We’d like to remind Forumites to please avoid political debate on the Forum.
This is to keep it a safe and useful space for MoneySaving discussions. Threads that are – or become – political in nature may be removed in line with the Forum’s rules. Thank you for your understanding.
📨 Have you signed up to the Forum's new Email Digest yet? Get a selection of trending threads sent straight to your inbox daily, weekly or monthly!
The Forum now has a brand new text editor, adding a bunch of handy features to use when creating posts. Read more in our how-to guide
GreenPencils, BluePencils, RedPencils and BODMAS
pate-ci0
Posts: 3,640 Forumite
Hi folks,
I don't want to bump this comp anymore Win Staedtler prize FB L/C, but there seems to be an epidemic of musunderstanding regarding arithmetical and mathematical rules. I feel equally amazed and terrified that so many people entering this competition have so little knowledge of simple arithmetic and indeed have a fixed but erroneous belief in a method which is completely WRONG.
There is only ONE set of mathematical rules to do with the precedence of applying operations within arithmetic calculations, and they are applied at all times. Some people call this BODMAS which stands for Brackets, Order (or pOwers), Division, Multiplication, Addition, Subtraction. If there are brackets, work out what is in the brackets first. If no brackets, ignore that and work out any numbers which have got powers eg 3 squared. If none of them, work out any Divisions and/or Multiplications and lastly do the Additions and Subtractions. Any ambiguities are resolved by working from left to right in the equation.
In the competition, you are presented with 3 formulae, using Green, Blue and Red pencils to represent numbers. The first is:
GreenPencil + GreenPencil = 10
so GreenPencil = 5
Next:
GreenPencil * BluePencil + BluePencil = 12
Whichever way you do this, 5*BluePencil + BluePencil = 12 gives you BluePencil = 2
Lastly:
GreenPencil * BluePencil - RedPencil * GreenPencil = GreenPencil
This is the one that is confusing folk who believe that if there are no brackets, BODMAS does not apply and you just work from left to right one at a time. WRONG! BODMAS always applies.
so:
5*2 - RedPencil*5 = 5
10 - 5*RedPencil = 5 then subtract 5 from both sides
5 - 5*RedPencil = 0 then add 5*RedPencil to both sides
5 = 5*RedPencil and lastly divide both sides by 5
1 = RedPencil
The INCORRECT way that many folk (and their KIDS, which is the terrifying part!) think is correct is this:
GreenPencil * BluePencil - RedPencil * GreenPencil = GreenPencil
5 * 2 - RedPencil * 5 = 5
10 - RedPencil * 5 = 5
Now what they want to do is subtract RedPencil from 10, but you don't know what RedPencil is, before multiplying the result by 5. So you either guess what RedPencil is or work your way up from one until you get the right answer (a REAL problem if it's a fraction!) or what you have to do is effectively multiply out the 'bracket' even though there is none:
50 - 5*RedPencil = 5 then add 5*RedPencil to both sides
50 = 5 + 5*RedPencil and subtract 5 from both sides
45 = 5*RedPencil and then divide both sides by 5
9 = RedPencil
to get the WRONG answer.
The ONLY way to get RedPencil equal to 9 is to USE brackets eg:
((GreenPencil * BluePencil) - RedPencil) * GreenPencil = GreenPencil
ie ((5*2) - RedPencil) * 5 = 5
gives (10 -RedPencil) * 5 = 5
Divide both sides by 5
gives 10 - RedPencil = 1
Add RedPencil to both sides
gives 10 - RedPencil + RedPencil = 1 + RedPencil
ie 10 = 1 + RedPencil
so RedPencil = 9
Sorry to belabour the point but this is the very basis of how we understand numbers!
Any comments?
I don't want to bump this comp anymore Win Staedtler prize FB L/C, but there seems to be an epidemic of musunderstanding regarding arithmetical and mathematical rules. I feel equally amazed and terrified that so many people entering this competition have so little knowledge of simple arithmetic and indeed have a fixed but erroneous belief in a method which is completely WRONG.
There is only ONE set of mathematical rules to do with the precedence of applying operations within arithmetic calculations, and they are applied at all times. Some people call this BODMAS which stands for Brackets, Order (or pOwers), Division, Multiplication, Addition, Subtraction. If there are brackets, work out what is in the brackets first. If no brackets, ignore that and work out any numbers which have got powers eg 3 squared. If none of them, work out any Divisions and/or Multiplications and lastly do the Additions and Subtractions. Any ambiguities are resolved by working from left to right in the equation.
