What's the answer to this very basic maths problem?

[h4rm0ny]

Eh? Obviously it's not the accepted method anymore, that convention has changed with time (which was my original point in response to your assertion that that had never happened in the history of mathematics).

Well not "obviously" no, since we have multiple people telling you that this is exactly how they work it out and you didactically insisting to the rest of us that how you think of it is the "accepted method". Rubbish. Assertion, assertion, assertion. But unfortunately in your case it is the argument fallacy rather than the mathematical kind that is followed by a proof. The very fact that people are reacting to you telling you that you're wrong is evidence that it's not accepted. Nor is it because we're "old". Here's MY hypothesis. You got the wrong end of the stick once, have never learnt otherwise because it comes up so seldom in your life and are now spouting off to other people that yours is "obviously" the "accepted" way because you've never questioned yourself. This is how it is taught in school and has been for a long, long time. There was no conclave of mathematicians where they suddenly decided to change it arbitrarily for no reason one day. It's just a misconception that may have grown because some calculators do it that way. And anyway, no mathematician would actually write it out that way whichever they meant. The whole BIMDAS thing is really only for teaching in schools. Beyond that level, it's redundant and unused because proper mathematical notation is used. The "division" symbol should really be dropped at Secondary School, imo.

It's pretty crazy seeing two so similar calculators giving correct/incorrect answers isn't it lol.

More an example of why you don't use calculators to determine mathematical process.

This is even funnier, the free built in Windows 10 calculator will give the correct answer of 9, however this calculator (which was one of the best on the planet when my father bought it) doesn't XD

It's not funny, it's because the free Windows 10 calculator is crap and the "best on the planet" calculator is not.

Simple explanation of the older method here:

I was never taught that the divisor means resolve everything to the right of it first and I don't know anyone else who says that, either. And yet, I still don't agree with you!

This is why you get old people getting mad/conused when they see young people answering 9 instead of 1

Is this all that you have? Endless repetition that "you're old so you're wrong". You keep stating yours is the accepted way, yet it's not accepted. This is tiresome.

EDIT: Also, everything Dowie just said. Only replace 'skeptical' with 'I have more doubts than a turkey invited to a Christmas party.'

 

[ianh]

Unless the answer is less than 4 my calculator just gives the answer as "A Suffusion of Yellow"

 

[danlightbulb]

You have to identify the terms in the equation first guys as I said in my post. It's pretty simple. The correct answer is 1.

The 'everything to the right of the divisor' argument is also wrong for the same reason.

 

[h4rm0ny]

Unless the answer is less than 4 my calculator just gives the answer as "A Suffusion of Yellow"

Heh. Nice one, Dirk Gently. Though apparently getting that makes me "old" according to ubersonic.

 

[ubersonic]

Thus I was asking for an example of your 'older method' - perhaps it does exist but I'd be a bit skeptical.

There's actually a video explanation here using the same example equation I posted: https://www.youtube.com/watch?v=URcUvFIUIhQ

It first goes through the current accepted methodology step by step explaining how it works, then goes through the previously accepted methodology step by step explaining how it worked. You may find that interesting.

NB: It also lists the date for the change in methodology as 1917 which being 100 years ago makes it confusing as to why many older people use it, the reason for this is because they were taught it by school teachers who were taught it in school themselves and through that cycle it remained being taught in some school classrooms right into the 60's/70's before it finally died out.

 

[dowie]

There's actually a video explanation here using the same example equation I posted: https://www.youtube.com/watch?v=URcUvFIUIhQ

possible but weak evidence - problem is that is a third party youtube and we don't have the source he's referring to nor do we know for sure whether he's been confused by multiplication by juxtaposition and made an assumption that this older method is simply applying to everything on the right when his example (and perhaps whatever he saw in the old textbook) could easily be explained by the juxtaposition next to the bracket having precedence over ordinary multiplication.division too

can you do what I asked re: your old calculator please as that would clear up quite easily at least where it does use your 'older method'

please type in 6÷2+3 and post a screenshot as you did previously

 

[danlightbulb]

NB: It also lists the date for the change in methodology as 1917 which being 100 years ago makes it confusing as to why many older people use it, the reason for this is because they were taught it by school teachers who were taught it in school themselves and through that cycle it remained being taught in some school classrooms right into the 60's/70's before it finally died out.

I was secondary school in the 90s so this is clearly wrong. I remember part of our maths lessons was explicitly demonstrating that typing things directly into a calculator gives the wrong answer. We had to do it the calculator way and then the right way. So it's always stick with me for that reason.

Terms identification first. In the equation 6÷2(3) the terms are 6 and 2(3). You evaluate those first according to BODMAS then you evaluate what's left. Blimey I hope you guys here never have to design bridges or aeroplanes.

