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But as a question it's designed to highlight a certain piece of knowledge which you get taught right at the beginning of your maths education and which you will never, ever need in real life - even if your career involves a pile of maths. So it seems a little unfair to berate people for having fogotten it
No, it's a piece of maths that should be imbedded so deeply that you never have to think about it and only really just a little more advanced than the action of addition, subtraction, multipication and division themselves.
Whilst berating may not be correct we wouldn't (and on this forum don't) tolerate a similar ignorance of English grammar (grammar is probably overstating it, this is probably about the level of basic sentance constuction) so why it accpetable to tolerate a similar level of mathematical illiteracy?
"That's exactly the same sum. Still vague? "No, because expressed in a way that's not vague. Vagueness is about the way something is expressed, not the result.
Right, so what I am getting at is that for some reason you accept that you do brackets first, and since that sum isn't vague then you obviously accept that you do order/indices/exponents next.
So you accept the first two rules of BODMAS, [i]"B first, then O"[/i], but for some reason you reject the [i]"then DM, then AS"[/i] part.
Why??
you will never, ever need in real life - even if your career involves a pile of maths
Okay, my career only involves some limited maths (software engineer) and I need this all the time.
Here are some common mathematical equations:
[code]y = mx + c[/code]
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If I want to use those then I [u]need[/u] to understand the order they are evaluated in. i.e. lets fill in the first one with some numbers (m=5.5, x=2, c=3)
[code]y = 5.5 × 2 + 3[/code]
Oh look it's gone all "vague" 🙄
Not directly related but ...
In the real world, [url= http://articles.cnn.com/1999-09-30/tech/9909_30_mars.metric.02_1_climate-orbiter-spacecraft-team-metric-system?_s=PM:TECH ]THIS[/url] is why you need to be specific.
If I remember right one team measured thrust in Newtons per meter sq. and the other measure in pounds per square inch. Unfortunately the raw figures turned out close enough to not be picked up, the result being several squillion dollars missing a planet and sailing off who knows where.
"[i]Here are some common mathematical equations:[/i]"
[b]None of which contain the multiplication sign.[/b] That's my point. No-one ever needs to remember operator precedence for [i]that operator[/i]. (Well, in truth, what really I mean of course is that [i]I've[/i] never needed to - I don't recall ever seeing a real-world equation which contains one.)
But yes, you're right, the syntax is a wholly arbitrary human invention and there's no reason to selectively reject any of it. I just think that since one piece of that syntax is pretty much never used, it's probably excusable to have forgotten about it.
No offence to anyone but If...IF anyones interested there is a great book out called "Get over your Math Phobia"
Or..
Maths for Dummies.
I'm not kidding around, they're both excellent books for those that feel they may need a teeeny weeeny bit of help in this area.
"[i]Whilst berating may not be correct we wouldn't (and on this forum don't) tolerate a similar ignorance of English grammar[/i]"
I can spot two spelling mistakes, one typo, one punctuation error and two grammatical mistakes in your post; so I wouldn't wander too casually into that analogy 😉
Bez - Agreed, it IS excusable to have forgotten about it - it't not really something that you'd use in everyday life unless you're a primary school maths teacher. But when the correct answer is pointed out and explained, and people STILL don't want to understand it, that's when we have a problem. I know it's melodramatic, but this is one of the problems of broken Britain; people would prefer, on the whole, to be ignorant as if it helps them in life somehow. If I ran the country, the 'zero crowd' would be rounded up to iron my shirts and clean my drains.
"[i]But when the correct answer is pointed out and explained, and people STILL don't want to understand it, that's when we have a problem.[/i]"
Quite true. I confess I didn't read pages 2-9 inclusive so may have missed the discussion branching somewhere along the line 🙂
I remember BIDMAS from school but I don't remember anything about using spaces instead of brackets. I got a B in maths as well 😕
double post
yeah, I got stuck too. looked at bodmas and pedmas and none mention what to do if there's a couple of random spaces in the equation.
can someone help?
i'm trying to type it all into my phones calculator and I get stuck just before the 'times' sign..... what key do I press for space, and where in bodmas does it tell me about that. thanks in advance. 😉
None of which contain the multiplication sign. That's my point.
