plugging in of numbers. Engineers love to do this kind of thing and take a perfectly nice equation, lump a bunch of stuff together and take a few implied logs for good measure and think it has meaning. 😛

I'd expect anyone who knows what they are doing to send something like x/y(a+b) rather than 48/2(9+3). Preferably with an extra pair of parens/brackets. Or send you TeX $\frac{x}{y}(a+b)$. This would assist in your sanity checking if, for example, you saw that x was a distance, y was a time and a and b were also times and you knew the expected answer was a distance you'd know that (x/y)*(a+b) was meant. If you were looking for acceleration you might go back to the author and ask, "did you mean (x/[y*(a+b)])?" instead of taking the original expression at its face value.

In the absence of context and any other information the answer is 288.

B

Of course not! I was simply giving an example of how I would have expected this to have been written in an email with two pairs of brackets, not that anyone actually did send anything like that. The equations we used were to do with modelling enzyme kinetics. So they were algebraic, nobody emailed an equation that said 1+1=2! 😀

Our fitting programme didn't use TeX, which was really annoying. It had standard models built in, but on one occasion we had to derive a model from scratch and the equation I used needed 47 pairs of brackets to make the stupid machine understand it! 😡

 

[ender land]

Thank you!

Division should be written as a fraction "_" or ( ... )^-1. Nobody with maths skills beyond that of a ten year old should be using "/". This question is using this notation only because MR forums aren't good for writing equations. We must think of this in our heads as being a fraction, and ask how it would be written, and your's makes the most sense.

ugh.

Someone already pointed out that "/" is used as "divide by" in programming. I do not know of a single programming language which would evaluate that expression to 2. Most would either give an error or 288. I use this symbol 100% of the time I use division on the computer.


What about the following expressions. I think part of the reason 2 is such a popular answer is most people without math/programming backgrounds are only used to seeing fractions like 1/2 or 2/3 and never would assume that 48/2 is mathematically evaluated in a similar sense.

1/2(x+y) or 2/3(x+4) should be much more "intuitively" obvious that the "/" sign does not mean fraction, but rather is a basic division sign.

 

[balamw]

on one occasion we had to derive a model from scratch and the equation I used needed 47 pairs of brackets to make the stupid machine understand it! 😡

And I'm sure if you had to share and discuss that with someone else by email, you would have sent the actual version that you were trying to get the machine to understand rather than paraphrasing it into some potentially unclear form.

IMHO this is an academic grade school math problem designed to trip people up who are still unclear about the rules, and to try and encourage the better use of additional parens to improve clarity.

B

 

[iStudentUK]

What about the following expressions. I think part of the reason 2 is such a popular answer is most people without math/programming backgrounds are only used to seeing fractions like 1/2 or 2/3 and never would assume that 48/2 is mathematically evaluated in a similar sense.

We've covered this. Someone with a programming background may use a/b. However, a mathematician would not. They would use-

a
b

I am saying this equation is meant to be thought of in terms of the second option, / is being used as a convenient alternative to _ because we are in a forum. I would say this is-

48 (9+3) = 288
2

But that step of converting into _ is important. As I say, we have covered this.

 

[chaoticbear]

Would you also make the same assumption if we had a consistent way of entering

?

That is how those of us in the 288 camp are interpreting "/" because that is how it has become to be used in all of the tools we use daily.

B

If it were a division symbol there instead of "/", I'd find it even more ambiguous. The lack of an operand between the two arguments in the denominator is the most compelling piece of evidence to me that it all belongs in the denominator.

 

[Rodimus Prime]

Nobody uses / when writing down by hand (they do when programming on a computer- fine), or at least they shouldn't. It doesn't matter if / has a strict definition if it is not strictly enforced. I did a chemistry degree, and that obviously involves maths. Yet, if someone had emailed by an equation like this I would have asked for clarification, because I know they are thinking in terms of two lines (using ______).

We have been over this before I know plenty of people myself included who use "/" for division when doing math by hand. Reason being is that is is quicker and easier to write than other methods.
My math skills are well beyond what most of the people here have. In terms of college credit hours I have 21 hours of math from Cal I and above. If you want to count my stuff before calculus I have 30 hours.
On top of those 21 hours of math I have all the classes that use heavy math in my engineering classes so safe to say that is a lot more. that "/" is used for division all the time in hand writing by students and professors. Only time I tend to go to fraction is when I have a fair amount of stuff above and below it.

I would write 48/(2(9+3)) as a big fraction. but the one given nope. More trouble than it is worth.

