Maths problem

[Padge]

11 minutes ago, marklaspalmas said:

 

So is your 1 to 6 order wrong? Shouldn't it be 1, 2 3=, 3=, 5=, 5=

My numbering is the error, should have been:

1. Brackets 
2. Exponents  
3. Multiplication
3. Division
4. Addition
4. Subtraction.

The order of the listing is to make the acronym used BEMDAS easier to remember.

Where equal weighting applies left to right is the convention.

 

 

[glossop saint]

46 minutes ago, marklaspalmas said:

 

So is your 1 to 6 order wrong? Shouldn't it be 1, 2 3=, 3=, 5=, 5=

Yes. Hence why BODMAS and BIDMAS also work. Division and multiplication are basically the same thing. Same as addition and subtraction (subtraction is addition of a negative number).

But always handy to have something to follow.

[unapologetic pedant]

1 hour ago, Padge said:

No it would be 2a -(2a*2a)+2a Or 8-(8*8)+8 the first operator is * thus it becomes 8-64+8  next 8-64 = -56 giving -56+8 which = -48.

Answer is -48

Think you are focussed on calculator function. I was referring to the role of brackets in algebraic equations where a(b - c) would not be written as b - c × a. 

When I first used a scientific calculator at school, I initially blundered when multiplying the sum of two numbers. The solution of course is to press the equals key after the addition/subtraction. 

[Padge]

4 minutes ago, unapologetic pedant said:

Think you are focussed on calculator function. I was referring to the role of brackets in algebraic equations where a(b - c) would not be written as b - c × a. 

When I first used a scientific calculator at school, I initially blundered when multiplying the sum of two numbers. The solution of course is to press the equals key after the addition/subtraction. 

You are answering the wrong question.

On a true scientific calculator the calculation is held in a stack and only when the = key is pressed does it perform the calculation using operational precedence of BOMDAS. The operational precedence has nothing to do with the calculator, it is a mathematical convention that is used by the programmer of the calculator.

Bill Gates' original Windows calculator would give the wrong answer as it didn't stack the operations but calculated each entry.

The answer is -48.

 

[unapologetic pedant]

54 minutes ago, Padge said:

You are answering the wrong question.

On a true scientific calculator the calculation is held in a stack and only when the = key is pressed does it perform the calculation using operational precedence of BOMDAS. The operational precedence has nothing to do with the calculator, it is a mathematical convention that is used by the programmer of the calculator.

Bill Gates' original Windows calculator would give the wrong answer as it didn't stack the operations but calculated each entry.

The answer is -48.

The OP had no brackets, real or implied.

Who determines the conventions of operational precedence? 

Algebraic convention would rearrange 8 - 8 × 8 + 8 to 8(8 -  + 8.

Edit: Should be an 8 and ) where that stupid face is. Can't get rid of it.

Edited December 18, 2023 by unapologetic pedant
a random emoji keeps appearing

[Padge]

25 minutes ago, unapologetic pedant said:

The OP had no brackets, real or implied.

Who determines the conventions of operational precedence? 

Algebraic convention would rearrange 8 - 8 × 8 + 8 to 8(8 -  + 8.

Edit: Should be an 8 and ) where that stupid face is. Can't get rid of it.

Having an X * / ÷ in a mathematical expression automatically implies that that part of the expression is bracketed and will take precedence, unless overruled by a higher precedence, i.e. 8+8*8 is really 8+(8*8) to get the + operation to occur first then you must use actual and not implied bracketing i.e. (8+8)*8

8+8*8 = 72

8+(8*8) = 72

(8+8)*8 = 128

Mathematical precedence has been built upon over centuries, the use of precedence was being used in the 17th century (the use of parenthesis, brackets, braces was around in the 1500's) , it was generally a gentleman's agreement between leading mathematicians. The advent of the printing press, making it easier to share information, made it more necessary, especially when it was used for text books, that everyone was using the same rules so that people got the same results when making calculations, this is when precedence would have become more formalized. In short it can't be pinned down to one person or establishment but has, like may conventions, been built up over a number of years, in this case centuries.

I would recommend Mathematics for the Million by Lancelot Hogben as a great history of mathematics,  Chapter 2 The Grammar of Size, Order and Shape explains a great deal about what means what. 

