The BODMAS mathematical rule.

[stevensfo]

Can a Mathematician put me out of my misery? I've been following a discussion on a Facebook group about the BODMAS rules, i.e. the order in which mathematical functions should be performed: Brackets..Order...Division etc.

The simple sum causing confusion is:

6 / 2(2+1) = ? Obviously the / is the symbol for division.

The answer is either 1 or 9.

Those who say it is 9, argue that, according to the BODMAS rule, you perform the (2+1), then 6 / 2 , so end up with 3 x 3 = 9.

However, instinctively I'd say that the 2(2+1) counts as one value, so you end up with 6 / 6 =1.

I'd also say that if the answer is 9, then surely the first part should be (6 / 2) to make it clear.

Steve.... feeling like a 12 year old staring down at his homework!

Moderator Message:
This question clearly does not have a single direct answer (or at least not one upon which everyone agrees) so I'm moving it to The Snug, leaving a link, so it can be pondered on ad infinitum. - Chris

[Dod101]

The answer is 1. the division is the equivalent of 6/2* (2+1). The brackets are there because that is one term and equals 3 which multiply by 2 gives 6. So 6/6 = 1. I have been taught then since I was about 5!

Anyone who says anything else is I am sorry to say talking nonsense. BODMAS =Brackets, Orders, Division, Multiplication, Addition and Subtraction. I have not strictly followed it because I never have but you could have done 6/2*(2+1) =6/2*3=3/3 =1 in strict accord with the BODMAS rules.

You do not need to be a mathematician to know that, just a reasonably competent school boy or girl.

Dod

[csearle]

Well my instinct is also an answer of 1.

I think maybe the problem comes from the way it is written down as a one-liner. If the "6 / 2(2+1)" was written with a normal division line separating numerator from denominator then the position of the (2+1) term would clearly show whether it was in the numerator or the denominator.

C.

[stevensfo]

You do not need to be a mathematician to know that, just a reasonably competent school boy or girl.

Thanks for confirming what I thought and that I'm not going mad.

The sad truth is, this was on a Facebook group for teacher training.

The sadder truth is, most of them argued that the answer is 9!

Steve

[modellingman]

The answer is 9.

a/bc is not equal to a/(bc), which is contrary to what the proponents of an answer of 1 require to support their argument.

Mathematically, division and multiplication have the same priority as operands because a/b is simply a multiplied by 1/b, the multiplicative inverse of b. By convention, ties are broken between operands of equal priority by applying precedence in a left to right order, so a/bc is equal to (a/b)c.Hence the answer is 9.

The same faulty logic that leads to an answer of 1 would require 6-3+(2+1) to be 0 rather than 6.

[nmdhqbc]

The answer is 9.

Fair enough answer.

[mike]

Putting

=6/2*(2+1)

into excel gives the answer 9.

[stevensfo]

Well, at least we agree that the average answer is 5. There, problem solved!

Steve

[Dod101]

If modellingman is correct then I have been wrong for the last 70 or so years. It has done me no harm.

Seriously though, he is now changing the rules. I am sure we all assumed that the / was intended to be the division line so that 6/2(2+1) was simply another way of writing 6 as the numerator and 2(2+1) as the denominator. He is now saying that 6/2 is one term which equals 3 and (2+1) is another which equals 3. Obviously the two terms together equal 9. So I do not think there is a 'correct' answer. it depends what the / is intended to mean.

Dod

[stevensfo]

Just found the original website:

http://powerfulmind.co/math-equation/?f ... ljWeKu7rRA

Yes, they argue that the answer is 9, but to be honest, I find it akin to bad punctuation. To make it clearer, the first part should be written using brackets: (6 / 2).

Steve

[eepee]

I fail to understand the a/(bc) given above.

Surely with the bracket worked out the line reads:-

6 / 2 x 3 ????

Which with multiplication preference gives the answer as 1 ????

Regards,
ep

[kempiejon]

6 / 2(2+1) = ? Obviously the / is the symbol for division.
This is school kid stuff isn't it?
so using the other division symbol (keyboard hack alt+0247)
6 ÷ 2(2+1) = ?
6 ÷ 2 x (3) = ?
3 x 3 = 9

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

[eepee]

There is a 'nightmare' explanation in this page:-
https://en.wikipedia.org/wiki/Order_of_operations

See the paragraph headed:-
Mixed division and multiplication

Regards,
ep

[UncleEbenezer]

6 / 2(2+1) = ? Obviously the / is the symbol for division.
This is school kid stuff isn't it?

