Simple Maths

lol

i didn't read the whole thread but i cant believe it got this long. are people actually confused about this?

multiplication and division happen in the same step in the order of operations, and are carried out in order from left to right.

48 / 2x = 24x

This is probably in this thread somewhere but I don't feel like reading that much about math

I learned this mnemonic in middle school that helped me a lot

Order of operations

Please Excuse My Dear Aunt Sally

Parentheses, Exponent, Multiplication, Division, Addition, Subtraction

Funny how these threads keep growing. The bigger the thread, the more people pass by without having read the thread and still making a post. With or without disclaimer. It's all fine with me.

At this point we should even pin this thread and see how much we can milk out of it. Or just simply put it in the nonsense bin. (And have a jazz in a couple of months.)

Heat.

  On 4/10/2011 at 9:00 PM, goDel said:

Some of you might like the next link:http://www.purplemath.com/modules/orderops2.htm

  Quote

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!)

 

So, apparently the answer does indeed seem to be 2. Personally, I think the "juxtaposition"-rule is ugly as hell. If there are rules, like the pemdas, you'd expect them to be applied consistently. If the page is not lying, I'd say this is mathS at its most inconsistent.

As I said, genuine equations use the vertical '___' division sign. This sign implies that the elements placed under or above the bar should be treated as if they were between parenthesis.

Now you can write equations in a purely linear way in order to represent genuine mathematical equations that use non-linear symbol such as the '___' division sign (that is, symbols that have left and right contexts as well as upper and lower contexts).

You'll always have to conform to more or less established norms to do this.

But I know another kind of standard. Computational mathematical expressions.

With a c-based compiler,

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

does not compute since 2(…) is mistaken for a function's name.

You have to write

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

Thus, multiplication indicated by placement against parentheses disappears as well as any ambiguity it can create.

  On 4/10/2011 at 10:54 PM, goDel said:

LOL

 

Apple macbooks don't explode, btw. Macs are awesome!!!!

 

 

(let's go there too!!!)

yeah, spotlight's calculator is neat, it can compute bitwise shifts (discovered this today). Unfortunately it can't spit out a result in binary form.

Uhm, you mean the horizontal '______' sign?

Have you discovered Grapher on your Mac already? It's awesome if you're following a calculus course.

  On 4/10/2011 at 9:00 PM, goDel said:

So, apparently the answer does indeed seem to be 2. Personally, I think the "juxtaposition"-rule is ugly as hell. If there are rules, like the pemdas, you'd expect them to be applied consistently.

IT'S NOT FUCKING UGLY, IT'S INCREDIBLY ELEGANT, SIMPLE, AND EASY TO FUCKING REMEMBER. BUT, some people need "PEMDAS" MNEMONIC DEVICES learn even the most trivial shit, and since "PEMDAS" would not be much of a mnemonic device if it where instead "pemdasbutrememberjuxtapositionprecedence", or even just PEJMDAS, they opted to take that nugget of info out just to make, and I reiterate, A BACKWARDS-ASS MNEMOOONIC DEVICEEEEE THAT HELPS WITH LEARNING THE ORDER OF OPERATIONS GAAAAHHHHH roll off the tongue better.

do you have mnemonic devices for remembering remembering if you're suppose to take your pants off before peeing?! THEY ARE KEEEEEEPING YOUUUUU STUUUUUUPID!

Sorry but i got IRL exasperated.

/allcapsragetrolling

/posting in this thread

  On 4/11/2011 at 8:34 AM, Lube Saibot said:

  On 4/10/2011 at 9:00 PM, goDel said:

So, apparently the answer does indeed seem to be 2. Personally, I think the "juxtaposition"-rule is ugly as hell. If there are rules, like the pemdas, you'd expect them to be applied consistently.

 

IT'S NOT FUCKING UGLY, IT'S INCREDIBLY ELEGANT, SIMPLE, AND EASY TO FUCKING REMEMBER. BUT, some people need "PEMDAS" MNEMONIC DEVICES learn even the most trivial shit, and since "PEMDAS" would not be much of a mnemonic device if it where instead "pemdasbutrememberjuxtapositionprecedence", or even just PEJMDAS, they opted to take that nugget of info out just to make, and I reiterate, A BACKWARDS-ASS MNEMOOONIC DEVICEEEEE THAT HELPS WITH LEARNING THE ORDER OF OPERATIONS GAAAAHHHHH roll off the tongue better.

 

do you have mnemonic devices for remembering remembering if you're suppose to take your pants off before peeing?! THEY ARE KEEEEEEPING YOUUUUU STUUUUUUPID!

 

Sorry but i got IRL exasperated.

 

/allcapsragetrolling

/posting in this thread

I don't see why this is elegant. Multiplication signs are hardly ever used, but under certain conditions it suddenly matters whether a certain sign is used or not. How is that elegant? The whole notion of different use of multiplication-signs is useless if you stick with the simpler (more elegant!?) set of rules. Moreover, being consequent and sticking with the simples set of rules forces people to use the friggin brackets in the first place. Even better, there wouldn't be discussions like this.

*starts shaving with occam's razor*

  On 4/11/2011 at 8:26 AM, goDel said:

Uhm, you mean the horizontal '______' sign?

