Maths problem

[unapologetic pedant]

20 minutes ago, The Hallucinating Goose said:

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. 

Would be more ambiguous with numbers.

You could write 1 - 2 × 3 + 4 as 3(1 - 2) + 4, but in the other option the bc term would be written as 23. You'd have to put (2 × 3), which would defeat the object.

As for exponents, no idea how to represent those on a computer.

[Padge]

1 hour ago, unapologetic pedant said:

As for exponents, no idea how to represent those on a computer.

The caret ^ i.e.  5^2 is 5 squared.

 

Edited to correct the spelling of caret.

 

Edited December 30, 2023 by Padge

[unapologetic pedant]

5 minutes ago, Padge said:

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

Not quite. I'm explaining why I originally misunderstood the point of the question. 

[unapologetic pedant]

17 minutes ago, Padge said:

The carat ^ i.e.  5^2 is 5 squared.

 

1 hour ago, unapologetic pedant said:

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.

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

Hope that clears everything up for @The Hallucinating Goose

[Padge]

Just to tidy up on representation of exponents in computing.

Modern applications using the latest font techniques do allow you to use traditional representations.

82 

Eight squared above is produced by using a font superscript on the two.

[Tommygilf]

5 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. 

It was one of the first things we did in year 7 as I recall. Its just an extension of brackets first. That is the simple and most common method, but as your example shows, there are wildly varying outcomes if there isn't an extended version to factor all functions.

[unapologetic pedant]

1 hour ago, Tommygilf said:

It was one of the first things we did in year 7 as I recall. Its just an extension of brackets first. That is the simple and most common method, but as your example shows, there are wildly varying outcomes if there isn't an extended version to factor all functions.

I still don't understand why you would be taught "brackets first" as some kind of golden rule. On the page, it's obvious. You don't need to memorize an acronym to know that c(a - b) derives from factorizing ac - bc.

The reason for typing (a - b) in first on a calculator is to avoid the bother of putting brackets around it.

[unapologetic pedant]

2 hours ago, Padge said:

82 

That looks much better.

BTW, I thought the caret on my keyboard was a circumflex for use in French.

[Padge]

2 minutes ago, unapologetic pedant said:

That looks much better.

BTW, I thought the caret on my keyboard was a circumflex for use in French.

The problem with using the superscript feature is not all fonts and applications can use it, so if you transfer the text from one application to another you may finish up with 82 instead of 82

Copy the 82  and paste into a reply on here and when given the option to past as rich or plain text select plain text and you will see the problem.

The uses of the caret are many and varied and it is also known as the circumflex character.

It is used in proof reading to indicate something is missing or needs adding.

It is also used in computing to indicate the Control Key, instead of writing CTRL+A (which selects all text) when writing it down you can use the short version ^A which indicates the same thing.

Basically the meaning of the Caret symbol depends on context.

 

 

[Tommygilf]

44 minutes ago, unapologetic pedant said:

I still don't understand why you would be taught "brackets first" as some kind of golden rule. On the page, it's obvious. You don't need to memorize an acronym to know that c(a - b) derives from factorizing ac - bc.

The reason for typing (a - b) in first on a calculator is to avoid the bother of putting brackets around it.

You're doing this in algebra, which takes for granted the prioritisation of a×c and b×c in the ac-bc example.

In actual numbers, you wouldn't write 48-68 to mean 4×8-6×8.

Most people don't take to maths, and don't see the factorisation you say as "obvious" at all. Having processes and rules to follow like BIDMAS/BODMAS helps people order their actions when solving an equation.

[Padge]

a=b is nonsense

Just to carry this on.

 

[unapologetic pedant]

5 hours ago, Tommygilf said:

Most people don't take to maths, and don't see the factorisation you say as "obvious" at all. Having processes and rules to follow like BIDMAS/BODMAS helps people order their actions when solving an equation.

Most mnemonics are chicken-and-egg. Only helpful if you're already conversant with the subject. What use is SOHCAHTOA to someone struggling to grasp the basics of trigonometry?

The question in the OP purportedly tests our knowledge of operational precedence. My argument is that in practice it's only testing whether we know how our calculator has been programmed. There wouldn't be much point reciting an acronym to a computer that was delivering 8 as the answer.

[unapologetic pedant]

12 minutes ago, Padge said:

a=b is nonsense

Hard to argue with that.

Is there a hidden meaning?

[Padge]

23 minutes ago, unapologetic pedant said:

Hard to argue with that.

Is there a hidden meaning?

No hidden meaning.

a=a+c is also a nonsense

a=5 is not a nonsense as long as you previously assigned the value 5 to a

a=b is also not a nonsense if...

a has been assigned a value of 5 and b has been assigned a value of 5

therefore a=b but without assignment it is nonsense 

if a =7 and b=5 then you need to assign the value to b to a for a=b to be correct.