Erm... did you miss how I filled out the equation? Look a multiplication sign. Would you fill it out differently?
I don't recall ever seeing a real-world equation which contains one.
It just tends to get omitted and the terms placed together:
[code]4 × a × c[/code] is exactly the same as
[code]4ac[/code] but we tend to use the latter style because it is more concise and avoids possible confusion between x and ×
But okay, how about division?
[code][u](4 + a / b)[/u] + 5
3[/code]
I can spot two spelling mistakes, one typo, one punctuation error and two grammatical mistakes in your post; so I wouldn't wander too casually into that analogy
Well that kind of demonstrates my point, the difference is I don't actually mind being corrected on such matters and I don't get huffy when people point out when I am wrong.
That being said however the rules of grammar and spelling are not fixed and change over time for no reason in particular. The rules of maths are not quite so flexible.
none mention what to do if there's a couple of random spaces in the equation.
can someone help?
yes, I can - they don't mention it because the spaces are meaningless.
[code]2 + 5 = 7[/code]
[code]2 + 5 = 7[/code]
Hope that helps.
"[i]It just tends to get omitted and the terms placed together[/i]"
THAT IS EXACTLY WHAT I HAVE BEEN SAYING! 🙂
Anyone who works with equations can remember the precedence of "a + 4b" because they see it every day; [i]that's how multiplication is written in the mathematical world[/i] - no-one ever writes "a + 4 x b" so it's easy to forget, or at least stumble over it, [i]especially[/i] when you're led into it by a purposefully-constructed algebraic equivalent of a tongue-twister.
The only reason the multiplication sign continues to exist is that you can't use the concatenation syntax with two numeric values: clearly "4 x 2" cannot be written as "42" (even though that is the answer, of course ;)). And the only time you ever need to write an expression which multiplies two constant numeric values is in primary school; hence that's the scope of its usefulness.
Okay. And division....?
but this is one of the problems of broken Britain; people would prefer, on the whole, to be ignorant as if it helps them in life somehow.
^^ Wot I said. And I stand by it.
Oh and..
no-one ever writes "a + 4 x b"
Well, in C code that would be:
x = a + 4 * b;
In Excel you would write:
= A1 + 4 * B1
So clearly coders and people that use spreadsheets do it.
And obviously if you had to enter it into a calculator yourself then you would need to use the multiply button at the appropriate point, no?
I use spreadsheets, I would write =A1+(4*B1)
I like to think brackets are a bit like paragraphs. They make things easier to read even though they don't always change the content/result
"[i]Okay. And division....? [/i]"
...does not involve the multiplication sign. I had absolutely no idea what point you were trying to make with it, so I ignored it 🙂
If I think about it then I guess you mean something like: what about "2 + 2 ÷ 2", but your post is written in the way division is written in normal mathematical circumstances, ie with precedence quite explicitly conveyed. In any case, it's the same thing: I've not seen "÷" used in anger for the best part of 30 years.
"[i]So clearly coders and people that use spreadsheets do it.[/i]"
1. That's the asterisk, not the multiplication sign. (See also "/" vs "÷" for all these points)
2. Use of the asterisk implies a context, ie computer code.
3. Once you have context, you can be more sure of correct precedence.
4. In that context, there is no alternative syntax, hence the asterisk is [i]required[/i] in order to perform multiplication and hence everyone who understands the asterisk as a multiplication operator is likely to be familiar with both the general concept of non-linear precedence and the relatively arbitrary precedence which specifically applies to it - this is [i]very, very different[/i] to the case of the multiplication sign, which is almost totally redundant beyond teaching people the basic concept of multiplication.
I'm totally familiar with precedence [i]in the context of computing[/i]. Had the question been,
[i]Here's some Javascript:
var i = 2+2*0;
alert(i);
What is displayed in the dialog?[/i]
Then the answer is "2", job done. The context is Javascript and precedence is indisputable - but you need to either know Javascript or make an assumption.
