I'm not one for maths, but I get 2.
If there's one thing I remember from school, it's that you do the bits with brackets first....
Just a stab in the dark, but I'm guessing that you haven't read the preceding 1,305 posts in this thread...?
======================
To me, the debate isn't (shouldn't be) over the acceptedness(?) of BODMAS/BEDMAS/BIDMAS at all, it's over whether "a/bc" means (a/b)*c or a/(bc), pure and simple.
To reiterate my stance: there is a bond in the "bc" expression and hence "a/(bc)" is right. I have never encountered otherwise.
1/2i = 1/(2i) = -0.5i
100/2π =100/(2π) = 16ish
Much as I'm struggling to believe that anyone has really and seriously used these terms (as typographically presented here) to mean (a/b)*c, 0.5i and 157ish respectively, I'll suspend my disbelief - hence my conclusion that "mu" is the answer: "re-ask the question in a better way".
Writing "2(9+3)" is unorthodox (as they're just numbers, not x's, π's etc) but that "bond" is still there and to be able to do the "48÷2" first, there should be a "*" before the "(" because
48÷2*(9+3) = 288
Also, I do believe we were given an equation to solve:
"48÷2(9+3) = ?"
(where "?" would normally be "x" or similar). There's an equals sign; it's an equation; solve it for "?".
Yes, it would be better expressed as "evaluate the expression 48÷2(9+3)", but to bicker over this is, in my book, pure red herringery served with more than a soupçon of pedantry. The main debate is over a different point and I don't think is going to go any further now. Great thread, though - loving how long and fast-growing it's been!
http://www.mathcentre.ac.uk/resources/workbooks/mathcentre/rules.pdf
"Anything in brackets must be done first. Then we evaluate any powers. Next we do any divisions and multiplications, working from left to right. And finally we do the additions and subtractions, again working from left to right."
http://www.mathcentre.ac.uk/resources/workbooks/mathcentre/rules.pdf
"Anything in brackets must be done first. Then we evaluate any powers. Next we do any divisions and multiplications, working from left to right. And finally we do the additions and subtractions, again working from left to right."
No wonder this country is in such a mess if the eggheads can't even work out a simple sum like this......it's what you get for leaving out common sense brackets and multiplication signs just to make a simple thing seem clever
cba to look at the links, but from your excerpts it looks like you're just hitting us with definitions of BODMAS. No-one's disputing that, AFAICT.
My aim was to stress the left to right rule, which the list of operations specified by BODMAS doesn't cover. This is important because some people here think that when two items are multiplied together without a multiplication sign that multiplication should be done first, even if it follows to the right of a division. Those references all say that is wrong.
In maths the multiplication sign is always omitted if at least one of the operands is a letter. However, all the references I quoted say to always proceed left to right, and none mention the question of whether there is a multiplication sign or not.
You'll have noticed that the references aren't just forum postings, wiki articles or blog entries, but from generally more authoritative sources.
A new operator, //, is the floor division operator. (Yes, we know it looks like C++'s comment symbol.) // always performs floor division no matter what the types of its operands are, so 1 // 2 is 0 and 1.0 // 2.0 is also 0.0.
A new operator, //, is the floor division operator. (Yes, we know it looks like C++'s comment symbol.) // always performs floor division no matter what the types of its operands are, so 1 // 2 is 0 and 1.0 // 2.0 is also 0.0.
Your google is (unintentionally) biased.
Please take a look at page 6 http://www.uea.ac.uk/jtm/1/lec1p5.pdf
I'm not a clever as you. Is the second "basic rule" giving ac/bd correct?
My aim was to stress the left to right rule, which the list of operations specified by BODMAS doesn't cover. This is important because some people here think that when two items are multiplied together without a multiplication sign that multiplication should be done first, even if it follows to the right of a division. Those references all say that is wrong.
In maths the multiplication sign is always omitted if at least one of the operands is a letter. However, all the references I quoted say to always proceed left to right, and none mention the question of whether there is a multiplication sign or not.
You'll have noticed that the references aren't just forum postings, wiki articles or blog entries, but from generally more authoritative sources.
