N Gauge Forum

This seems to be doing the rounds at the moment. There are 2 correct answers depending on your method.

8 ÷ 2(2 + 2) = ?

Answer = 1,  but it depends on whether you were taught to apply operator priority (BODMAS or similar acronym).   There are always loads of these questions going round the internet.    The world needs to be consistent!

QuoteAnswer = 1,

thats the old answer ,the modern day answer is 16, so  to be safe my answer is  7.5

From what I was taught in skool my answer was 1

It must be 42 - since that's the answer to life, the universe and everything  :D

Quote from: Newportnobby on August 01, 2019, 02:19:19 PM
From what I was taught in skool my answer was 1

Yes indeed.   Trouble is people use calculators these days which take in and evaluate the expression in a linear fashion, unless you use a posh scientific calculator which accepts the entire expression before parsing and evaluating it.

To avoid ambiguity the expression really requires additional parentheses (and ideally additional operators) to clarify the required operator priority instead of relying on conventions

8 / (2 x (2 + 2 )) = 1
(8 / 2) x (2 + 2) = 16

Crazy, isn't it?!  When I'm writing software to a specification I do sometimes have to insist the writer of the spec clarifies their formula/expressions to avoid such ambiguity.

Quote from: Newportnobby on August 01, 2019, 02:08:01 PM
This seems to be doing the rounds at the moment. There are 2 correct answers depending on your method.

8 ÷ 2(2 + 2) = ?

Hi

I get 16 using BODMAS

Expression in brackets first
2 + 2 = 4
Division next as it is the next operation in left to right order
8 / 2 = 4
Leaving
4 * 4 = 16

It would only be 1 if the formula was written 8/(2(2+2)

Cheers

Paul

I was also taught BODMAS in school (in the early 2000s), so to apply that literally (ie division before multiplication) I'd do:

(2 + 2 ) then (8/2), and multiply = 16

Americans seem to be taught PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction), which clearly reverses multiplication and division anyway, so following that I can see you could do:

2*(2+2), then divide that by 8 = 1

Google reckons 16.

All these things show you is that you need to be clear when writing equations!

Edit: cross posted with Paul, who's saying the same thing!

All you lot that were taught BODMAS and/or PEMDAS must have gone to posh schools - I was taught rithmatic! And anyway, I was wondering why there wasn't an operator before the first bracket!

Doesn't need to be, it's implicit that that means multiply.

Quote from: dannyboy on August 01, 2019, 03:45:36 PM
All you lot that were taught BODMAS and/or PEMDAS must have gone to posh schools - I was taught rithmatic! And anyway, I was wondering why there wasn't an operator before the first bracket!

This doesn't happen often, but I agree with you. They ought to learn how to write equations correctly.

See, I said some of you must have gone to posh schools.  ;). Who decided that if there is no operator, you should insert a multiplication sign! Nobody told me that.  :)

posh skool ? the only bits of mafs i  remember  woz          B4I√u ru/16 and 2 (4/3 pi R^3)

Noooo it means you have an 8' layout ÷ 2 up 2 down track = 8 loco's running simultaneously!  :)

Know wonder the country is in such a mess with finances if you can get two or three different answers to the same mathimatical question .
I give up on on this posh stuff like BODMAS etc etc .Know wonder those that went to posh schools usualy end with posh jobs it's because they can fiddle the books by useing all these different methods .

Bob Tidbury

I made it 1.  The acronyms are new to me.

School days were a long time ago for me, though.

When interviewing Bright Young Things, I have been know to ask them what's twice times the half of two-thirds!

Best wishes.

John

educational games to test  our patience, skills and helping one another on this forum ????

You didn't think that the 'N Gauge Forum' was all about n gauge stuff did you?   :no: We could write our own encyclopaedia with the knowledge on here.  :)

a few medieval brain testers



https://www.railadvent.co.uk/2019/08/so-how-did-northern-train-cities-get-there-names-transpennine-express-finds-out.html (https://www.railadvent.co.uk/2019/08/so-how-did-northern-train-cities-get-there-names-transpennine-express-finds-out.html)

agree with you there dannyboy

Quote from: dannyboy on August 01, 2019, 03:50:18 PM
See, I said some of you must have gone to posh schools.  ;). Who decided that if there is no operator, you should insert a multiplication sign! Nobody told me that.  :)

Always been a thing. 2Y means 2 times Y, you don't need to write a multiplication symbol.

Exactly. I was taught that multiplication means "lots of"

So 3y means 3 lots of y, in other words, y+y+y, or 3 times y.

