The BODMAS mathematical rule.

[jfgw]

BODMAS as well as telling me to do the brackets first also tells me to apply the operations left to right.

Indeed. One might even mischievously add that the D comes before the M in BODMAS, regardless of being to the left of it in the example.

The mischievous one should then be reminded of the rules. BODMAS etc. are not rules, they are mnemonics. The use or misuse of a mnemonic neither dictates nor changes the rule.

Julian F. G. W.

[XFool]

Putting

=6/2*(2+1)

into excel gives the answer 9.

You think that's a recommendation?

The Windows(8) Scientific Calculator refuses to even enter it as given (probably wisely). My hand calculator gives the answer as 1.


P.S. But you haven't gone with the original expression, which I did above. Both the Windows Scientific Calculator and my calculator also gives 9 when entered as 6/2*(2+1)

[XFool]

With these values for a, b and c, what I am saying through my inequality is that 6/2(2+1) is not the same as 6/(2(2+1)).

But, as they are different expressions - with the first seeming ambiguous and the second being unambiguous - how does that help?

6/2(2+1) is 9, whereas 6/(2(2+1)) is 1.

6/(2(2+1)) is undoubtedly 1. Whereas 6/2(2+1) appears ambiguous and could arguably evaluate to either 1 or 9 depending upon how you interpret it and proceed. It can easily be disambiguated to give a result 9 by either of:

(6/2)(2+1) OR 6/2*(2+1) OR (2+1)6/2

[Alaric]

Whereas 6/2(2+1) appears ambiguous and could arguably evaluate to either 1 or 9 depending upon how you interpret it and proceed.

It is ambiguous. What is wrong with writing everything that's supposed to be the numerator to the left of the "/" and everything that's the denominator to the right?

[johnhemming]

The underlying problem is that the definition of numerator and denominator involve the y axis and not the x axis.

Hence whereas
6
___________
2(2+1)

Is 1.

6/2*(2+1) is not the same. The convention here is that 2+1 are not part of the denominator, but multiply the result of 6/2.

Numerator

the number above the line in a vulgar fraction showing how many of the parts indicated by the denominator are taken,

From a computing perspective 6/2(2+1)=6/2*(2+1)
Which only has one possible result and is not the same as 6/(2*(2+1))

[GoSeigen]

My take on this is that the ambiguity here is in the notation, not the rules of precedence.

It is clear and unambiguous that mixed multiplication and division operations are evaluated from left to right.

The question is: what does the notation in the OP mean? That notation is IMO ambiguous and the fault may be with the writer who has not made clear his intention. Others have pointed out that the symbol "/" can be interpreted as the replacement for the line separating numerator and denominator in a fraction. So, was the author representing a single fraction, or alternatively was he writing out a single line of operations and lazily failing to point this out explicitly and ambiguously omitting the multiplication symbol between the 2 and the parentheses? [The latter notation in some readers' minds may imply a further set of parentheses thus: 6/(2(2+1)), just as the multiplication is not shown with a symbol but implied ]

So the answer to me is that the author needs to be asked, or the correct interpretation inferred from the context. Both interpretations are arguable. Neither calls into question the precedence of operations or understanding of the same: the problem is in the intended meaning of the notation. If an author wishes to avoid such ambiguity he should express his thoughts more clearly.


GS

[PinkDalek]

The OP clarified his OP here viewtopic.php?p=185744#p185744

The formula is (6/2)(2+1)

The answer is nine.

Fools have been carrying on regardless.

[XFool]

From a computing perspective 6/2(2+1)=6/2*(2+1)
Which only has one possible result and is not the same as 6/(2*(2+1))

From the perspective of whose "computer"; or which "computer"?

From a Microsoft Windows 8.0, Scientific Calculator perspective: 6/2*(2+1) is undoubtedly 9, whereas 6/2(2+1) is an unparsable (indeed non allowed) expression. From my handheld calculator's perspective while 6/2*(2+1) is also 9, 6/2(2+1) is 1.

And from my late, lamented, HP RPN calculator's perspective 6/2(2+1) would also have been 1, 'cos that's how the interpreter (my brain) would have parsed it.

e.g. 6/2(2+1) == 6 Ent 2 Ent 2 Ent 1 + * / (other versions are available - some would even get you 9!)

[GoSeigen]

The OP clarified his OP here viewtopic.php?p=185744#p185744

The formula is (6/2)(2+1)

The answer is nine.

Fools have been carrying on regardless.

1. The clickbait article linked to contains items of complete nonsense. I don't see how it helps the debate. e.g.:

"Next, you need to convert the “2 (3)” into “2 x 3,” because the “Exponents/Orders” part of PEMBAS/BODMAS demands that you remove the brackets, leaving behind an order.

In this case, the order is multiplication. " [Huh???! My bold.]