Had the question been,
[i]Here's some pseduocode:
i = 2+2*0;
print(i)
What is displayed?[/i]
Then the answer would be "2, assuming the operator precedence is conventional and you haven't defined some bonkers language". The context is computer languages and the precedence is standardised, but there's still a small assumption you need to make in order to give a simple answer.
But ask any non-programmer the above questions and you'll get a selection of answers including 2, 0, "could be 0 or 2, I dunno" and "no idea", because they probably don't know how precedence is defined for those domains.
Most people simply don't need to know operator precedence in the real world. There's no shame in it.
Also, people who are familiar with operator precedence conceptually and who know [i]a specific precedence in a specific domain and using specific operators[/i] (such as me) simply don't need to know [i]specific[/i] precedence using operators that they [i]never use[/i] (let alone operators that [i]no-one[/i] uses), and - more than that - it would be foolish to assume that the [i]specific[/i] operator precedence which they know from their familiar context would be universally applicable in all contexts.
everyone who understands the asterisk as a multiplication operator is likely to be familiar with both the general concept of non-linear precedence and the relatively arbitrary precedence which specifically applies to it
Not arbitrary at all - exactly the same rules as elsewhere.
Most people simply don't need to know operator precedence in the real world. There's no shame in it.
There's shame in attempting to argue that those who do know it are wrong. Or in then trying to make out that such ignorance is somehow cool.
but your post is written in the way division is written in normal mathematical circumstances, ie with precedence quite explicitly conveyed
Really, look at the equation. Is the term in that numerator equivalent to
[code](4+a) / b[/code] or [code]4 + (a/b)[/code] then?
If you know the correct answer then you are applying BODMAS. Well done.
See also "/" vs "÷" for all these points
I must have missed the meeting where it was decided that / is only used in computer code.
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That equation from the discussion on [url= http://en.wikipedia.org/wiki/Quadratic_equation ]Vieta's formulas[/url]. François Viète dies in 1603. Not sure what computer he used. 😀
Most people simply don't need to know operator precedence in the real world. There's no shame in it.
I disagree. I think not being able to do basic arithmetic that a 9 year old can/should do, even when given a calculator, is pretty shameful. YMMV.
There's shame in attempting to argue that those who do know it are wrong. Or in then trying to make out that such ignorance is somehow cool.
This!
Yes I agree but you're onto a loser, either you are arguing with idiots in public or you're being trolled, either way you lose.[i]There's shame in attempting to argue that those who do know it are wrong. Or in then trying to make out that such ignorance is somehow cool.[/i]This!
Even tho you are correct 🙂
In the spirit of genuine enquiry, how many people can recall instances of needing to remember BODMAS in their working lives? All I have is a dim recollection from school that has never been used since. I am quite prepared to accept that this may be unusual.
you are arguing with idiots in public or you're being trolled, either way you lose.
But that describes [i][u]every[/u][/i] day on STW 😀
how many people can recall instances of needing to remember BODMAS in their working lives?
I can. Obviously. But I am likewise prepared to accept that may be unusual.
I wouldn't say I "remember BODMAS" though, as I didn't know that mnemonic till this thread, I just know the right order. It's more or less built-in these days.
Hugely impressive this is still going:
I wouldn't say I "remember BODMAS" though, as I didn't know that mnemonic till this thread, I just know the right order. It's more or less built-in these days.
Yes, I don't remember the mnemonic, either. But I'm nearly as old as you!
Basic maths is important in everyday life, its just that we take it for granted.
The one I love is:
The stock market/price of something goes down by 5%
The next day, the price rises by 5%
And the number of people who say, "phew, back to where we started!'.
It makes you want to weep.
Percentage changes are important in my work, which is why I'm careful to get them right. But my question was specifically about BODMAS.
how many people can recall instances of needing to remember BODMAS in their working lives?
Well I certainly used operator precedence this morning when I was calculating the cross sectional areas of some pipework. Granted I didn't specifically think BODMAS but I did make sure that I squared the diameter before doing the multipication or division.
The stock market/price of something goes down by 5%
The next day, the price rises by 5%And the number of people who say, "phew, back to where we started!'.
