# BIDMSA not BIDMAS

Discussion in 'Mathematics' started by david_douis, Sep 21, 2020.

1. ### david_douisNew commenter

Join my campaign and teach order of operations using BIDMSA and not BIDMAS.
a simple change for a lot of gain.

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2. ### gainlyStar commenter

BIDMSA does work better, the only reason I can think why it isn't used is that it doesn't make a pronounceable word.

3. ### maths126New commenter

You're quite right - it does work better. A compelling argument!

4. ### frustumStar commenter

Good idea. We've already changed from BODMAS to BIDMAS, so change is possible!
I teach adults and usually make the point that BIMDSA=BIDMAS, it's just harder to say, but I hadn't noticed that BIDMSA just works.

The biggest problem is that very many adults remember BIDMAS without remembering what else their maths teacher said about it. That included my daughter's year 6 teacher - I had to send a very carefully worded letter the day after my daughter had an argument with her about it. The teacher did take it on board - she told my daughter she must have been taught wrongly at school, although I have more faith in maths teachers, and suspect she just didn't remember fully.

5. ### briancantOccasional commenter

Given that any subtraction is just the addition of a negative number and division is just multiplication by the reciprocal of a number, aren't A and S the same importance, as are M and D. So there is no point in swapping their order to create an unpronounceable word.

7. ### frustumStar commenter

I teach adults; they mostly remember BIDMAS, but they do not remember that D=M and A=S.

I preferred teaching PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. This listing reminds pupils the ranks of the operations, but it is important to add that where there are operations of the same rank, then they are addressed from left to right:
1. Parentheses
2. Exponents
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)
So, when faced with a series of operations of the same rank, pupils just operate from left to right. For instance, 15 ÷ 3 × 4 is not 15 ÷ (3 × 4) = 15 ÷ 12, but is rather (15 ÷ 3) × 4 = 5 × 4, because, going from left to right, you get to the division sign first.

Last edited: Oct 8, 2020
9. ### martinyip65New commenter

Sorry but I do not agree that subtraction is the result of addition of a negative number.
Consider taking 3 apples away from 10 apples...in what way can you consider the 3 apples to be given a negative status?
If you were to add temperatures together where one of them was negative, then YES you are technically adding a negative which results in subtraction, but to equate this idea to the former is to misunderstand the difference between negativity and subtraction.

When I teach 'BIDMAS', I do emphasise the interchangeable order of D and M and of A and S.
It is a guide but not an exact strict order.
The lack of understanding of D and M being inverse operations (and A and S) and therefore equal 'status' in 'BIDMAS' is something that needs promoting. I'm not saying it is easy but sticking to one version of BIDMAS (et al) or another is to continue to bypass the problem.

andyfrost16 likes this.
10. ### david_douisNew commenter

I was not talking about apples but since you mentioned it... "3 apples to be given" is exactly what gives a negative status to that action. "+a" you put apples in the basket, "-a" you remove apples from the basket. The two opposite actions that a mathematical group needs, as well as a single binary operation "+" to do a succession of actions. I have 10 apples in my basket, then I give 3 away, then I put 4 back in...
10+(-3)+(+4)....
The rest is a matter of interpretation, but not a matter of opinion.
To be clear, I obviously do not mention group theory to my students but this was aim to us, mathematicians who studied at degree level and understand that the sign "-" means "opposite".

To come back to my original issue, I agree that none of these acronyms are the panacea, and if teachers are successful in teaching a version with a "but" attached, then fair enough.
Despite the fact that it is difficult to pronounce, I am still convinced that BIDMSA is the only version that does not require a "but if ", it is the strict order .... May be I am wrong, but so far I have not seen any evidence to contradict it.

11. ### andyfrost16New commenter

So if we take a, b to be natural numbers, where 0 < a < b. Then for (b-a) does it still make sense to think of this as b + (-a) given that (-a) is not a natural number?

12. ### briancantOccasional commenter

Yes, you can add any sort of number to a natural number.

13. ### andyfrost16New commenter

If
If the universal set is the natural numbers, then you are confined to using elements within the natural numbers.

14. ### briancantOccasional commenter

The Natural numbers aren't closed under subtraction or division so it makes no sense when teaching BIDMAS to confine yourself to this set of numbers.