 

[ncl]

There's only 1 right convention and only 1 right answer here though.

Well no. Both conventions are used. That's why you get a 50/50 ratio on the answers, here and on nearly all the boards this question appeared (since this question appeared on quite a lot of boards). And it has nothing to do with math knowledge or skills. You'll have mathematicians, physicists, engineers, etc. in both camp.

Bored at work, I made some research on the subject. Apparently, this "debate" has been going for quite some time (like here, Feb 2000). It looks like the juxtaposition=grouping rule originated in printing (in order to minimize cost or improve readability of inline expressions, I don't know). Lots of text books used this rule. The AMS had this text (through the wayback machine):

You can help us to reduce production and printing costs by avoiding excessive or unnecessary quotation of complicated formulas. We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division.

So, no. There is not only 1 right convention and 1 right answer here. Or, if you really want one, since the AMS text is the closest thing to an "official" document I could find on the matter, the right answer is 2. If you wanted 288, you'd have to write it: 48(9+3)/2 or explicitely put the multiplication operator.

But, just for the record, I am in the 288 camp 🙂

 

[balamw]

The AMS had this text (through the wayback machine):

I fail to see how the example really represents that rule or has bearing on the discussion at hand.

Here are the two equations:

and

I interpret the integral and dt as an implied bracket that surrounds the integrand and defines the variable and domain of integration, and I can see why the second form is cheaper to print than a displayed equation that uses \over.

EDIT: Are they saying that the brackets are needed around the (1/2 \pi i) to stop it from being interpreted as

B

 

[benbondu]

I fail to see how the example really represents that rule or has bearing on the discussion at hand.

FTA--

We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division.

I think that is the relevant sentence.

 

[iStudentUK]

We have been over this before I know plenty of people myself included who use "/" for division when doing math by hand. Reason being is that is is quicker and easier to write than other methods.

It isn't quicker to write / compared to ___ . Both are the same.

I can't remember a single textbook, paper or lecturer who systematically uses / when writing when I was an undergrad. The only time I use it is where there is a e^(x/y) or something in the denominator of a fraction as it makes everything fit better. Just do a quick google image search for "maths", "math", "algebra" or "equation". 95% of the time in both writing and in print a fraction is used, not a / .

I'd be willing to bet / is very much in the minority.

 

[Don't panic]

it comes down to this:

the expression x/yz is equal to
[a] x/zy
xz/y
[c] xy/z
[d] 42

 

[balamw]

I think that is the relevant sentence.

I know it is. How does it relate to the concrete examples they use which I posted above? I still fail to see it. Which multiplication by juxtaposition is given precedence over division?

it comes down to this:

the expression x/yz is equal to
[a] x/zy
xz/y
[c] xy/z
[d] 42

Just to mix memes you could have worked in a ... profit! in there. The underpants gnomes would be proud.

B

 

[benbondu]

Bored at work, I made some research on the subject. Apparently, this "debate" has been going for quite some time (like here, Feb 2000). It looks like the juxtaposition=grouping rule originated in printing (in order to minimize cost or improve readability of inline expressions, I don't know). Lots of text books used this rule. The AMS had this text (through the wayback machine):

Nice find. I'd never heard of the juxtaposition=grouping rule, but I think it makes sense. I originally answered 288, but I'm leaning more towards 2 now.

The expression is better written 48/2*(9+3) if you want it to evaluate to 288.

 

[dukebound85]

The answer is 288.

Anyone with a decent education is taught B.E.D.M.A.S not PEDMAS.

Brackets.Exponents. Division.Addition/Subtraction in that order!

/End thread.

Uhhh BEDMAS=PEDMAS=PEMDAS=PEDMSA=BEMDSA and so on you know right?

Anyone with a decent education knows that

Thank you!

Division should be written as a fraction "_" or ( ... )^-1. Nobody with maths skills beyond that of a ten year old should be using "/". This question is using this notation only because MR forums aren't good for writing equations. We must think of this in our heads as being a fraction, and ask how it would be written, and your's makes the most sense.

You keep saying this and I disagree. There is nothing wrong with using it

We have been over this before I know plenty of people myself included who use "/" for division when doing math by hand. Reason being is that is is quicker and easier to write than other methods.
My math skills are well beyond what most of the people here have. In terms of college credit hours I have 21 hours of math from Cal I and above. If you want to count my stuff before calculus I have 30 hours.
On top of those 21 hours of math I have all the classes that use heavy math in my engineering classes so safe to say that is a lot more. that "/" is used for division all the time in hand writing by students and professors. Only time I tend to go to fraction is when I have a fair amount of stuff above and below it.