[unapologetic pedant]

35 minutes ago, Padge said:

Having an X * / ÷ in a mathematical expression automatically implies that that part of the expression is bracketed and will take precedence, unless overruled by a higher precedence, i.e. 8+8*8 is really 8+(8*8) to get the + operation to occur first then you must use actual and not implied bracketing i.e. (8+8)*8

I got as far as A-level maths and that was nearly 40 years ago. As mentioned earlier, I was aware that my calculator followed the implied-brackets rule. Can't remember if we were specifically taught it for sequential written calculations. Probably were and I've forgotten.

I suppose in algebraic equations something like (2a × 3b) would be the one term 6ab. So the brackets are superfluous.

[JohnM]

1 hour ago, Padge said:

Having an X * / ÷ in a mathematical expression automatically implies that that part of the expression is bracketed and will take precedence, unless overruled by a higher precedence, i.e. 8+8*8 is really 8+(8*8) to get the + operation to occur first then you must use actual and not implied bracketing i.e. (8+8)*8

8+8*8 = 72

8+(8*8) = 72

(8+8)*8 = 128

Mathematical precedence has been built upon over centuries, the use of precedence was being used in the 17th century (the use of parenthesis, brackets, braces was around in the 1500's) , it was generally a gentleman's agreement between leading mathematicians. The advent of the printing press, making it easier to share information, made it more necessary, especially when it was used for text books, that everyone was using the same rules so that people got the same results when making calculations, this is when precedence would have become more formalized. In short it can't be pinned down to one person or establishment but has, like may conventions, been built up over a number of years, in this case centuries.

I would recommend Mathematics for the Million by Lancelot Hogben as a great history of mathematics,  Chapter 2 The Grammar of Size, Order and Shape explains a great deal about what means what. 

Mathematics for the Million by Lancelot Hogben

Spot on. Recommended. Just donated my printed copy  but it can be downloaded from this legitimate site: https://archive.org/details/HogbenMathematicsForTheMillion/mode/1up

[Padge]

26 minutes ago, unapologetic pedant said:

I suppose in algebraic equations something like (2a × 3b) would be the one term 6ab. So the brackets are superfluous.

Replace a with 4 and b with 5 and you get 2*4*3*5 gives 8*3*5 which gives 24*5 which = 120. 6ab becomes6*4*5 gives 24*5 which = (you saw this coming) 120.

A common question when I was doing applied maths was to do what you did above, i.e be given an expression such as 2a x 3b and asked to simplify it, the simplification would be 6ab, since 2 and 3 are constants they can, in that example, be combined to be one constant, a and b are variables so must be kept separate.

The rules of precedence include a lot more than the ones discussed here, the ones here are the ones needed for the original post. 

6/2*3 =1 or 9? there is a rule for that. This is where my first list comes in (simplified for the particular question from the OP), the accepted norm is that a/bc is treated as a/(bc) (which means multiplication and division are not treated as equally weighted) or in this case 6/(2*3) =1. This example shows that under certain conditions a weighting can be applied to what in other circumstances would be an equal weighting.

 

[Padge]

oops

Edited December 19, 2023 by Padge

[unapologetic pedant]

3 hours ago, Padge said:

6/2*3 =1 or 9? there is a rule for that. This is where my first list comes in (simplified for the particular question from the OP), the accepted norm is that a/bc is treated as a/(bc) (which means multiplication and division are not treated as equally weighted) or in this case 6/(2*3) =1. This example shows that under certain conditions a weighting can be applied to what in other circumstances would be an equal weighting.

This illustrates my point that calculations are not usually set down in the form of the OP.

The above would be written with a as the numerator and bc the denominator. Or if c were intended as a multiplier of the fraction a over b, it would be written as ac over b. There would be no need for brackets in either case.

[Padge]

2 hours ago, unapologetic pedant said:

This illustrates my point that calculations are not usually set down in the form of the OP.

The above would be written with a as the numerator and bc the denominator. Or if c were intended as a multiplier of the fraction a over b, it would be written as ac over b. There would be no need for brackets in either case.

Just as there is no need for brackets in 8-8*8+8 as the use of * implies the middle two 8s are bracketed, brackets are often used for clarity, especially in more complex equations.

[unapologetic pedant]

5 hours ago, Padge said:

Just as there is no need for brackets in 8-8*8+8 as the use of * implies the middle two 8s are bracketed, brackets are often used for clarity, especially in more complex equations.

