Besides this new post of yours I see you added a lot to your post before that one ... so I am going to deal with both of those.

An "implied/implicit multiplication" just means that a multiplication symbol isn't there but it is understood ... like 3(4+5) ... we understand is 3 x (4 + 5) or A ÷ BC we understand B and C are to be multiplied so is B x C ... explicit multiplication is where the multiplication symbol is there like 3 x 5.

There are some math teachers who also don't really understand PEMDAS/BODMAS/BEDMAS and they teach it wrong ... I watched the video and it was good ... yes there was a multiplication sign between the number and the parenthesis group  ... that is why she dropped the parenthesis when she was done ... that isn't new ... there is no need for it anymore ...  I'm over 60 years old ... it is how it has always been ...

4 to the power 2-2 x( 8 ÷2) + 6

she wrote

4 to the power 2-2 x 4 + 6

what did you want her to write this ...

4 to the power 2-2 x( 4) + 6

and if she did what difference would it make ??? ... none ... there is no longer any need for there to be a parenthesis there around the 4 anymore ... your concern about "dropped parenthesis" is a non issue ... if you have 4(1+3) it equals 4(4) = 16 here you can't just drop the parentheses unless you insert the implied multiplication sign ... also in that calculator I linked to you can put 4(4) in it and get 16 ... seems you are trying to say that not only can the OP equation NOT be solved but that 4(1+3) can't be solved ... because you have to drop the parenthesis ... that isn't what that video "taught" ... she said since they were not needed anymore ... if they are still needed you keep them or convert them to multiplication sign ...

Do notice she said in the beginning that the P has to do with what is INSIDE the parenthesis so nothing about anything outside the P ... this equation in the OP ...you wouldn't get in 5th grade or probably even higher classes ... it is purposely written to cause ambiguity and confuse ...

So back to dealing with the OP equation ... there is more than one possible answer because there are different "systems" in math to deal with such and it depends on which system you use.  In standard PEMDAS/BODMAS/BEDMAS implied multiplication DOES not take precedence over explicit multiplication or division ... however there has always been some who prefer to have implied multiplication (you can also search the terms implicit multiplication) take precedence over explicit multiplication and division.  For Physicists they often use equations where they need (a(b+c)) or they need  A ÷ (BxC)... so instead of having to write that all the time they "understand/agree" that an implied multiplication takes precedence over an explicit multiplication or division so they can have a "shorter" way to write it.  What they teach in school is not usually this modified PEMDAS/BODMAS/BEDMAS ... and that is why if you took a standard test and they had the equation in OP the answer would be 16.  Also most calculator companies have different calculators to handle the two different systems and you need to get the right calculator for what system you WANT to use.  That link I put up for YOU for a calculator I purposely put up one that uses standard PEMDAS/BODMAS/BEDMAS ... I could also put up one that uses modified PEMDAS/BODMAS/BEDMAS from the same company, but if you just typed n 4(4) you would get 16 in it also ... BECAUSE there is only the implied multiiplicaton.

So let's look at the OP equation again ...

8÷2(1+3) =

8÷2(4) =

At this point it depends on which system you use ...

If you use the standard PEMDAS/BODMAS/BEDMAS where implied multiplication DOES NOT take precedence over explicit multiplication or division (no such thing as implied division) you work left to right for divisions and multiplications (even implied multiplications)

8÷2(4) =

4(4) =

4

If you use the modified PEMDAS/BODMAS/BEDMAS where implied multiplication DOES take precedence over explicit multiplication or division (no such thing as implied division) you first work left to right with the implied multiplications then work left to write for divisions and explicit multiplications

8÷2(4) =

8÷8=

1

But it is not about the P/B (parenthesis/brackets) needing to be done first ... it is on whether implicit multiplication takes precedence over division or explicit multiplications.  And that is why I asked you about

A ÷ BC =

Where A = 3 , B = 2, C = 30 ...

Also concerning my equation ...