?? You say on the one hand:
"When two items are multiplied together without a multiplication sign that multiplication should be done first... Those references all say that is wrong."
and then
"none [of the references] mention the question of whether there is a multiplication sign or not"
How can they say it's wrong without mentioning it?
I think also that perhaps there's confusion caused by whether "BODMAS" merely means the order of operations with those initial letters (yes, in pairs) OR the rule/convention that talks about that order TOGETHER WITH the left-to-right aspect.
It's entirely correct, as you'd expect. You're trying to blur the distinction between the horizontal line and the slash; the former groups everything beneath it as if inside an implied set of brackets, the latter does not.
Indeed, if you hold your mouse over the expression with the horizontal bar, under "Input:", the alt image text shows the expression using a slash and brackets.
?? You say on the one hand:
"When two items are multiplied together without a multiplication sign that multiplication should be done first... Those references all say that is wrong."
and then
"none [of the references] mention the question of whether there is a multiplication sign or not"
How can they say it's wrong without mentioning it?
Because if that rule existed I would have expected at least one source to mention it. None do, which implies (but does not prove) that there is no such rule.
I think also that perhaps there's confusion caused by whether "BODMAS" merely means the order of operations with those initial letters (yes, in pairs) OR the rule/convention that talks about that order TOGETHER WITH the left-to-right aspect.
BODMAS is an acronym for remembering that part of the convention for evaluating expressions that specifies the order of operations. The convention also includes the additional aspects that division and multiplication have the same priority as each other, and that addition and subjtraction have the same priority as each other, and the left to right rule.
If you went up to the board in any of the maths lectures I went to and wrote
ac/bd = acd/b
(like that, on one line, with slashes) you'd have been greeted with howls of derisive laughter.
From some quarters perhaps, but those who understood the rule would have nodded in agreement, although probably wondering why the horizontal bar format wasn't being used.
Because if that rule existed I would have expected at least one source to mention it. None do, which implies (but does not prove) that there is no such rule.
Which is very different to them actually saying that it's wrong, which is what you said.
From some quarters perhaps, but those who understood the rule would have nodded in agreement
It's not to do with understanding the rule; it's to do with understanding that "ab" has a subtle, yet definite, different meaning than "a*b" does, and using BODMAS on that entity.
re ac/bd: Most quarters would have thought that if you meant acd/b then you'd write (ac/b)d
Comments
Just a stab in the dark, but I'm guessing that you haven't read the preceding 1,305 posts in this thread...?
======================
To me, the debate isn't (shouldn't be) over the acceptedness(?) of BODMAS/BEDMAS/BIDMAS at all, it's over whether "a/bc" means (a/b)*c or a/(bc), pure and simple.
To reiterate my stance: there is a bond in the "bc" expression and hence "a/(bc)" is right. I have never encountered otherwise.
1/2i = 1/(2i) = -0.5i
100/2π =100/(2π) = 16ish
Much as I'm struggling to believe that anyone has really and seriously used these terms (as typographically presented here) to mean (a/b)*c, 0.5i and 157ish respectively, I'll suspend my disbelief - hence my conclusion that "mu" is the answer: "re-ask the question in a better way".
Writing "2(9+3)" is unorthodox (as they're just numbers, not x's, π's etc) but that "bond" is still there and to be able to do the "48÷2" first, there should be a "*" before the "(" because
48÷2*(9+3) = 288
Also, I do believe we were given an equation to solve:
"48÷2(9+3) = ?"
(where "?" would normally be "x" or similar). There's an equals sign; it's an equation; solve it for "?".
Yes, it would be better expressed as "evaluate the expression 48÷2(9+3)", but to bicker over this is, in my book, pure red herringery served with more than a soupçon of pedantry. The main debate is over a different point and I don't think is going to go any further now. Great thread, though - loving how long and fast-growing it's been!
ETA: "Mathsgate", ROFL!
EATA: from the referred-to thread: It's not just me, then!