 

[ubersonic]

Well not "obviously" no, since we have multiple people telling you that this is exactly how they work it out and you didactically insisting to the rest of us that how you think of it is the "accepted method".

O.o

You and I are (or were at least, not sure if you're going for a straw-man now) in agreement on what is the currently accepted method. The only disagreement was that you claim that accepted methods have never changed in the history of mathematics, which is what I was attempting to disprove. By citing that equation, for which the accepted method has changed in the last century, and demonstrating the change in accepted methodology.

It's not funny, it's because the free Windows 10 calculator is crap and the "best on the planet" calculator is not.

I'm not sure if you read what you were replying too or not, but the "crap" Windows calculator gave the correct (using currently accepted methodology) answer of 9. My old scientific calculator (which was previously the best model) did not. Which was funny considering the Windows calculator is free and that one cost a lot back in the day, hence me mentioning it for comedy value.

 

[dowie]

Terms identification first. In the equation 6÷2(3) the terms are 6 and 2(3). You evaluate those first according to BODMAS then you evaluate what's left. Blimey I hope you guys here never have to design bridges or aeroplanes.

that isn't correct as explained previously, I wouldn't focus too much on 'BODMAS', I've explained why you can have situations where the convention is that 2(3) takes precedence over explicit multiplication/division but you seem to be working on the assumption that this is as a result of the 'B' in 'BODMAS' which is clearly wrong as that would lead it to take precedence over powers too and that wouldn't be like any convention

if you're strictly following 'BODMAS' then you'd get the answer 9

 

[ubersonic]

I was secondary school in the 90s so this is clearly wrong.

I don't mean to sound condescending, but if you were taught in the 90's then you wouldn't have been taught something old that died out 30 years prior would you?

 

[h4rm0ny]

There's actually a video explanation here using the same example equation I posted: https://www.youtube.com/watch?v=URcUvFIUIhQ

It first goes through the current accepted methodology step by step explaining how it works, then goes through the previously accepted methodology step by step explaining how it worked. You may find that interesting.

NB: It also lists the date for the change in methodology as 1917 which being 100 years ago makes it confusing as to why many older people use it, the reason for this is because they were taught it by school teachers who were taught it in school themselves and through that cycle it remained being taught in some school classrooms right into the 60's/70's before it finally died out.

What I see is a comments section filled with people disagreeing. And you've just conceded that despite an American journal deciding it should be done differently, it continued to be taught the other way long, long after. I think you've just established very firmly that your approach is NOT "obviously accepted". Nobody I know does it that way. I'm fairly certain it's still often taught in our schools in the order we say. It doesn't matter to actual real mathematics because the symbol isn't used in real world maths by actual mathematicians. It's just a convenience for helping young children understand because young children need a symbol to know something is there. They've had + and - symbols so they require ones for multiplication and division. Just putting numbers and brackets next to each other confuses them. so discrepancies persist in how it is taught in different places.

However, in the interests of putting this to rest I actually pulled down a GCSE Mathematics revision book from 2004 when I tutored somebody in mathematics. Surprisingly (to me), I found that it listed BODMAS and put division ahead of multiplication when it came to adjacent operations. So it seems there has been a reversal in policy as ubersonic says. At least on the part of British schoolboards. I'll note though that the specific lines in the text book state that the student should use parentheses ("brackets") to make sure their calculator does things in the right order.

So, I'll concede the point. Ubersonic is correct that there has been a decision on the part of bodies such as British exam boards that it should be done in BODMAS order. I maintain though that it's far from universally accepted. The huge number of people who disagree mean it isn't by definition. And I'll say again that BODMAS / BIMDAS are just tools for teaching children. It makes no difference to real maths which is why such discrepancies in approach can persist.

 

[danlightbulb]

I'm not strictly following BODMAS I think you're missing what I'm trying to say.

You are all assuming that

6÷2(3)

Is the same as

6÷2×3

It's not the same.

In the second equation there are three terms, and you evaluate straight as BODMAS. Answer is indeed 9.

In the first equation there are two terms!!! This is the fundamental difference.

The absence of the operator in the 2nd term means it is a single term evaluated first. It's that simple. You don't just add in the operator because it suits you!

Take it rewritten:

a÷b(c)

This is clearly a÷bc I.e. two terms! You would always evaluate this as a/(bc)

 

[h4rm0ny]

You and I are (or were at least, not sure if you're going for a straw-man now) in agreement on what is the currently accepted method.

No we weren't. I use (in the hypothetical situations where it comes up - see my comments elsewhere about not actually using the division symbol normally) BIMDAS. Which is Brackets, Indices, Multiplication, Division, Addition, Subtraction. You stated BODMAS which is Brackets, Orders (same thing as Indicies), Division, Multiplication, Addition, Subtraction.