2-4÷6+7x5+3÷17x5-3÷6÷12+3 =

I used that equation for the problem of those who want to have everything to the left of a divide sign be divided by what is to the right  and it would be "hard" to solve it using that system ... and yes it is not hard for those using PEMDAS/BODMAS/BEDMAS because yes it makes it easy  ... and it had no implied multiplication so there was not that "problem" ... hey but you got to do your basic math properly lol and no you didn't get the right answer ... I did it and got a different answer than you and so looked at what you did and well first thing I saw is that you said (4÷6) = 24 ...after that I didn't look for anymore errors ... seems I am not the only one needing sleep ... :)

I think we have made a lot of progress here and it is something that has been going around the internet for a long time ... and it is nice having someone who is interested in understanding what is going on to discuss this with ...

Forgetting about the game and Fury, much to my loss,I was still figuring things out, so I think I answered your latest question on completion of my post.

I watched another video which posed the same problem with a different question 3 x 3÷3(1+2), the answers being 9 or 1. 

Unfortunately the video was not in English but the end of the video, depicting a  flat earth and Galileo, left me with the impression,"Some things in this world never change, but some things do." 

There are still sixty seconds in a minute,  but the second is no longer a 60th of a minute. 100 ml is no longer the same as 100 cc.

Scientists still make mistakes which is why they had to go and fix the Hubble telescope. 

Returning later again, to your earlier post. 

Unless your tiredness did make you a mistake,It seems I might be inconsistent with my answers to your question 

A ÷ BC =? and the question, 8÷2(1+3) = ? Alice posed.

Since I didn't see "implied multiplication" in  A ÷ BC =?, I would have said A ÷ B x C using the left to right rule to give 45 and 1. Though now I am unsure if BC doesn't just mean multiply ,and wondering if technically it is implied multiplication.

The implied multiplication does give 0.05 and 1.

Unfortunately my memory cannot recall that kind of implied multiplication being included at the time I learned BODMAS.

I just recall that brackets meant multiplication, and took precedence over division. 

Especially as I also recall that division had to be done first, none of this equality malarky and PEMDASLR so you can remember,

Please Excuse My Dear Aunt Sally Love Ron.

I cannot countenance that 8÷2(1+3) = 16, except as earlier, that typing the question into a browser converts the question to 8/2(1+3 )and gives the answer as 16,and to get the answer 1, you are obliged to write 8÷(2(1+3))= instead.

I would disagree with

Using PEMDAS/BODMAS/BEDMAS you have:

8÷2(1+3) =

8÷2(4) =

4(4) =

16

 If we use an outdated way of dealing with this where everything on the left side of the divide sign is divided by the right side of the divide sign we have:

8÷2(1+3) =

8÷2(4) =

8÷8 =

1

This may be outdated, but is it really? I would say that it has nothing to do with everything on the left side being divided by the right, but exactly follows  BODMAS i.e. what is in the brackets takes precedence and as you mentioned earlier the brackets are an implied multiplication.

I ought to have said "if ONE drops the brackets" rather than "if YOU drop the brackets" .The dropping of brackets idea came from a video

I watched.

For everyone who cited BODMAS or its equivalent and arrived at

8÷2(1+3) =

8÷2(4) =

Those that converted the brackets to a simple multiplication and followed the Left to Right rule must come up with the answer 16,

but is this interpretation a newer convention of the power of the brackets, or have they like politicians answered the question they wanted to answer, rather than the question they were asked?

Those that have retained the power of the brackets over both the division and left to right rule, must come up with the answer 1.

The maths teacher is this video.https://www.bing.com/videos/search?q=BODMAS&qpvt=BODMAS&view=detail&mid=2F1E0AD41CC31395E6BC2F1E0AD41CC31395E6BC&&FORM=VDRVRV
uses PEMDAS and a somewhat different convention where  multiply comes before division in the acronym but are equivalent but obey the left to right rule.  The question asked  is    4 to the power 2-2 x( 8 ÷2) + 6 .  

Notice the x sign before the brackets, which she drops after completing 8÷2, they are no longer needed because the required operation is clear, perhaps this is the new convention and brackets no longer mean retain the brackets and follow PEMDAS

Using her system of PEMDAS would seem to  solve easily(?) your 2-4÷6+7 x 5+3÷17 x 5-3÷6÷12+3 = easily(?),

 2-(4÷6)+(7 x 5)+[(3÷17) x{ 5-<(3÷6)÷12>}]+3 =

 2-(24)+(35)+[0.18 x{ 5-<(0.5)÷12>}]+3 = 

2-(24)+(35)+[0.18 x{ 5-0,42}]+3 =

 2-24+35+[0.18 x 4.58]+3 = 

2-24+35+0.82+3 =16.82 hopefully.