But there was no * in the OP. Only the standard multiplication symbol. And most people would assume an implied equals sign after 8 - 8. Likewise the calculator on my computer, as I've just discovered.

Don't misunderstand, I'm sure you're right that the implied-brackets convention ought to be observed and that the correct answer is -48. My first thought was that no uncertainty would arise if the sequence were a collection of algebraic expressions, since there would be three terms with the equivalent of 8 × 8 written as 64.

Been pondering the sequence a - b × -1, which according to the implied-brackets convention would be a + b.

As distinct from (a - b) × -1 which in an equation would be written as -(a - b) i.e. b - a.

[Padge]

1 hour ago, unapologetic pedant said:

1. But there was no * in the OP. Only the standard multiplication symbol. And most people would assume an implied equals sign after 8 - 8. Likewise the calculator on my computer, as I've just discovered.

2. Don't misunderstand, I'm sure you're right that the implied-brackets convention ought to be observed and that the correct answer is -48. My first thought was that no uncertainty would arise if the sequence were a collection of algebraic expressions, since there would be three terms with the equivalent of 8 × 8 written as 64.

3. Been pondering the sequence a - b × -1, which according to the implied-brackets convention would be a + b.

As distinct from (a - b) × -1 which in an equation would be written as -(a - b) i.e. b - a.

1.I have a computing background so my default multiplication operator symbol is *, it avoids confusion that can occur when using x in programming. * and x are interchangeable.

2. The OP was a maths question not an algebra question, it is aimed at showing an understanding of precedence.

3. Convention would be to put -1 in brackets, to indicate it is a negative number and not a typo a-b x (-1) or a-(b x(-1)). The rest has nothing to the original maths question and a refer you to answer 2.

 

@marklaspalmas Just to clear things about the multiplication precedence, you may have noticed I gave multiplication precedence over division in an earlier example a/bc or a/b*c. This occurs because of the convention of using a vinculum to represent division.  The line above b * c (the vinculum), was used in the 16th/17th century by some mathematicians instead of brackets as an indication of precedence, what was below the line had precedence adding something above the line indicates division after what is under the vinculum has been calculated. The slash / representing division operates the same as the vinculum i.e. what is 'below' has precedence.

Edited December 19, 2023 by Padge

[unapologetic pedant]

On 19/12/2023 at 14:06, Padge said:

2. The OP was a maths question not an algebra question, it is aimed at showing an understanding of precedence.

A final belated thought -

My first post on this was a trifle facetious. Made the mistake of replying to the OP without reading the thread.

However, am I not right that a series of operations like this is only relevant to a computer program? i.e. it wouldn't appear in written maths, where a multiplication symbol between two terms would imply one term. Only when all terms had been simplified would you proceed.

I mentioned possessing a scientific calculator at school. It was seldom used. We had been warned that calculators were not allowed in exams. Books of logarithms were still standard issue. 

[Tommygilf]

BODMAS/BIDMAS is correct. Multiplication takes precedence before addition/subtraction.

I don't know, or really care, exactly why, but it just does. 

I did my maths (i)GCSE in 2014...

[Padge]

1 hour ago, unapologetic pedant said:

A final belated thought -

My first post on this was a trifle facetious. Made the mistake of replying to the OP without reading the thread.

However, am I not right that a series of operations like this is only relevant to a computer program? i.e. it wouldn't appear in written maths, where a multiplication symbol between two terms would imply one term. Only when all terms had been simplified would you proceed.

I mentioned possessing a scientific calculator at school. It was seldom used. We had been warned that calculators were not allowed in exams. Books of logarithms were still standard issue. 

It doesn't just apply to computer programming, I did applied maths when a computer was the size of a house and read punch cards. We were taught the rules of precedence (though by then you should know them, but it did go into some lesser known ones) and encouraged to use brackets to emphasise precedence thus helping to avoid errors by people misunderstanding precedence (a lot of people understood brackets first but ignored or failed to understand mathematical precedence).

I got my first scientific calculator around 1988, Casio fx-82c. I still have it and it still works, it gives the correct answer with or without brackets.

Edited December 29, 2023 by Padge

[unapologetic pedant]

50 minutes ago, Padge said:

It doesn't just apply to computer programming, I did applied maths when a computer was the size of a house and read punch cards. We were taught the rules of precedence (though by then you should know them, but it did go into some lesser known ones) and encouraged to use brackets to emphasise precedence thus helping to avoid errors by people misunderstanding precedence (a lot of people understood brackets first but ignored or failed to understand mathematical precedence).