 

Have you discovered Grapher on your Mac already? It's awesome if you're following a calculus course.

horizontal, yes

Yes, i use it every now and then.

If you're looking for a spreadsheet editor/analyzer, just go for Igor Pro.

It can sort a 150 000 lines * 30 rows table in like … 2 seconds.

Has its own procedural language as well as a quite large set of pseudo-random generators. You can even build your own GUIs.

Thanks for the tip! Looks great, but I'm afraid that with the amount of data I have to work with, I'm forced to stick with SAS. These fast and spiffy tools all tend to work with the entire dataset from memory (RAM). When using 32-bit systems with less then 4 gigs of ram on datasets which often exceed 10 gigs.... SAS. It sucks, but there isn't another practical solution as far as I can tell.

BEDMAS

CHRISTMAS

  On 4/11/2011 at 6:03 AM, Calx Sherbet said:

not as simple as you thought, disparaissant

This is why I'll always suck at math.

  On 4/11/2011 at 8:34 AM, Lube Saibot said:

  On 4/10/2011 at 9:00 PM, goDel said:

So, apparently the answer does indeed seem to be 2. Personally, I think the "juxtaposition"-rule is ugly as hell. If there are rules, like the pemdas, you'd expect them to be applied consistently.

 

IT'S NOT FUCKING UGLY, IT'S INCREDIBLY ELEGANT, SIMPLE, AND EASY TO FUCKING

I loled. ^^^

i see it got pluralized, sticking by my demand that it be mathseseseseses

or at least mathses come on mods

LOL

luke on a roll!

i thought lube had a different set of glasses, btw?

2, lol.

who knew that i'd ever use highschool math... on an internet forum as well...

The reason this is so fucking confusing is that never in any textbook do you see a problem written out in this way, nor do they put emphasis on stronger multiplicative grouping when juxtaposition is involved. Grouping is clear, and in almost all circumstances when there is multiplication by juxtaposition the divisor is under a fraction bar(actually, most textbooks beyond 5th grade rarely use division symbols in expressions). That is why intuitively it is 2, but going by what most probably remember from order of operations, it seems that it is actually 288. But since apparently there is(according to the article quoted above) in fact a mostly agreed upon rule that when 2 numbers are adjacent implying multiplication, they are to be grouped into one entity first and foremost, disregarding what is to the left, the only time it actually makes a difference is with the classic division symbol. Although wikipedia seems to suggest that order of operations does not work that way, at least when using a '/' symbol:

  Quote

Similarly, care must be exercised when using the slash ('/') symbol. The string of characters "1/2x" is interpreted by the above conventions as (1/2)x. The contrary interpretation should be written explicitly as 1/(2x). Again, the use of brackets will clarify the meaning and should be used if there is any chance of misinterpretation.

note: wikipedia makes no mention of a difference when it comes to the '÷' symbol when used in expressions.

So where are we again in this argument? I'm sure this has been settled somewhere and written out more clearly than I have but what the fuck? How the fuck is this still happening?

hey watmm

(24/2)/(12/2)=?

(6*4)/(6/2)=?

(4/2)(12/2)/(24/2)=?

(6*2)(6*2)/(6/2)=?

(8/4)(3*4)=?

(8/4)(3*4)/(3*2)=?

(8/4)(3*4)/(3*2)+(9*4)=?

(8/4)(3*4)/(3*2)+9*4=?

fuckin...

for what it's worth, i asked two of my math teachers about this. both of them said the answer is 288 (one has a masters in mathematics, the other a phd). the one with the masters originally said it was 2, then conceded that it was 288 a few seconds later and told me she was truly embarrassed that she thought it was 2. :P

  On 4/13/2011 at 5:00 AM, kaini said:

hey watmm

 

(24/2)/(12/2)=?

(6*4)/(6/2)=?

(4/2)(12/2)/(24/2)=?

(6*2)(6*2)/(6/2)=?

(8/4)(3*4)=?

(8/4)(3*4)/(3*2)=?

(8/4)(3*4)/(3*2)+(9*4)=?

(8/4)(3*4)/(3*2)+9*4=?

fuckin...

that fails to illustrate the problem though, you need something adjacent to the divisor. Like (8/4)(2*2)/4(2+2), according to this site (see third example down) the answer is 1/2 but according to basic high school and wikipedia order of operations the answer is 8.

  On 4/13/2011 at 4:51 AM, Bubba69 said:

The reason this is so fucking confusing is that never in any textbook do you see a problem written out in this way

exactly. that's why mathematicians are latex-addicts.

ok

(8/4)(2*2)/4(2+2)

let's do the shit inside brackets first LIKE YOU'RE FUCKING SUPPOSED TO

(8/4)(2*2)/4(2+2)=

(2)(4)/4(4)=

(2*4)/4*4=

8/16=

0.5

edit: and i know - my aim was to introduce the logical steps leading up to the calculation in the OP gradually...

  On 4/11/2011 at 9:17 AM, essines said:

BEDMAS

yes.

BEDMAS is a far superior acronym to PEMDAS. Seems to be a Canada/US thing, I grew up with BEDMAS, but when I moved to the states for highschool, the first lesson of Algebra 1 was PEMDAS...