So if ..,

a=7 and b =5

then you need to say a a == b for a=b to be correct, == means assign the value on the right to the variable on the left and then a=b becomes true.

 

 

Edited December 30, 2023 by Padge

[unapologetic pedant]

7 hours ago, Padge said:

The problem with using the superscript feature is not all fonts and applications can use it, so if you transfer the text from one application to another you may finish up with 82 instead of 82

This is a random point, nothing to do with the quote -

Re the EXP key on the fx-82. The number for pi comes up when you press. I thought this key would be for exponents and Euler's number. How does this relate to the In key where the inverse function is e^x?

[unapologetic pedant]

9 minutes ago, Padge said:

No hidden meaning.

Why did you announce that a = b is nonsense?

What's the context?

[Padge]

11 minutes ago, unapologetic pedant said:

This is a random point, nothing to do with the quote -

Re the EXP key on the fx-82. The number for pi comes up when you press. I thought this key would be for exponents and Euler's number. How does this relate to the In key where the inverse function is e^x?

I suggest you start here https://archive.org/details/manualzilla-id-7062852

 

[Padge]

5 minutes ago, unapologetic pedant said:

Why did you announce that a = b is nonsense?

What's the context?

a is a value and b is a value, without knowing the value of a and b you do not have a clue if a = b. = means equals, equals means the same as, how do you know a is the same as b if you do not know the value of a or b. 

Without knowing what values have been assigned to each variable the statement is nonsense,

 

[Tommygilf]

Just now, unapologetic pedant said:

Most mnemonics are chicken-and-egg. Only helpful if you're already conversant with the subject. What use is SOHCAHTOA to someone struggling to grasp the basics of trigonometry?

The question in the OP purportedly tests our knowledge of operational precedence. My argument is that in practice it's only testing whether we know how our calculator has been programmed. There wouldn't be much point reciting an acronym to a computer that was delivering 8 as the answer.

No it is testing knowledge of operational precedence. 

Older and non scientific calculators cannot do this. As my teachers said, the calculator can only provide the answer to what you input. Knowing multiplication comes before addition and subtraction (in this case), makes a material difference. 

Likewise, with small numbers such as this, we don't need necessarily need the use of calculators - so one needs to know the BIDMAS order of things.

Of course mnemonics, or in this case, an acronym, mean nothing without context or education. That isn't a major point of debate really.

[unapologetic pedant]

7 minutes ago, Padge said:

I suggest you start here https://archive.org/details/manualzilla-id-7062852

 

I've definitely still got the fx-82 manual. Somewhere.

[Padge]

4 minutes ago, unapologetic pedant said:

I've definitely still got the fx-82 manual. Somewhere.

I suggest you read it rather than ask me for the answer.

[unapologetic pedant]

2 minutes ago, Tommygilf said:

Older and non scientific calculators cannot do this. As my teachers said, the calculator can only provide the answer to what you input. Knowing multiplication comes before addition and subtraction (in this case), makes a material difference. 

Likewise, with small numbers such as this, we don't need necessarily need the use of calculators - so one needs to know the BIDMAS order of things.

Give an example from a maths text book, where the operations are set out like the question in the OP.

i.e. where you would feel it necessary to run through an acronymic checklist, familiarity with rudimentary notation would not suffice.

[unapologetic pedant]

26 minutes ago, Padge said:

a is a value and b is a value, without knowing the value of a and b you do not have a clue if a = b. = means equals, equals means the same as, how do you know a is the same as b if you do not know the value of a or b. 

Without knowing what values have been assigned to each variable the statement is nonsense,

Does this relate specifically to something I, or someone else, posted?

Edited December 30, 2023 by unapologetic pedant

[Padge]

4 minutes ago, unapologetic pedant said:

Give an example from a maths text book, where the operations are set out like the question in the OP.

i.e. where you would feel it necessary to run through an acronymic checklist, familiarity with rudimentary notation would not suffice.

Once again you miss the point of the OP. You are really struggling with the concept of explaining precedence. the people on here must have had a joint hallucination despite being miles, years and cultures apart.

 

1 minute ago, unapologetic pedant said:

Does this relate specifically to something I, or someone else, has posted?

No, you seem to have missed my point of moving on to a new but similar concept of confusion. Go back and read.

[Tommygilf]

5 minutes ago, unapologetic pedant said:

Give an example from a maths text book, where the operations are set out like the question in the OP.

i.e. where you would feel it necessary to run through an acronymic checklist, familiarity with rudimentary notation would not suffice.

The OP's example is precisely that. We had loads where there was a multiplication or division or indices written after an addition or subtraction in an equation where the whole point of the question was to assess whether you knew the order of priority as per BIDMAS.

Maths was at least initially taught to me on the basis of not having a calculator, so that when one had the use of one, one knew what to input to get the correct answer. Scientific calculators that allow replication directly of equations on a page have made that skill somewhat redundant, but knowing it harms nobody.