Yes, it's just like getting used to the fact that if you travel 100 miles north, 100 miles east, 100 miles south and 100 miles west, you don't end up where you started. 🙂
how many people can recall instances of needing to remember BODMAS in their working lives?
As explained numerous times up there, shop workers who deal with cash do it daily without even thinking about it.
"[i]Not arbitrary at all - exactly the same rules as elsewhere.[/i]"
That means it's consistent, not that it isn't arbitrary. The world could have defined addition and subtraction as having precedence over multiplication and division.
"[i]There's shame in attempting to argue that those who do know it are wrong. Or in then trying to make out that such ignorance is somehow cool.[/i]"
I was doing neither - not sure what your point is.
"[i]the term in that numerator[/i]"
Whoops - sorry. You got me there. I skimmed it and saw the large division symbol but missed that one.
"[i]That equation from the discussion on Vieta's formulas[/i]"
I notice the use of nice clear parentheses in it 🙂
"[i]I disagree. I think not being able to do basic arithmetic that a 9 year old can/should do, even when given a calculator, is pretty shameful. YMMV.[/i]"
No, MMdoesn'tV, but what I'm trying to say is that there's a difference between being able to do something and being able to understand something that is written. Now, I'll grant you, that second part is still important but it's different. The thing is that in this specific question, the way it's written is a way in which no-one writes things outside of early education, so it's easy to forget. I can do maths pretty well, but to be honest, I either forgot or didn't think hard enough, because I've not seen anything written in that form and with that operator in nigh on 30 years.
When I get to the point in life where my son is learning calculus and starts asking me questions about integration and differentiation, I know that despite being fluent in it 20 years ago I'll have to read up on it again before I'll be able to help. The reason for this is that I simply haven't needed to do any calculus for about 15 years.
Now, the thing is that pretty much everyone can add "2 + 2" and can keep going with that. Pretty much everyone can multiply "2 x 0". People could forget what "2 + 2 x 0" is because [i]they haven't had to deal with arithmetic operator precedence in decades[/i].
The thing is that the STW population all sits at computers, so it's a fairly numerate place. Everyone who's posting now is probably at work, which implies they do a numerate job at a computer - as a population sample it's probably above average intelligence and above average in terms of numeracy and literacy, and crucially probably above average in terms of needing to deal with numbers on a regular basis.
But still very few of us would ever see an expression like "2 + 2 + 2 + 2 + 2 * 0" which - don't ignore this point because it's important - [i]is designed to trip people up[/i].
I've forgotten some of my calculus. Some other people have forgotten some of their operator precedence (or in some cases haven't, but have just made a mistake because they haven't concentrated enough on some totally irrelevant question on Facebook - whoop-de-doo). [i]It's the same thing but on a different level.[/i]
I'm not saying innumeracy is cool, and if that's what anyone infers that from what I've said then their literacy is as questionable as anyone's numeracy. But there is no shame in forgetting things that you simply don't need to know. (Should I be ashamed that I can no longer speak Latin?) Forgetting or mistaking operator precedence in that equation is not the same thing as being unable to deal with numbers, it's simply not being able to readily recall a piece of syntax which is pretty much unused in anyone's life.
While we're here, assuming you have a full driving licence, without looking it up what's the stopping distance of a normal car at 60mph? You know, one of those pieces of information you were taught once and have never needed since. If you get it wrong, can I start a thread to take the piss out of you and complain about Broken Britain?
if you travel 100 miles north, 100 miles east, 100 miles south and 100 miles west, you don't end up where you started.
Provided you start in the right place you do.
As explained numerous times up there, shop workers who deal with cash do it daily without even thinking about it.
Do they? Or do they just count out the change? It's a long time since I worked in a shop...
In the spirit of genuine enquiry, how many people can recall instances of needing to remember BODMAS in their working lives? All I have is a dim recollection from school that has never been used since. I am quite prepared to accept that this may be unusual.
Yesterday, when I was writing a very simple script to check whether a given number in a sequence was even or odd.
Also when I wanted to buy a sandwich and needed to know if I had £2.30 or £34,000 in change in my pocket.