Yep. Though I'm sure many (most?) schoolkids these days deal with a lot more of that in the context of their computers: for example, logical AND/OR/NOT, exponentiation, shift/rotation, negation, etc. Not to mention nonstandard rules introduced by particular packages. Easy rule there (now that the era of every-byte-counts is long past): if there's potential for confusion, use brackets.

so using the other division symbol (keyboard hack alt+0247)
6 ÷ 2(2+1) = ?
6 ÷ 2 x (3) = ?
3 x 3 = 9

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.

[modellingman]

a/bc is not equal to a/(bc)

I fail to understand the a/(bc) given above.

The inequality is true for all non-zero real numbers a, b and c, so it is true for any specific set of values. Therefore

let a represent the initial 6 of "6/2(2+1)"
let b represent the 2 immediately to the right of the "/" (division) symbol
let c represent the expression "(2+1)" (which obviously evaluates to 3)

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)).

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

Thanks for the Wikipedia link. Interesting to know that there is PEMDAS, BEDMAS and BIDMAS as well as our old friend BODMAS and that the editors of a few obscure scientific journals have decided to re-write the conventions of mathematical notation to give an implied multiplication operator a higher precedence than division or explicit multiplication operators.

If modellingman is correct then I have been wrong for the last 70 or so years. It has done me no harm.

Seriously though, he is now changing the rules. I am sure we all assumed that the / was intended to be the division line so that 6/2(2+1) was simply another way of writing 6 as the numerator and 2(2+1) as the denominator. He is now saying that 6/2 is one term which equals 3 and (2+1) is another which equals 3. Obviously the two terms together equal 9. So I do not think there is a 'correct' answer. it depends what the / is intended to mean.

Dod

The whole point about teaching and using the conventions of mathematical notation is to avoid the need to make any assumptions about the intended meaning of an expression.

It is also part of the conventions that where an operand is omitted between two numerical values, there is an implied multiplication operator. If the expression had instead been written equivalently in fuller form as 6/2x(2+1) would you still argue that the denominator to the division operation is 2x(2+1)?

If the answer is yes, then this flies in the face of convention by applying a right-to-left (rather than left-to-right) prioritisation of the multiplication and division operations. If it is no then that says that two mathematical expressions, equivalent except that one is using an implied multiplication sign and the other an explicit sign, can evalute to completely different values - which seems nonsensical to me.

Someone else as well as the editors of a few obscure scientific journals also seems to be changing the rules (ie the conventions of mathematical notation), but its not me.

[richlist]

Now come on folks......the answer is 9......we all know it's 9.

This sounds to me a bit like... [Deleted.]

Moderator Message:
Sorry but whilst I sympathize with your now-deleted sentiment, DAK is really not the right place to talk about the politics of leaving the EU. - Chris

[Dod101]

It is also part of the conventions that where an operand is omitted between two numerical values, there is an implied multiplication operator. If the expression had instead been written equivalently in fuller form as 6/2x(2+1) would you still argue that the denominator to the division operation is 2x(2+1)?.

No of course not. That is perfectly clear. If the question were written out by hand it would also I suppose be perfectly clear but when typing the use of / is ambiguous and therein lies the disagreement, because I assumed as I think I said, that it applied to everything after it (and it often could) but you claim it only applies to the first term after it.

Dod

[XFool]

All just goes to show that Reverse Polish Notation is much better.

[k333]

I can't remember seeing this sort of ambiguity in a mathematics course or a computer program. Writing x=a/bc is just asking for trouble!

- K

[XFool]

Can a Mathematician put me out of my misery? I've been following a discussion on a Facebook group about the BODMAS rules, i.e. the order in which mathematical functions should be performed: Brackets..Order...Division etc.

The simple sum causing confusion is:

6 / 2(2+1) = ? Obviously the / is the symbol for division.

The answer is either 1 or 9.

Those who say it is 9, argue that, according to the BODMAS rule, you perform the (2+1), then 6 / 2 , so end up with 3 x 3 = 9.

However, instinctively I'd say that the 2(2+1) counts as one value, so you end up with 6 / 6 =1.

I'd also say that if the answer is 9, then surely the first part should be (6 / 2) to make it clear.

Steve.... feeling like a 12 year old staring down at his homework!

I'd say, in the circumstances, it's a badly formed/printed expression. Why would anyone not remove all doubt by the simple expedience of using additional parentheses? Or, more simply, reformatting the expression on the page as:

(2+1) 6/2