In the competition, you are presented with 3 formulae, using Green, Blue and Red pencils to represent numbers. The first is:
GreenPencil + GreenPencil = 10
so GreenPencil = 5
Next:
GreenPencil * BluePencil + BluePencil = 12
Whichever way you do this, 5*BluePencil + BluePencil = 12 gives you BluePencil = 2
Lastly:
GreenPencil * BluePencil - RedPencil * GreenPencil = GreenPencil
This is the one that is confusing folk who believe that if there are no brackets, BODMAS does not apply and you just work from left to right one at a time. WRONG! BODMAS always applies.
so:
5*2 - RedPencil*5 = 5
10 - 5*RedPencil = 5 then subtract 5 from both sides
5 - 5*RedPencil = 0 then add 5*RedPencil to both sides
5 = 5*RedPencil and lastly divide both sides by 5
1 = RedPencil
The INCORRECT way that many folk (and their KIDS, which is the terrifying part!) think is correct is this:
GreenPencil * BluePencil - RedPencil * GreenPencil = GreenPencil
5 * 2 - RedPencil * 5 = 5
10 - RedPencil * 5 = 5
Now what they want to do is subtract RedPencil from 10, but you don't know what RedPencil is, before multiplying the result by 5. So you either guess what RedPencil is or work your way up from one until you get the right answer (a REAL problem if it's a fraction!) or what you have to do is effectively multiply out the 'bracket' even though there is none:
50 - 5*RedPencil = 5 then add 5*RedPencil to both sides
50 = 5 + 5*RedPencil and subtract 5 from both sides
45 = 5*RedPencil and then divide both sides by 5
9 = RedPencil
to get the WRONG answer.
The ONLY way to get RedPencil equal to 9 is to USE brackets eg:
((GreenPencil * BluePencil) - RedPencil) * GreenPencil = GreenPencil
ie ((5*2) - RedPencil) * 5 = 5
gives (10 -RedPencil) * 5 = 5
Divide both sides by 5
gives 10 - RedPencil = 1
Add RedPencil to both sides
gives 10 - RedPencil + RedPencil = 1 + RedPencil
ie 10 = 1 + RedPencil
so RedPencil = 9
Sorry to belabour the point but this is the very basis of how we understand numbers!
Any comments?
0
Comments
-
-
OneYorkshireLass wrote: »My brain hurts.
That's why pencils have erasers on the end....0 -
I thought it was BIDMAS these daysYour = belongs to you
You're = you are0 -
Possibly. Still just an acronym, Indices instead of Order/pOwer, a rose by any other name.....
Reminds me, need to get may Bidmas Tree soon...0 -
In a strange way this is kind of what is happening to the world today. Call the truth fake news and some people will believe the truth is fake.
Perhaps this shows we are teaching maths so poorly that people do not understand the basic principles anymore. I actually never really liked BODMAS as it implies addition takes priority over subtraction.
Thank you for taking the time to type out the answer in detail. I doubt it will help but i feel better.Rational judgement, now, at this very moment.
Virtuous action, now, at this very moment.
(Wisdom, Courage, Self-control, Justice)
Willing acceptance - now, at this very moment - of what you can’t change0 -
I just hope Staedtler know how to do it - some people hedged their bets by giving both answers and explanations as to why, which I initially thought was a bit daft, but maybe not if the promoters did it wrong!2018 - £562 2019 - £130 2020 - £276 2021 - £106 2022 - £1400
-
No you ca't say both answers. There is only one correct answer.Rational judgement, now, at this very moment.
Virtuous action, now, at this very moment.
(Wisdom, Courage, Self-control, Justice)
Willing acceptance - now, at this very moment - of what you can’t change0 -
You lost me very early on- never liked Maths and they only gave the brightest that type of question when I was in school.
But at least I know to do the brackets first- so thanks for that.
0 -
I agree with pate-ci0
GreenPencil * BluePencil - RedPencil * GreenPencil = GreenPencil
The "elegant" way to solve this is to divide throughout by GreenPencil to get
BluePencil - RedPencil = 1 ...... ie. RedPencil = BluePencil - 1 ...... ie. RedPencil = 1
BTW, Spreadsheets such as Excel automatically use BIDMAS
0 -
pate-ci0 you will be pleased to know that a winner has been drawn and the answer is confirmed as 1.0
This discussion has been closed.
Confirm your email address to Create Threads and Reply
Categories
- All Categories
- 354.5K Banking & Borrowing
- 254.4K Reduce Debt & Boost Income
- 455.5K Spending & Discounts
- 247.4K Work, Benefits & Business
- 604.2K Mortgages, Homes & Bills
- 178.5K Life & Family
- 261.7K Travel & Transport
- 1.5M Hobbies & Leisure
- 16.1K Discuss & Feedback
- 37.7K Read-Only Boards