"Division and Multiplication. Start on the left and work them out in the order that you find them."
http://www.channel4.com/programmes/dispatches/articles/kids-dont-count-bodmas
"What it in fact means that brackets are evaluated first, then division and multiplication are to be done before addition and subtraction, but each of these pairs of operations are to be evaluated from left to right."
http://www.mathematics.me.uk/BODMAS.pdf
"For operators of the same priority, we simply evaluate left-to-right."
http://www.mathcentre.ac.uk/resources/workbooks/mathcentre/rules.pdf
"Anything in brackets must be done first. Then we evaluate any powers. Next we do any divisions and multiplications, working from left to right. And finally we do the additions and subtractions, again working from left to right."
http://www.uea.ac.uk/polopoly_fs/1.141672!BODMAS.pdf
"Importantly, when two or more operations of the same order appear one-after-another, the operations should be carried out from left-to-right. "
http://www3.wolframalpha.com/input/?i=1%2F2x
How could they have got this so wrong?
cba to look at the links, but from your excerpts it looks like you're just hitting us with definitions of BODMAS. No-one's disputing that, AFAICT.
Excellent!
(And wrong, btw .)
What I want to know is how we should evaluate
http://www.digitalspy.co.uk
Does the "//" mean just the "www" goes on top, or do we work out the three dot-products first then double-divide the result, or what?
So...what is the answer then?
I'm glad someone's paying attention.
I'm not wrong, because the correct answer to a silly question is a silly answer.
In maths the multiplication sign is always omitted if at least one of the operands is a letter. However, all the references I quoted say to always proceed left to right, and none mention the question of whether there is a multiplication sign or not.
You'll have noticed that the references aren't just forum postings, wiki articles or blog entries, but from generally more authoritative sources.
Truth is stranger than fiction:
http://docs.python.org/reference/lexical_analysis.html#operators
The following tokens are operators:
+ - * ** / [highlight]//[/highlight] %
<< >> & | ^ ~
< > <= >= == != <>
http://docs.python.org/release/2.2.3/whatsnew/node7.html
A new operator, //, is the floor division operator. (Yes, we know it looks like C++'s comment symbol.) // always performs floor division no matter what the types of its operands are, so 1 // 2 is 0 and 1.0 // 2.0 is also 0.0.
Please take a look at page 6
http://www.uea.ac.uk/jtm/1/lec1p5.pdf
I'm not a clever as you. Is the second "basic rule" giving ac/bd correct?
?? You say on the one hand:
"When two items are multiplied together without a multiplication sign that multiplication should be done first... Those references all say that is wrong."
and then
"none [of the references] mention the question of whether there is a multiplication sign or not"
How can they say it's wrong without mentioning it?
I think also that perhaps there's confusion caused by whether "BODMAS" merely means the order of operations with those initial letters (yes, in pairs) OR the rule/convention that talks about that order TOGETHER WITH the left-to-right aspect.
As they have it, ac above a horizontal line and bd below it, is correct and abides by the standard.
As you have it, very differently, ac/bd is wrong as that of course is acd/b.
It's entirely correct, as you'd expect. You're trying to blur the distinction between the horizontal line and the slash; the former groups everything beneath it as if inside an implied set of brackets, the latter does not.
Indeed, if you hold your mouse over the expression with the horizontal bar, under "Input:", the alt image text shows the expression using a slash and brackets.
You stirrer, you! There's NO "of course" about it at all!
If you went up to the board in any of the maths lectures I went to and wrote
ac/bd = acd/b
(like that, on one line, with slashes) you'd have been greeted with howls of derisive laughter.
Well, perhaps not, mathematicians not being known for such extroversion, but you know what I mean.
Erm... I kinda really hate to do this to you, but...
http://www3.wolframalpha.com/input/?i=48%2F2%289%2B3%29
Which is very different to them actually saying that it's wrong, which is what you said.
It's not to do with understanding the rule; it's to do with understanding that "ab" has a subtle, yet definite, different meaning than "a*b" does, and using BODMAS on that entity.
re ac/bd: Most quarters would have thought that if you meant acd/b then you'd write (ac/b)d
Only according to p% of the votes, where
p = (48÷2*(9+3))/100+40
(because happily, as I write, the 288ers have 42.88% in the poll).
And, just for clarity, 42.88<57.12
Not that DS polls mean anything, of course.