However, I've conceded that the British educational authorities agree with you. Certainly not how I and I believe most people we taught, however!

 

[danlightbulb]

I don't mean to sound condescending, but if you were taught in the 90's then you wouldn't have been taught something old that died out 30 years prior would you?

I meant that I was schooled in the 90s and i was taught what you are all referring to as the old way. I was also taught the difference between what a calculator says and the right evaluation of a formula. Something missing here it seems.

 

[h4rm0ny]

I'm not strictly following BODMAS I think you're missing what I'm trying to say.

You are all assuming that

6÷2(3)

Is the same as

6÷2×3

It's not the same.

In the second equation there are three terms, and you evaluate straight as BODMAS. Answer is indeed 9.

In the first equation there are two terms!!! This is the fundamental difference.

The absence of the operator in the 2nd term means it is a single term evaluated first. It's that simple. You don't just add in the operator because it suits you!

Take it rewritten:

a÷b(c)

This is clearly a÷bc I.e. two terms! You would always evaluate this as a/(bc)

I retract my concession! danlightbulb raises a valid and correct point. The implicit multiplication does commute the equation to the right of the division side to a single, discrete value! Well spotted!

Although ubersonic can simply re-write their example as 6÷2×(1+2) and resume their argument.

 

[danlightbulb]

I retract my concession! danlightbulb raises a valid and correct point. The implicit multiplication does commute the equation to the right of the division side to a single, discrete value! Well spotted!

Although ubersonic can simply re-write their example as 6÷2×(1+2) and resume their argument.

Thank you. It is a fundamental mathematical skill to identify the terms in a formula before blindly applying BODMAS.

If the formula was rewritten 6÷2x(1+2) then I would concede the answer is 9, because we once again have 3 terms in the equation. No probs with that at all.

 

[dowie]

I retract my concession! danlightbulb raises a valid and correct point. The implicit multiplication does commute the equation to the right of the division side to a single, discrete value! Well spotted!

it doesn't necessarily, I've already explained this in post #68 on the previous page

implicit multiplication or multiplication by juxtaposition can, by some conventions, take precedence over explicit multiplication/division

I provided a screen shot of two calculators where the different conventions have been implemented even, I thought people had read and understood that post as it highlights exactly where the majority of the confusion comes from re: this question being posted online

danlightbulb however isn't correct in his previous claim that the right hand term ought to be evaluated together because of the 'B' in BODMAS, that would indicate that implicit multiplication is given precedence over powers which is dubious and not a convention anywhere

 

[h4rm0ny]

On reflection, I conceded the point with ill-grace given how stridently I've been telling ubersonic they're wrong.

My apologies. If the British schoolboard now defines the division symbol as having higher precedence than the multiplication symbol then that's about as close as we'll get to it being the case that there is an accepted method in the UK as ubersonic says.

Honestly, these symbols should be dispensed with once their job as a teaching aid is done.

 

[h4rm0ny]

danlightbulb however isn't correct in his previous claim that the right hand term ought to be evaluated together because of the 'B' in BODMAS, that would indicate that implicit multiplication is given precedence over powers which is dubious and not a convention anywhere

I think danlightbulb is correct, but it's only relevant because we have an ugly mixture of high school mathematics and real mathematics. We have implicit operators in one part of the sum "2(3)" and explicit, i.e. chained, operators in another part ("÷"). They really shouldn't be mixed in the first place. Either proper mathematical notation should be used throughout, e.g.

or else explicit chain operators should be used throughout. danlightbulb, imo, identified that by mixing the two, you had to follow both sets of rules. In which case the "2(3)" would have to be treated as a single discrete value.

 

[danlightbulb]

danlightbulb however isn't correct in his previous claim that the right hand term ought to be evaluated together because of the 'B' in BODMAS, that would indicate that implicit multiplication is given precedence over powers which is dubious and not a convention anywhere

Conceded. I should have been clearer. I was trying to say that the bracketed term should be treated as a term in it's own right, which I clarified later on.

To your first point, I know of no teaching that would split a term that is shown without an operator for the purposes of evaluating it in a different order. That wpuld be fundamentally wrong.

3x + 6y ÷ 8z

Has three terms in it. You would be out of your mind to write this as

3*x + 6*(y÷8)*z

Wouldn't you?



@h4rm0ny I agree the original formula is badly written. Hence why the skill of identifying terms is so crucial here and why there is only one right answer. In more complex formula, identifying terms correctly and then the order of evaluation is critical. This is what I was taught (90s). I agree a lot of people probably have problems with it.