As ntpntpntp implies, there is only one correct answer, and that answer is a question. That question is:'What exactly do you mean by "8/2(2+2)"'

Microsoft Excel says there's an error in the formula and offers a x before the bracket which means the answer becomes 16. That's what it was when I was at school too so it must be right  :P

Let y=(2+2)

2y=8

8/8=1

8/2(2+2)=1. I thought the missing explicit * grouped the 2(2+2) together? And that's how my Sharp calculator calculates the answer to be 1.

It would be 16 if it was expressed as 8/2*(2+2) and the Sharp agrees!

Mark

the same conclusion doing mental arithmetic i had

Just typing the original expression into the calculator on this phone gives 16.

You glad you did not teach mathematics

I taught Physics - lot of maths involved!  ;)

Ok george. Probably best not to repeat my physics teacher ' s habits here. I did better at maths, history and cricket.

I'm curious but I won't ask

Teacher taught newton's theories, bits about hawkings but smoked 20 a day plus had breath that was enough to put people off and i was under 16. Those were the days

I'm amazed/pleased to see the number of replies but it is obvious opinions differ dependent on what/how you were taught or what device you have. A bit like "How do you clean your track?" but with just two possible answers :D

There is confusion in all disciplines, because of historical reasons.

A confusing one when teaching physics was electric current. DC current in reality moves from negative to positive, but, it was initially thought to flow positive to negative.

This is important because it determines the direction of electromagnetic fields, and if kids got the current direction wrong, it made the rest of their calculations wrong.

Luckily the examining board at the time in NSW clarified that all exam questions were based on "conventional" current flow.

I think it's more that it's an ambiguously written question, which just means it's inherently open to interpretation. There is no right or wrong, because the way the question is posed is poor. Basically it's something designed to cause debate on the internet. Like this.

It's obviously a 'slow-news' week in model railway world.

Brain food, I guess. A bit like crosswords, even though I have some mates who have PhDs and love 'em.

Perhaps that's why I'm not Dr Bealman  ;)

I HATE crosswords. To me it's like lying on an Australian beach cooking yerself in the sun. You're achieving nothing, made nothing, contributed nothing.

(Heaps of Aussies still do this, by the way)*

There.

I'll bet I've stirred a hornet's nest here  ;D

* As did a young Bealman on arrival on these shores  ;)

Meh, people have different interests. Not sure qualifications are a relevant factor in that. I believe there's more to a PhD than enjoying crossword puzzles... ;)

Quote from: Bealman on August 02, 2019, 10:13:19 AM
There is confusion in all disciplines, because of historical reasons.

A confusing one when teaching physics was electric current. DC current in reality moves from negative to positive, but, it was initially thought to flow positive to negative.

This is important because it determines the direction of electromagnetic fields, and if kids got the current direction wrong, it made the rest of their calculations wrong.

Luckily the examining board at the time in NSW clarified that all exam questions were based on "conventional" current flow.

I was taught current direction was opposite to electron flow.

Yes indeed, Malc. Conventional current.  :beers:

The thing I used to hate teaching was Lenz's Law. I still have difficulty getting me head around it.

What was funny though, was supervising exams. You could always tell when the kids got to the electromagnetic questions because they started contorting their hands into funny shapes

Ah yes, that takes me back, left hand motor rule, right hand generator rule.

Happy days.

Quoteright hand generator rule

or geneRIGHTor as drumed into us.
On the subject of selective teaching,why is ohms law  not taught properly, W=VI doesn't work 100% of the time.

http://www.sengpielaudio.com/FormulaWheel-ElectricalEngineering.htm (http://www.sengpielaudio.com/FormulaWheel-ElectricalEngineering.htm)

BUT....

Real answer is:

(https://www.ngaugeforum.co.uk/SMFN/gallery/albums/Bealman's_old_photos__amp;_magazines/Dir_3/main_24347.jpg)

Maxwell's equations - not bad for a Scotsman!  :thumbsup:

Quote from: Bealman on August 02, 2019, 10:13:19 AM
There is confusion in all disciplines, because of historical reasons.

A confusing one when teaching physics was electric current. DC current in reality moves from negative to positive, but, it was initially thought to flow positive to negative.

Very many thanks for this, George.  I have remained at the 'initially' stage until today.  I have wired all the layouts that I've attempted to build on this assumption (apart, of course, for the tracks where trains ran in the 'opposite' direction).
The wiring harnesses on my old motorcycles all start at the positive terminal on the battery.  The negative terminal is attached to the frame.  The frame acts as a sort of common return as we railway modellers understand it.  Presumably, the positive to negative current flow assumption was still current (sorry) when these machines (or their ancestors!) were designed.

Like you, I'm not one for crossword puzzles.  I'd rather have half-an-hour with a good book.

Thanks again and best wishes.

John

Cheers, John.