2. Nowhere in that article or the linked post does it state that the original question involved the expression "(6/2)(2+1)". The OP stated that writing it that way would make the expression clearer, but he was in no way clarifying his OP by saying that, at least not in my understanding. I don't see the OP altering his original statement of the problem as involving the expression: "6/2(2+1)"=, which is what I and other posters have been discussing.


GS

[XFool]

1. The clickbait article linked to contains items of complete nonsense.

Even that article, after declaring the correct answer to be '9', goes on to declare that it could also be '1' if you were using an earlier in the 20th century interpretation of BODMAS!

As an aside, I can't even remember BODMAS in my schooldays. The first time I can ever recollect coming across it was in my 50s when I was volunteering in a local college as a classroom assistant in numeracy.

[XFool]

The OP clarified his OP here viewtopic.php?p=185744#p185744

The formula is (6/2)(2+1)

The answer is nine.

Fools have been carrying on regardless.

Yeah. The answer to (6/2)(2+1) is undoubtedly 9.

Now, clever clogs, what's the 'answer' to: 6/2(2+1)?

My hand calculator says it's 1. My Windows Scientific Calculator won't commit itself...
Actually it gives 2, as it throws out the first 2 to evaluate 6/(2+1), with a chained calculation. Of course, if you calculate intermediate results...

[richlist]

......and my brain tells me the answer is 9

Do we really have to revert to name calling ?

There are two different opinions......

[XFool]

......and my brain tells me the answer is 9

Do we really have to revert to name calling ?

There are two different opinions......

Exactly.

"Is this a drawing of a cube going into the page or out of the page?"

[PinkDalek]

Now, clever clogs, what's the 'answer' to: 6/2(2+1)?

Start here viewtopic.php?f=9&t=15165.

[XFool]

Now, clever clogs, what's the 'answer' to: 6/2(2+1)?

Start here viewtopic.php?f=9&t=15165.

No.

Start here: viewtopic.php?f=9&t=15165#p185788

[XFool]

My hand calculator says it's 1. My Windows Scientific Calculator won't commit itself...
Actually it gives 2, as it throws out the first 2 to evaluate 6/(2+1), with a chained calculation. Of course, if you calculate intermediate results..

Actually, if you calculate intermediate results left to right, the Windows Scientific Calculator calculates 6/2(2+1) as 3, 'cos it throws away the 6/2 = 3 to start again with (2+1) = 3.

So there we have the final answer. Using the Windows Scientific Calculator and going left to right 6/2(2+1) is definitely either 2 OR 3.

Windows, huh!

[XFool]

BTW.

Anyone know why mirrors reverse left to right but not top to bottom?

[PinkDalek]

… 2. Nowhere in that article or the linked post does it state that the original question involved the expression "(6/2)(2+1)". The OP stated that writing it that way would make the expression clearer, but he was in no way clarifying his OP by saying that, at least not in my understanding. I don't see the OP altering his original statement of the problem as involving the expression: "6/2(2+1)"=, which is what I and other posters have been discussing.

Yes, you are probably correct but I didn't bother reading the referenced article. I took To make it clearer, the first part should be written using brackets: (6 / 2). as a clarification/amendment of/to the OP, rather than a correction of whatever had been written in the article, incorrectly from my end it seems.

Supplementary question.

Does anyone know how an inanimate object, such as clogs, can be deemed to be clever or not? An answer would appear to be here:

https://www.theanswerbank.co.uk/Phrases ... 90907.html

Fellow > Boots > Clogs.

[GoSeigen]

… 2. Nowhere in that article or the linked post does it state that the original question involved the expression "(6/2)(2+1)". The OP stated that writing it that way would make the expression clearer, but he was in no way clarifying his OP by saying that, at least not in my understanding. I don't see the OP altering his original statement of the problem as involving the expression: "6/2(2+1)"=, which is what I and other posters have been discussing.

Yes, you are probably correct but I didn't bother reading the referenced article. I took To make it clearer, the first part should be written using brackets: (6 / 2). as a clarification/amendment of/to the OP, rather than a correction of whatever had been written in the article, incorrectly from my end it seems.

So, at the risk of repeating myself, the use of notation in the equation 6 / 2(2+1) leaves an ambiguity based on whether one interprets an extra set of parentheses as being implied ["6/(2(2+1))"] by the way the equation was written: whether because of the omitted multiplication sign or by assuming a single fraction is being notated.

GS

[swill453]

So, at the risk of repeating myself, the use of notation in the equation 6 / 2(2+1) leaves an ambiguity based on whether one interprets an extra set of parentheses as being implied ["6/(2(2+1))"] by the way the equation was written: whether because of the omitted multiplication sign or by assuming a single fraction is being notated.

The computer scientist in me is saying that spaces aren't significant, other than as separators when necessary (and obviously not necessary in this case).

So 6 / 2(2+1) is the same as 6/2(2+1) and 6/2 * (2+1).

If BODMAS didn't mean D before M and A before S, there wouldn't be much point to it.

Scott.