The BODMAS mathematical rule.

[Dod101]

There are not two opinions; there are two answers depending on how you interpret the /, as I said some posts ago. Strictly speaking, and the way the question was originally composed, the answer is of course 9, but I (wrongly it would seem) assumed that the / was assigning everything after it as the denominator, in which case the answer is 1.

I had never before this thread heard of BODMAS, we were simply taught how to do it at school. And I would not call this mathematics; it is plain simple arithmetic, a very modest branch of mathematics.

Dod

[XFool]

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.

So perhaps there isn't... Because, AFAIK, BODMAS really only means 'D AND M' before 'A AND S', not D before M or A before S.

https://en.wikipedia.org/wiki/Order_of_ ... Definition

https://en.wikipedia.org/wiki/Order_of_ ... iplication

https://en.wikipedia.org/wiki/Order_of_ ... #Mnemonics

"These mnemonics may be misleading when written this way. For example, misinterpreting any of the above rules to mean "addition first, subtraction afterward" would incorrectly evaluate the expression

10 − 3 + 2.

The correct value is 9 (and not 5, as if the addition would be carried out first and the result used with the subtraction afterwards)."

etc.

[swill453]

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.

So perhaps there isn't... Because, AFAIK, BODMAS really only means 'D AND M' before 'A AND S', not D before M or A before S.

You're right of course, I take back my last sentence. I stand by the first part of the post though.

Scott.

[XFool]

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).
...
I stand by the first part of the post though.

Yes, a computer would ignore all the spaces. But a human likely wouldn't. To a human (at least to this one), as originally written, the second 2 is strongly associated with the term in parenthesis: 2(2+1). And we all know 2(x+y) = 2x+2y which, readily evaluates if x and y are numbers, say to Z. So we see 6/Z where, in this case Z is 6, so 6/6 = 1.

Now, if anyone has time on their hands and is feeling bored, they could manually subject 6/2(2+1) to Dijkstra's Shunting-Yard algorithm and then the same again to a Recursive Descent Processor and see if they give the same answer and report back!

- https://en.wikipedia.org/wiki/Shunting-yard_algorithm
- http://blog.roboblob.com/2014/12/16/rec ... l-numbers/

Me with my past history with HP calculators - not to mention FORTH - would, of course, favour the former.

[GoSeigen]

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

Scott.

It doesn't mean that, and there is a point. Division and multiplication are evaluated with equal priority, working from left to right. Same applies to addition and multiplication. In other words BODMAS has the same meaning as BOMDSA etc -- it's just more pronouncable/memorable as "BODMAS".

The point is that by understanding and following the convention, everyone knows the meaning of an equation.


Having thought a bit more about this, I must concede that if one believes the answer is ambiguous it is only because of (arguably reasonable) assumptions, e.g. the equation was formerly typeset but has been put on one line without modification. If its purpose and context was merely to illustrate BODMAS then it looks to me as if it has been contrived to look ambiguous in order to make the point. If the context is machine OCR of a typeset page then my and others' earlier points about multiple interpretation stand.

In most circumstances such expressions should be taken at face value, i.e. the OP's expression evaluating to 9 and not 1.

GS

[jfgw]

BTW.

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

Eh?

Write something on a piece of paper. Stand in front of a mirror while holding the paper, words facing you, with your left hand holding the middle of the left side and your right hand holding the middle of the right side. Flip the paper over using just your fingers and look at the paper in the mirror. You will see that mirrors do not reverse left to right at all, they reverse top to bottom.

Julian F. G. W.

[GoSeigen]

BTW.

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

:twisted:

Eh?

Write something on a piece of paper. Stand in front of a mirror while holding the paper, words facing you, with your left hand holding the middle of the left side and your right hand holding the middle of the right side. Flip the paper over using just your fingers and look at the paper in the mirror. You will see that mirrors do not reverse left to right at all, they reverse top to bottom.

Julian F. G. W.

Is it a flat mirror or a spherical one?

GS

[UncleEbenezer]

"These mnemonics may be misleading when written this way. For example, misinterpreting any of the above rules to mean "addition first, subtraction afterward" would incorrectly evaluate the expression

10 − 3 + 2.

The correct value is 9 (and not 5, as if the addition would be carried out first and the result used with the subtraction afterwards)."

etc.

That's why it was mischievous[1] to point that out up the thread.

The operative rule here is Order. The O in BODMAS. Comes before either D or M, so has precedence.

[1] (mischievous? Wot, me?)

[swill453]

The operative rule here is Order. The O in BODMAS. Comes before either D or M, so has precedence.

The O in BODMAS stands for Orders, numbers involving powers or square roots. It doesn't have anything to do with the order that the expression is written.

Scott.

[XFool]

BTW.

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

Eh?