I got my first scientific calculator around 1988, Casio fx-82c. I still have it and it still works, it gives the correct answer with or without brackets.

Mine's very similar. Casio fx-82 without the "c". Cost me 10 quid in 1978. Also, still works.

[Padge]

6 minutes ago, unapologetic pedant said:

Mine's very similar. Casio fx-82 without the "c". Cost me 10 quid in 1978. Also, still works.

Is it not an fx-80 being bought in 78? 82's only came out in (obviously the start of a year thing that eventually reached PC software*) 1982

* Don't know that is actually why it became the 82

[unapologetic pedant]

1 hour ago, Padge said:

Is it not an fx-80 being bought in 78? 82's only came out in (obviously the start of a year thing that eventually reached PC software*) 1982

* Don't know that is actually why it became the 82

I'd post a picture if I knew how to. Two things for absolutely certain - It's an fx-82 and it cost £10. The mind might be playing tricks regarding the date it was bought. Could have sworn it was at the start of secondary school in 1978. Maybe I got it later for the O Level curriculum?

I googled "Casio fx-82", and my model goes for £15 on eBay.

[Padge]

6 minutes ago, unapologetic pedant said:

I'd post a picture if I knew how to. Two things for absolutely certain - It's an fx-82 and it cost £10. The mind might be playing tricks regarding the date it was bought. Could have sworn it was at the start of secondary school in 1978. Maybe I got it later for the O Level curriculum?

I googled "Casio fx-82", and my model goes for £15 on eBay.

So does the 82c

They are a cracking calculator.

You can check out the history here:- http://www.arithmomuseum.com/album.php?cat=c&lang=en&am=17&s=30&p=30

 

[The Hallucinating Goose]

8 hours ago, Tommygilf said:

BODMAS/BIDMAS is correct. Multiplication takes precedence before addition/subtraction.

I don't know, or really care, exactly why, but it just does. 

I did my maths (i)GCSE in 2014...

I did my maths GCSE in 2011. I was in the top ability group and even did an extra Statistics GCSE on top of Advanced Maths but still didn't know about BODMAS/BIDMAS, though I did hate maths and just pratted about with my mates in most lessons so it could have just completely passed me by. 

[unapologetic pedant]

3 hours ago, The Hallucinating Goose said:

I did my maths GCSE in 2011. I was in the top ability group and even did an extra Statistics GCSE on top of Advanced Maths but still didn't know about BODMAS/BIDMAS, though I did hate maths and just pratted about with my mates in most lessons so it could have just completely passed me by. 

I'm labouring my point but what the heck -

A question in a maths text book would never give you a - b × c + d. It would always be written as c(a - b) + d or a - bc + d.

Likewise with exponents, if you were given a times b to the power of c, you would know it wasn't (a × b) to the power of c since that would be written as a to the power of c times b to the power of c.

In all instances, knowledge of rudimentary notation would suffice. No need for an acronymic mantra. You'd only have to bear operational precedence in mind when using a calculator.

Edited December 30, 2023 by unapologetic pedant

[The Hallucinating Goose]

8 minutes ago, unapologetic pedant said:

I'm labouring my point but what the heck -

A question in a maths text book would never give you a - b × c + d. It would always be written as c(a - b) + d or a - bc + d.

Likewise with exponents, if you were given a times b to the power of c, you would know it wasn't (a × b) to the power of c since that would be written as a to the power of c times b to the power of c.

In all instances, knowledge of rudimentary notation would suffice. No need for an acronymic mantra. You'd only have to bear operational precedence in mind when using a calculator.

I am rubbish at maths. In your equations you've posted here, can you replace the letters with numbers so I can see how these equations would actually work, please? I've tried doing that myself and I'm just getting confused. 

[Padge]

37 minutes ago, unapologetic pedant said:

I'm labouring my point but what the heck -

A question in a maths text book would never give you a - b × c + d. It would always be written as c(a - b) + d or a - bc + d.

Likewise with exponents, if you were given a times b to the power of c, you would know it wasn't (a × b) to the power of c since that would be written as a to the power of c times b to the power of c.

In all instances, knowledge of rudimentary notation would suffice. No need for an acronymic mantra. You'd only have to bear operational precedence in mind when using a calculator.

Once again you have misunderstood the point of the original question.