On further research on the problem.

It would seem that the BODMAS  convention has been changed, and brackets are no longer required after completing the operation inside, 

After dropping the brackets,you no longer have an operand to connect the rest of the equation, so I repeat that as originally written, the problem is unsolvable. 

The only way round this is that after completing the contents, the brackets are an implied simple multiplication.or the addition of another operand is required to clarify what to do with the contents of the brackets.The modern answer would seem to be 16, and the older answer 1.

To Summarize:

The answer 1 and 16 can be given and support can be produced for each of them ... the equation should not really be written like it is ... if I had to give only one answer and couldn't explain it I would give 16.  And if I could explain it I would also give 16.  But it isn't the "only" possible answer if proper explanation is given since we don't have a universal standard for dealing with it.  To make it clear it needs more parentheses/brackets. 

------------------------------------------------------------------

Using PEMDAS/BODMAS/BEDMAS you have:

8÷2(1+3) =

8÷2(4) =

4(4) =

16

------------------------------------------------------------------

If we use an outdated way of dealing with this where everything on the left side of the divide sign is divided by the right side of the divide sign we have:

8÷2(1+3) =

8÷2(4) =

8÷8 =

1

This is outdated for many reasons ... first let us look at what would happen here ... this was done in the past for some simple equations where people were trying to convey what the answer here shows ...

2+3÷3+2 =

5÷5 =

1

However this is so far away from PEMDAS/BODMAS/BEDMAS which would be

2+3÷3+2 =

2+1+2 =

3+2 =

5

So everyone who used this way of doing 8÷2(1+3) = 1 do you want to also say 2+3÷3+2 = 1 ???

And when there are multiple divisions to be done in an equation well I think you could start getting confused ... what would you do with ...

2-4÷6+7x5+3÷17x5-3÷6÷12+3 =

yea I guess it could be done ... but again wouldn't be PEMDAS/BODMAS/BEDMAS and well it isn't how it would be done these days or I think even in the past

------------------------------------------------------------------

Then we have a modified form of PEMDAS/BODMAS/BEDMAS which is used by mostly physicists ... it has to do with implied multiplication having higher precedence over explicit multiplication and division.  Parentheses can be one way for multiplication to be implied but it is not the only way.  So it is not because of the parentheses but because of the implied multiplication caused by the parentheses that would give you this.

8÷2(1+3) =

8÷2(4) =

8÷8 =

1

I would think if you gave the reasoning that PEMDAS/BODMAS/BEDMAS requires you to do parentheses (brackets) first and the 2 is part of the brackets you wouldn't get full credit for this ... if you said that implied multiplication has higher precedence over explicit multiplication and division you have a good chance to get full credit.  Some calculators have implied multiplication having higher precedence than explicit multiplication and division and will give the answer 1 to the OP equation as posted. 

So let's look at another equation and see what you would come up with SINCE parentheses (brackets) are not always necessary for implied multiplication.

A ÷ BC =

Where A = 3 , B = 2, C = 30 ... what would be your answer?

If you say 0.05 then you are being consistent with the modified form of PEMDAS/BODMAS/BEDMAS and with an answer of 1 for the OP, since in the equation BC is implied multiplication it needs to be done first.

3 ÷ 60 =

0.05

If you say 45 then you are being consistent with the "normal" PEMDAS/BODMAS/BEDMAS and with an answer of 16 for the OP.  Here division and multiplication are done in the order from left to right that they appear with no precedence for implied multiplication.

1.5 x 30 =

45

Big difference between 0.05 and 45 ... and yes I tried to make it simple to illustrate the difference between PEMDAS/BODMAS/BEDMAS and the modified form of PEMDAS/BODMAS/BEDMAS.  I will see if I can get better examples ... but you see this has nothing to do with parentheses (brackets) but with whether the multiplication is implied and not explicit.