Write something on a piece of paper. Stand in front of a mirror while holding the paper, words facing you, with your left hand holding the middle of the left side and your right hand holding the middle of the right side. Flip the paper over using just your fingers and look at the paper in the mirror. You will see that mirrors do not reverse left to right at all, they reverse top to bottom..

Is that with one foot off the ground or both feet off the ground at the same time?

[XFool]

BTW.

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

Eh?

Write something on a piece of paper. Stand in front of a mirror while holding the paper, words facing you, with your left hand holding the middle of the left side and your right hand holding the middle of the right side. Flip the paper over using just your fingers and look at the paper in the mirror. You will see that mirrors do not reverse left to right at all, they reverse top to bottom.

IF you are being serious... I think you MEAN "mirrors don't reverse left to right, they reverse front to back" - NOT "top to bottom", which is err confusing.

[jfgw]

IF you are being serious... I think you MEAN "mirrors don't reverse left to right, they reverse front to back" - NOT "top to bottom", which is err confusing.

I was being as serious as I assumed you were (i.e., not very).

Julian F. G. W.

[stewamax]

The O in BODMAS stands for Orders, numbers involving powers or square roots. It doesn't have anything to do with the order that the expression is written.

When I was at school BODMAS was taught as Brackets OF Division .... etc, in the sense of "half OF 100".
Not saying it was correct...

And if anyone wants to see the commutative, associative and distributive laws working hard, Google for continued fractions - the things of which the Beautuful Mind mathematician Ramanujan was a master.

[XFool]

And if anyone wants to see the commutative, associative and distributive laws working hard, Google for continued fractions - the things of which the Beautuful Mind mathematician Ramanujan was a master.

Err... Beautiful Mind wasn't about Ramanujan, surely? It was about John Nash.

https://en.wikipedia.org/wiki/A_Beautiful_Mind_(film)

The more recent Ramanujan film was The Man Who Knew Infinity.

https://en.wikipedia.org/wiki/The_Man_W ... nity_(film)

[stewamax]

Quite right!! And I have the book as well. Oh shame on me.

[swill453]

When I was at school BODMAS was taught as Brackets OF Division .... etc, in the sense of "half OF 100".
Not saying it was correct...

We were always taught that "of" in an expression is the same as multiplication.

half of 100 = 0.5 x 100

So that being the case, O meaning Of would be superfluous.

Scott.

[johnhemming]

The operative rule here is Order. The O in BODMAS. Comes before either D or M, so has precedence.

The O in BODMAS stands for Orders, numbers involving powers or square roots. It doesn't have anything to do with the order that the expression is written.

Scott.

Which is why my daughter is taught bidmas (index indices)

[DrFfybes]

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.

Yes and no.

The written example quoted is sloppy because it misleads with inappropriate spacing. the space either side of the Division symbol implies that the formula to the right is intended to be the complete denominator

Therefore as written in this thread, it reads like 6 / (2(2+1)) which give the answer of 1.

However, the original question is 6 ÷ 2 (1+2) with a space before the brackets,which does give the answer of 9, although they then change the spacing in the video.

Try reversing/inverting the formula.....

(1+2)2 / 6 = ??

Is that 1 or 1/9?

Paul

[XFool]

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.

Eh?

It would undoubtedly be faulty logic to conclude 6-3+(2+1) equals 0 rather than 6. But why would anyone conclude that? It would only be 6 if it was written such as: 6-(3+(2+1))

In this case these two examples are impossible to confuse - no faulty logic anywhere! Not so with the OP.

[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.

Eh?

It would undoubtedly be faulty logic to conclude 6-3+(2+1) equals 0 rather than 6. But why would anyone conclude that? It would only be 6 if it was written such as: 6-(3+(2+1))

In this case these two examples are impossible to confuse - no faulty logic anywhere! Not so with the OP.

OK, I will try and clarify what I meant in the final sentence of the post you quoted.

The faulty logic in the original expression ("6/2(2+1)") was to give precedence to the (implied) multiplication operator over the division operator. Multiplication and division have equal precedence and cases of equal operator precedence are resolved in mathematical expressions by applying operators in a left-to-right order. The faulty logic applies them incorrectly in a right-to-left order yielding an incorrect result of 1. Applying them in a left-to-right order yields a correct result of 9.

In the expression "6-3+(2+1)" the sub-expression in the brackets is evaluated first to yield 3 (just as in "6/2(2+1)") so the expression is equivalent to "6-3+3". The two operators of addition and subtraction have equal precedence. Applying them in a right-to-left order (the "faulty logic" way) yields a result of zero whereas applying them in the (correct) left-to-right order yields the correct result of 6.

That's all I meant by "same faulty logic that leads to an answer of 1 would require 6-3+(2+1) to be 0 rather than 6." Both incorrect results flow from the incorrect use of right-to-left ordering of operations of equal precedence.