To be honest, it doesn't really matter what convention you adopt with DC wiring, as a long as you don't swap over halfway through!

In my head, I've always thought of positive as feed, and negative as return.

As you know, stick a loco on a bit of track, connect wires from a suitable voltage source, and it will go. Swap the wires around, and it gans the other way!

Talking of books, that pic above is from a book called Einstein's Hero's.  :thumbsup:

Although I can remember those BODMAS instructions, I have used my trusty programmable CASIO calculator.
Must be correct cos it got me through all my qualification exams!
According to the calculator - the answer is 1  :)
Therefore ..... : for the calculation of bills I have to pay - I will use the calculator. For the acceptance of any payments I will use Google answers  ;D

Arrrrggghhhh!!!!
Just tried it with the multiplication sign inserted where multiplication is assumed .........
..... answer is 16  :o
Must needs take me off to a hermits cave ... need to contemplate reality  :confused1: :confused1:

I'm surprised that people are getting 1 - you can only do that if you add in extra brackets.

BODMAS is pretty clear that the correct answer is 16. (2+2) = 4 (Brackets first) as is 8 / 2 = 4 (Division) then the Multiplication of 4 x 4.

The question is ambiguous. I'd argue that 8 ÷ 2(2 + 2), can give you 8 ÷ 2(4), giving 8 ÷ 8.

If it was written as 8 ÷ 2x (where x = 4), you'd not divide the 8 by 2 and then multiply by 4, you'd multiply the 2 by 4 and then divide the 8 by the resulting 8.

Both versions are right and so if the equation were real, it'd need to be rearranged into a non-ambiguous version.

@stevewalker (https://www.ngaugeforum.co.uk/SMFN/index.php?action=profile;u=5329) yes and that's how I would read it: 8 / 2(4) = 1 

As I posted way back the expression is written in an ambiguous way and if I were dealing with this as a specification for software I would require the originator to clarify the requirement.

Agree. That's why it's out and about on the internet. Stirs up stuff like thinking, which maybe is no bad thing  :thumbsup:

Educational game think it is

Quote from: stevewalker on August 05, 2019, 10:20:28 PM
The question is ambiguous. I'd argue that 8 ÷ 2(2 + 2), can give you 8 ÷ 2(4), giving 8 ÷ 8.

If it was written as 8 ÷ 2x (where x = 4), you'd not divide the 8 by 2 and then multiply by 4, you'd multiply the 2 by 4 and then divide the 8 by the resulting 8.

Both versions are right and so if the equation were real, it'd need to be rearranged into a non-ambiguous version.

Hi

Even then it would be 16 as division has a higher precedence than multiply.

Cheers

Paul

I'm starting to think we've exhausted all possibilities here!

Is this why every project goes over time and budget, the person submitting the project has calculated the higher value and the person accepting it has calculated the lower value?

Geoff

Thats a good point geoff

Quote from: geoffc on August 06, 2019, 09:30:24 AM
Is this why every project goes over time and budget, the person submitting the project has calculated the higher value and the person accepting it has calculated the lower value?

Geoff

Ah well, too easy then.

NewportNobby?

Please explain  ;D

Going by how I was taught the 8 ÷ 2(2 + 2) would equal 1.
However, the insertion of a space in front of the bracket i.e. 8 ÷ 2 (2 + 2) would lead me to the answer of 16 but, then again, I'm a dunderhead.

Quote from: PaulCheffus on August 06, 2019, 09:24:17 AM

Even then it would be 16 as division has a higher precedence than multiply.

Cheers

Paul

Actually they're equal, although obviously the D comes first in BODMAS, as I said, in the American version they use PEMDAS; the point is that multiplication and division have a higher precedence than addition and subtraction. Then you work left to right.

Can we all agree that the answer is 1, (or 16), depending on your way of working out the formula and then put this to bed please?  :headbutt:

But I'm down under....

Everything is back to front  :worried:

Quote from: dannyboy on August 06, 2019, 10:09:22 AM
Can we all agree that the answer is 1, (or 16), depending on your way of working out the formula and then put this to bed please?  :headbutt:

I still say that the answer is 42 - but that we'll need a more powerful computer to work out what the question is  :laugh3:

Quote from: njee20 on August 06, 2019, 10:06:33 AM

Quote from: PaulCheffus on August 06, 2019, 09:24:17 AM

Even then it would be 16 as division has a higher precedence than multiply.

Cheers

Paul

Actually they're equal, although obviously the D comes first in BODMAS

Hi

Nope that's the reason the (D) division comes first as it is more important than multiply. That's what I and the rest of the people in my office were taught at school in the 70s.