------------------------------------------------------------------

And it's been over 36 hours since I have had any sleep so I hope I didn't mess any of that up and I hope I explained adequately.  The answer 1 and 16 can be given and support can be produced for each of them ... the equation should not really be written like it is ... if I had to give only one answer and couldn't explain it I would give 16.  And if I could explain it I would also give 16.  But it isn't the "only" possible answer if proper explanation is given since we don't have a universal standard for dealing with it.  To make it clear it needs more parentheses/brackets. 

Hello Jarls!

We have an exercise for you that seems easy only at first glance. Can you solve it and explain your answer? 

8/2=4

1+3=4

() Imply multiply

There are several versions of this mathematical conundrum to be found on the internet, this one is slightly different, has it just been regurgitated,or was this the one that started the whole thing?

www.msn.com/en-gb/news/world/mathematician-gives-answer-to-simple-sum-that-has-been-dividing-the-internet/ar-AAFfILw?li=BBoPWjQ

Effectively they are saying it is ambigously written,but was this ambiguity never the case,or arose as a result of changes in the way things are taught and wriiten now,ignorance of original meanings and ways of doing things?

If something is unique,theres only one of them.

You cant have give more effort than 100%

I like this language version of the same idea, taken from the article linked above.

"This is like a maths version of the sentence 'He fed her cat food'.

Does it mean the man gave some food to a cat? Or he fed some cat food to a woman?

"It's impossible to tell from the information we've been given."

The article says it would be clear but an obelus is missing, so I looked that up seems in mathematics that the ÷is an obelus,and there clearly is one of those, so I am not sure what she meant.

Further wiki says this

#A  "Historically, the obelus has also been used to represent subtraction in Northern Europe; such usage continued in some parts of Europe (including Norway and, until fairly recently, Denmark).[5] In Italy, and Russia the obelus is sometimes used to denote a range of values, in engineering context.

#B The ISO 80000-2 standard for mathematical notation recommends only the solidus or fraction bar for division, or the colon for ratios; it says that the obelus "should not be used" for division.

So  with reference to part #A , some in those countries ,where 8÷2(1+3) = ? becomes 8 - 2(1+3)  =? might get even more answers  to the puzzle like 0 or 24.

      with reference to part #B , the puzzle should not even contain ÷

A finger down icon is needed!

Is this a place for silly questions? Whats more it is commented as "for the wise". I am sick!

Apologies,

I used "you" again instead of "one".

The video was there, so either it wont link, or it was " lost in translation"

I hadnt meant to shoot you down in flames, the expression arose because I misread a post, by only reading the text, I stumbled into someone criticizing your analysis, when it fact it was the reverse.

Let us suppose the OP put forward same equation and asked ... what are possible solutions for this "equation" using reasoning that is used by those that need to solve these type of equations for their profession.

1) 1

2) 16

3) 1 and 16

4) Neither 1 or 16

KROW said:

 If we use an outdated way of dealing with this where everything on the left side of the divide sign is divided by the right side of the divide sign we have:

8÷2(1+3) =

8÷2(4) =

8÷8 =

1

This may be outdated, but is it really? I would say that it has nothing to do with everything on the left side being divided by the right, but exactly follows  BODMAS i.e. what is in the brackets takes precedence and as you mentioned earlier the brackets are an implied multiplication.

I didn't say dealing with this with the equation solved as is listed above was outdated I said that doing it for the reasons to have everything on the left side of the division symbol divided by what was on the right side of the division symbol was outdated. 

This equation is valid if one is doing it because an implied multiplication takes precedence over an explicit multiplication or division ... NOT BECAUSE brackets takes precedence ... what is in the brackets does take precedence but the 2 is not "in the brackets" ... and everyone who tried to do it this way wanted to put the reason forward as it is because the brackets take precedence.  But that is not what is going on ... it would be because an implied multiplication takes precedence over an explicit multiplication or division and nobody put forward that reason. It is one of the ways that this equation is done by certain professions ...

And not surprising that you would disagree with 16 being a possibility... :) ... even though numerous calculators will solve it with a 16 ... so ... so ... how about ...