I would write 48/(2(9+3)) as a big fraction. but the one given nope. More trouble than it is worth.

You would be surprised at how many here have as much or more education than what you listed. I hate it when people throw "credentials" around lol

But I agree, anyone that has done a technical background in college has taken a crapload of math in terms of dedicated courses as well as courses like in physics or engineering that is essentially a math class with application

Regarding "/", I use it all the time still as it allows me to write an equation out in one line vs more lines. I do however, notate the equation in a clear form with ()

 

[benbondu]

I know it is. How does it relate to the concrete examples they use which I posted above? I still fail to see it. Which multiplication by juxtaposition is given precedence over division?



B

Sorry. It's the (1/2 \pi*i)-- nothing to do with the integral as far as I can tell. The juxtaposition=grouping rule ensures it is not interpreted as (0.5* \pi*i)

 

[Don't panic]

I know it is. How does it relate to the concrete examples they use which I posted above? I still fail to see it. Which multiplication by juxtaposition is given precedence over division?



Just to mix memes you could have worked in a ... profit! in there. The underpants gnomes would be proud.

B

hehe, don't want to upset ncl and knightwrx too much.

but, seriously that is the crux:
if you think that x/yz is the same as x/zy, then you should be a "2" guy,
if you think that x/yz is the same as xz/y, then you should be a "288" guy,
if you think that x/yz is the same as xy/z, then you should pass the joint,
if you think that x/yz is the same as 42, then you probably have a tail and white fur

EDIT:

push it even more:
y/2x=7

what is y for x=3?

 

[balamw]

Sorry. It's the (1/2 \pi*i)-- nothing to do with the integral as far as I can tell. The juxtaposition=grouping rule ensures it is not interpreted as (0.5* \pi*i)

I guess it shows I'm a physicist at heart, I didn't even interpret the 2 pi i as possibly being separable into bits. It's a single number. 😛

I do see that that should not be interpreted as (1/2)*(pi*i) and doesn't need to be typeset as 1/(2*pi*i). However in ASCII text without other context I would still find the (1/2 pi i) to evaluate to the same thing as (pi i)/2.

Weird.

B

 

[-aggie-]

Until this guy comes into this thread, no one knows the answer. 🙂

 

[Shaun.P]

Correct me if I am wrong, but I was taught to do operations in this order:

Brackets
Of
Divide
Multiply
Add
Subtract

i.e. BODMAS



48/2(9+3)

1. Do brackets first. Within the brackets is an add sum, so you do that and you get 48 / 2(12)

2. Now "Of" 2(12) is the same as 2/1 of 12 which is simply 24. So now we have 48 / 24

3. 2

 

[iStudentUK]

Correct me if I am wrong, but I was taught to do operations in this order:

Brackets
Of
Divide
Multiply
Add
Subtract

i.e. BODMAS

I was taught BODMAS, and the O stands for "order". As in power or indices. It refers to things like x^2 (x squared). x(y) is just multiplication.

 

[balamw]

Of

How is "Of" different from multiplication or division?

Where do your exponents or "orders" go?

How do you interpret this per your prescription?

10 - 3 + 2 = ?

B

 

[dukebound85]

Until this guy comes into this thread, no one knows the answer. 🙂

Nah, we need the Q in here lol

Correct me if I am wrong, but I was taught to do operations in this order:

Brackets
Of
Divide
Multiply
Add
Subtract

i.e. BODMAS



48/2(9+3)

1. Do brackets first. Within the brackets is an add sum, so you do that and you get 48 / 2(12)

2. Now "Of" 2(12) is the same as 2/1 of 12 which is simply 24. So now we have 48 / 24

3. 2

of? not exponent or order?

 

[Rodimus Prime]

You would be surprised at how many here have as much or more education than what you listed. I hate it when people throw "credentials" around lol

But I agree, anyone that has done a technical background in college has taken a crapload of math in terms of dedicated courses as well as courses like in physics or engineering that is essentially a math class with application

Regarding "/", I use it all the time still as it allows me to write an equation out in one line vs more lines. I do however, notate the equation in a clear form with ()

Oh I know people do.
But I am also willing to bet that a vast majority of the people who selected the 2 for the answer have fairly little math comparably.
This is breaking down more to the people who have the degrees based in math/ engineering to those who do not.

Which group do you think is going to understand the rules of math better. The people with heavy math based degrees or those who do not.