Cheers

Paul

What is Bodmas (https://www.theschoolrun.com/what-is-bodmas)

(https://www.theschoolrun.com/sites/theschoolrun.com/files/u9/bodmas_order.png)

QuoteMultiplication and division have the same level of order so complete from left to right

That echoes what I was taught in the 00s. Otherwise if you're in the US then multiplication is more important.

Quote from: njee20 on August 06, 2019, 10:39:58 AM
What is Bodmas (https://www.theschoolrun.com/what-is-bodmas)

(https://www.theschoolrun.com/sites/theschoolrun.com/files/u9/bodmas_order.png)

QuoteMultiplication and division have the same level of order so complete from left to right

That echoes what I was taught in the 00s. Otherwise if you're in the US then multiplication is more important.

Hi

Note it says if you have a calculation involving division and multiplication complete them as they appear left to right. Division is left of the multiplication hence first in that equation.

Cheers

Paul

Left to right as they appear in the equation you realise, not left to right in the acronym BODMAS...? They have the same precedence.

Whether D or M are equal doesn't affect the outcome in this case as we still go left to right so the first calculation is brackets (2+2) = 4. Then L to R you do the D next 8/2 = 4 then M 4 x 4 = 16.

For those still insistent that the answer can be 1, sorry but it can't be unless you are using a different system or adding brackets that don't exist. It isn't ambiguous, that is the whole point of BODMAS (and this question)!

Quote from: njee20 on August 06, 2019, 11:00:04 AM
Left to right as they appear in the equation you realise, not left to right in the acronym BODMAS...? They have the same precedence.

Hi

Please read all of what was written specifically the line below
Division is left of the multiplication hence first in that equation.

Cheers

Paul

BODMAS is a principle not a rule and it is the principle of "the order of computation".

When you step into more complex algebra the order holds but varies due to "variables" that cannot be resolved during calculation.

In the following you have to multiply the contents of the adjacent brackets together first before you resolve the contents of the brackets.

(ax+by)(ay+bx)=a²xy+b²xy+abx²+bay²=xy(a²+b²)+ab(x²+y²) =

That still basically follows the same principles...

Quote from: PaulCheffus on August 06, 2019, 11:29:52 AM

Please read all of what was written specifically the line below
Division is left of the multiplication hence first in that equation.

Goodo. We both agree that it's 16 FWIW, like Mike I can't see how anyone can make it 1, but division and multiplication are of equal precedence in BODMAS.

Now... who wants to punctuate this entirely reasonable sentence: :-)

"James while John had had had had had had had had had had had a better effect on the teacher"

James, while John had had "had", had had "had had"; "had had" had had a better effect on the teacher.

..possibly....

Cheers. Jon  :)

Correct! Was Wikipedia involved!? ;)

Quote from: njee20 on August 06, 2019, 11:44:54 AM
That still basically follows the same principles...

Quote from: PaulCheffus on August 06, 2019, 11:29:52 AM

Please read all of what was written specifically the line below
Division is left of the multiplication hence first in that equation.

Goodo. We both agree that it's 16 FWIW, like Mike I can't see how anyone can make it 1, but division and multiplication are of equal precedence in BODMAS.

Now... who wants to punctuate this entirely reasonable sentence: :-)

"James while John had had had had had had had had had had had a better effect on the teacher"

Hi

Not a clue. English was never my strong point :)

Cheers

Paul

I think you've all been had  :D

Quote from: njee20 on August 06, 2019, 11:50:59 AM
Correct! Was Wikipedia involved!? ;)

No....I vaguely remembered something similar from school... my friend James and I solved it differently.

Where I had had "James, while John had had "had", had had "had had"; "had had" had had a better effect on the teacher" my friend James had had  "James, while John had had "had had", had had "had"; "had had" had had a better effect on the teacher"; "James, while John had had "had", had had "had had"; "had had" had had a better effect on the teacher" had a better effect on the teacher.

But I think both were equally correct.

Cheers Jon  :)

The division sign is the issue. If the equation is written like Mr Abbott would have done on a blackboard at my primary school we get:

                             8   
                         2(2+2)

Therefore the answer is one

Or maybe not

                          8     (2+2)
                          2

I don't think I really care anymore.

John P

Quote from: jpendle on August 07, 2019, 09:46:59 PM
The division sign is the issue. If the equation is written like Mr Abbott would have done on a blackboard at my primary school we get:

                             8   
                         2(2+2)

Therefore the answer is one

Or maybe not

                          8     (2+2)
                          2

I don't think I really care anymore.

John P

8    *    1
2       (2+2)

:D

Quote from: jpendle on August 07, 2019, 09:46:59 PM

I don't think I really care anymore.

I think you're not alone so I'll close it now. :locked:
If anyone wants it unlocked just let me know