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Maths Café

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andrew_langstone 18 September 2012 16:02

Another teacher in my department asked this question to her students earlier today;

18 - 1 + 1

BIDMAS says you should add before subtracting giving you;

18 - 1 + 1

= 18 - 2

= 16

But this is incorrect, the answer should be 18.

Has anyone encountered this before/have any thoughts on it? My only solution for the kids is to change it to be BIDMSA, but that doesn't sound as nice when said!


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MarkDawes 18 September 2012 17:21
Hello Andrew,

This is a common misunderstanding!  

I see BIDMAS/BODMAS/PEMDAS/etc as an aide memoire rather than a strict mnemonic or recipe to follow.

If all you know is BIDMAS(etc) then there are all sorts of calculations that will cause problems, such as 
\frac{3+5}{10} , where the addition has to be carried out before the division.

Another issue is where pupils misunderstand the word "order" in the title of "order of operations" and end up changing the order of the operations rather than just working one out in advance of another.  For example:  20 - 3 x 4, where pupils often do 3 x 4 and then subtract 20, giving -8.

As I see it, we have conventions about which parts of calculations take precedence over others.  Addition and subtraction are equally important, so these are calculated in order (in the absence of other things, such as brackets).  

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Graham1970 18 September 2012 23:38 - Last edited by Graham1970 on 18 September 2012 23:41
\frac{3+5}{10} It is intriguing to to me that at the moment I am reading taming the infinite by Ian Stewart and I am up to the part where all the ideas that folk have had about complex analysis and calculus have been been proved with mathematics. Thus giving them  a sound footing.

But to me it seems that we are now completing the circle by asking ourselves what does that piece of maths in the corner mean and who has the right answer?  A linguistics problem?

Three plus the result of five being divided by ten.  Sounds greek to me

Three plus five all over ten.  mmm a bit northern ecky thump lad to me. ( I am from the north so you pinko lefty PC liberal types who hate themselves and like to persecute others for your failings as human beings can just ...................................  fill in the blank space)
OOh fractions! Is that 3 bits of a  ten added to 5 bits of a ten?

You can express it is as language in many different ways to many different people and all will interpret differently. Where you will earn your corn is by translating their linguistic interpretation of what they see on the board back into the correct mathematics

CRY HADDOCK ! Let slip the cods of war!
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Christine_Jones 20 September 2012 13:33

BIDMAS/BODMAS, and the alternatives the Americans use, are not definitions, rules or anything official, as has been said above. The reason this doesn't work:

18 - 1 + 1

= 18 - 2

= 16

is because the rule is a guideline not written in stone. Has this been encountered before? Yes, far too many times since a lot of people get caught up in these being rules not guidelines. The TES maths forum has several long running posts on this issue where otherwise sensible people become very upset about such a simple issue.

You can usually spot when a student has used the calculator on their mobile as it doesn't follow the idea embedded in BODMAS. Of course with everyone having apps on their ipads this happens less frequently now.

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SarahW 24 September 2012 18:49 - Last edited by SarahW on 24 September 2012 19:51
When I teach this I would stress the following two points:

a) Addition does not come before subtraction, I just say to them  it is just easier to say bodmas than bomdsa so I always stress that division/multiplication are equal and add subtract are equal importance but that d/m come before and a/s  to try and stop them becoming fixated on the mnemonic. They would then  work from left to right once it is only adds or subtractions.

 b) the 1 is not a 1 it is a minus 1.
When teaching addition subtraction you teach them to work from left to right but you can also look at how they can be shuffled as long as the sign in front stays with them, hence they should practise and know that this example would be -1 +1 =0 so 18+0=18

I tend to describe them as building blocks when you are just looking at adding and subtracting, draw boxes round them including the sign and shuffle them , or use cards to reorder and show they give the same answer. This then leads onto further work with other operations.
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sallyb 24 September 2012 23:33
I always write


to emphasise that when there is only division and multiplication left, or only addition and subtraction then you must work from left to right. as in 12/3/4 = 4/4 = 1  {not 12/.75 = 16}

I also handle the fraction line problem when we discuss what the B stands for - those who think they might forget that the line in a fraction also acts as a bracket are advised to remember the B as brackets and "barline" - anything to help them remember there are other ways of bracketing numbers together without drawing brackets.
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Rob.dando 29 September 2012 18:41
Hi Andrew,

clearly -1 +1 = 0 not -2
therefore we get

18 - 0 = 18 
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Jmersh 06 November 2018 18:47

Just seen this acrticle.  Glad to see Rob.dando answer as that is how I see it.

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PhysicsChris 18 November 2018 18:38

I have older students where it is revision. I use the symbols and put them in pair going up from + and - at the bottom to brackets at the top. For the issue with division I way if in doubt put brackets around the numerator part and brackets around the denominator part. I also give pairs of brackets and contents silly names to help with ignornng the contents until needed.

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