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.
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Solve this simple math problem: 48/2(9+3)
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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
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!
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.
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
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.
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.
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.
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):
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
I fail to see how the example really represents that rule or has bearing on the discussion at hand.
Here are the two equations:
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
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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.
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
Uhhh BEDMAS=PEDMAS=PEMDAS=PEDMSA=BEMDSA and so on you know right?
Anyone with a decent education knows that
You keep saying this and I disagree. There is nothing wrong with using it
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 ()
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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)
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?
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
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
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
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.
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
Until this guy comes into this thread, no one knows the answer.
Nah, we need the Q in here lol
of? not exponent or order?
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.
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