While we're here, assuming you have a full driving licence, without looking it up what's the stopping distance of a normal car at 60mph? You know, one of those pieces of information you were taught once and have never needed since. If you get it wrong, can I start a thread to take the piss out of you and complain about Broken Britain?
There is a difference between learning a fact and learning a rule.
The world could have defined addition and subtraction as having precedence over multiplication and division.
No it couldn't - it's far more fundamental to the whole way maths works.
But still very few of us would ever see an expression like "2 + 2 + 2 + 2 + 2 * 0" which - don't ignore this point because it's important - is designed to trip people up.
Yes, but it's quite clearly designed to trip people up. Hence anybody with any sense at all would look at it quite carefully. The issue being people who don't know the correct way to do it when they do think about it carefully (and then attempt to justify their incorrectness).
While we're here, assuming you have a full driving licence, without looking it up what's the stopping distance of a normal car at 60mph? You know, one of those pieces of information you were taught once and have never needed since. If you get it wrong, can I start a thread to take the piss out of you and complain about Broken Britain?
Ner, ner, ner - strawman alert, strawman alert.
While we're here, assuming you have a full driving licence, without looking it up what's the stopping distance of a normal car at 60mph
240 feet. About as useful in my everyday life as remembering BODMAS. Why is my brain cluttered with such useless facts?
Should I be ashamed that I can no longer speak Latin?
ecce in pictura est puella. 😉
Also when I wanted to buy a sandwich and needed to know if I had £2.30 or £34,000 in change in my pocket.
No you didn't.
That means it's consistent, not that it isn't arbitrary. The world could have defined addition and subtraction as having precedence over multiplication and division.
no.
in your pocket.
2 x £1 coins
0 x £2 coins.
how much cash do you have. a) £0 b) £2
there is a reason that we do it like this. 🙂
I get your point Bez, but the whole idea that this is some arcane piece of knowledge that no one actually uses still sticks in my craw.
As folk keep saying, people do this all the time with change and just don't realise it.
Going back a bit, you said an equation like:
y = c + mx
Is obvious because it doesn't actually have a multiplication sign in it. Odd, but fair enough.
So what do you do when you need to stick some figures in that?
Say I tell you "[i]Right Bez, m = 1.4545 and c = 10, what is y when x is 6.2352[/i]"
Okay you might not write down the expanded equation with a multiply sign in it, but you're presumably going to reach for a calculator (unless you're better at multiplying in your head than me) which means you'll be needing to press that multiply button at the correct point and you'll need to know what order to enter it in.
No?
"[i]As folk keep saying, people do this all the time with change and just don't realise it.[/i]"
No. Absolutely irrelevant, and this is key to the whole discussion.
They do the maths, yes. They [i]don't[/i] write down an expression on paper. That's one of my key points - the ability to do something is not the ability to read an expression of the act.
Take Prince as an example. Love or loathe his music, anyone who's seen or heard him live should attest to the fact that he's a musical genius - plays just about every instrument, each of them better than most people play one, and is one of the most prolific writers on the planet into the bargain. But allegedly can't read standard musical notation. This does not make him incapable of "doing music", though it would - by definition - make him illiterate in the context of standard notation. They're quite different.
Picking coins out of your pocket and figuring out what you've got is the act of doing some maths, and is absolutely [i]not[/i] the act of expressing the operation you performed in a specific notation, nor is it the act of reading an expression that someone has written to describe in atomic detail the process they performed in figuring out whether they could afford a sandwich.
"[i]Going back a bit, you said an equation like y = c + mx is obvious because it doesn't actually have a multiplication sign in it. Odd, but fair enough.[/i]"
It's no more or less [i]inherently[/i] obvious. It's arguably more obvious to those who "do maths", but by virtue of being more [i]familiar[/i].
"[i]Ner, ner, ner - strawman alert, strawman alert. [/i]"
An arguably poor analogy, but not a straw man; since I'm not distorting the opposing argument, I'm merely seeking to test it against an alternative scenario.
[i]Hugely impressive this is still going[/i]
Yeah, but what is it [i]about[/i] ?