Maths problem

[unapologetic pedant]

a^b × a^c = a^(b + c)

(a^b)^c = a^bc

How do I know the above without the benefit of BIDMAS/BODMAS/BOMDAS/BEDMAS/PEMDAS?

[unapologetic pedant]

5 hours ago, unapologetic pedant said:

And magically we now have a fourth variant of the incantation certified to unlock the mysteries of mathematics and open the minds of an otherwise innumerate global populace.

Correction - fifth variant. I overlooked BOMDAS, which gets a mention on page 2.

[The Hallucinating Goose]

I can't believe this has caused such a discussion. Who'd have thought there were so many maths enthusiasts on here! 

[Spidey]

On 17/12/2023 at 22:10, The Hallucinating Goose said:

If you work out this maths problem, what answer do you get? 

8 - 8 x 8 + 8

 

I don't know if maths is taught differently these days but apparently the answer I get is not correct. 

BODMAS ?

[Tommygilf]

18 hours ago, Spidey said:

BODMAS ?

Brackets, Operations/Order, division multiplication addition subtraction. 

PEDMAS, as I suspected, is an American variation based on the terminology preference for parentheses vs brackets, and exponents vs the British examples.

Ultimately, people learn using rules and frameworks.

[Tommygilf]

19 hours ago, unapologetic pedant said:

a^b × a^c = a^(b + c)

(a^b)^c = a^bc

How do I know the above without the benefit of BIDMAS/BODMAS/BOMDAS/BEDMAS/PEMDAS?

You know it without having to use those, well done. Would you like a medal? 

You seem really irked by the fact that clearly most people understand ordering of operations with the aid of a mnemonic rather than some belief in the sanctity of mathematical notations denoting priority self-evidently. You've also completely disregarded this being the way it is taught across at least the English speaking world in the early stages of mathematical education for students.

[tonyXIII]

On 18/12/2023 at 11:04, JohnM said:

The brackets are implied. Confirmation from TonyXIII, please.

 

Only just seen this. Apologies.

The order is BODMAS or PEMDAS. The first operation to do is Brackets or Parentheses, then it's Exponents or Indices. I'm not sure why BODMAS has an O. Then, you do Multiplication and Division, which have equal priority, followed by Addition and Subtraction, which also have equal priority. In the event of equal priority, you work from left to right, but this is the final priority and only comes into play AFTER everything else.

So, 8-8x8+8. As Padge has pointed out, the first operation is multiplication - 8x8 equals 64 - this leaves you with 8-64+8 which are equal priority  so work from left to right ( 8-64 equals -56 ) and then -56 + 8 comes to -48.

So, Padge gets 10 out of 10 and a gold star, as does JohnM for pointing out that, in this sequence and others, there are implied brackets round the multiplication and division operators  so he also gets 10 out of 10 and a gold star. (As does anyone else who got it right. I've better things to do than read the whole thread.)

Happy New Year to everyone, regardless of your mathematical prowess.

[unapologetic pedant]

57 minutes ago, Tommygilf said:

You know it without having to use those, well done. Would you like a medal? 

You seem really irked by the fact that clearly most people understand ordering of operations with the aid of a mnemonic rather than some belief in the sanctity of mathematical notations denoting priority self-evidently. You've also completely disregarded this being the way it is taught across at least the English speaking world in the early stages of mathematical education for students.

You sound considerably more irked than I am. It does seem rather odd that there are so many versions of this acronym. And that some recall it as an essential part of their maths education while others have no recollection at all. As someone in the latter category, I'm merely expressing scepticism regarding its status. Award a medal for impertinence, if you wish.

I posted the two truths involving indices because I don't think they respond well to the acronym.

Examples like a + b × c are apparently used to test knowledge of operational precedence. My main gripe is that beyond that, I can't think of other contexts where the second and third terms would not be simplified to a + bc. Why else would question-setters factorize one term bc into two terms b × c ?

When presented with a^c × b^c or a^c + b^c, why would we need to run through BEMDAS to check that exponents come before multiplication or addition i.e. why on earth would anyone think that an index belonged to anything other than the number/letter it was written to the upper-right of?

[Padge]

25 minutes ago, unapologetic pedant said:

You sound considerably more irked than I am. It does seem rather odd that there are so many versions of this acronym.

Versions exist because like pavement and sidewalk different countries despite using a common language use different language. To not realise that is either dumb or deliberately argumentative.

28 minutes ago, unapologetic pedant said:

I'm merely expressing scepticism regarding its status.

 You have been given multiple examples of its use and status.

To not realise that is either dumb or deliberately argumentative.

30 minutes ago, unapologetic pedant said:

Examples like a + b × c are apparently used to test knowledge of operational precedence. My main gripe is that beyond that, I can't think of other contexts where the second and third terms would not be simplified to a + bc. Why else would question-setters factorize one term bc into two terms b × c ?

I the real world people work in numbers and not algebraic expressions, hence people in the real world would not use 4+65 when what they mean is 4+6x5.

To not realise that is either dumb or deliberately argumentative.

Happy New Year.

To not realise it is a New Year is either dumb or deliberately argumentative.

[Tommygilf]

35 minutes ago, Padge said:

Versions exist because like pavement and sidewalk different countries despite using a common language use different language. To not realise that is either dumb or deliberately argumentative.

 You have been given multiple examples of its use and status.

To not realise that is either dumb or deliberately argumentative.

I the real world people work in numbers and not algebraic expressions, hence people in the real world would not use 4+65 when what they mean is 4+6x5.

To not realise that is either dumb or deliberately argumentative.

Happy New Year.

To not realise it is a New Year is either dumb or deliberately argumentative.

Thank you !

[unapologetic pedant]

1 hour ago, Padge said:

Versions exist because like pavement and sidewalk different countries despite using a common language use different language. 

PEMDAS is the only one of the five where that would be a plausible explanation. The other four have all been cited by posters who have gone through the English education system.

We don't teach four variants of multiplication tables or the English alphabet. Unsurprisingly, everyone has a common recollection of those.

 

1 hour ago, Padge said:

You have been given multiple examples of its use and status.

None that weren't specifically aimed at testing knowledge of operational precedence.

 

1 hour ago, Padge said:

I the real world people work in numbers and not algebraic expressions, hence people in the real world would not use 4+65 when what they mean is 4+6x5.

They would say 4 + 30. And a two-letter algebraic expression representing the equivalent of the number 30 in a textbook maths question would be one term not two.

In the real world, if you ordered 4 of one item and 6 of another item, then repeated the order 5 times, you'd be somewhat miffed to receive one lot of the 4 and 5 lots of the 6.

If you wanted 4 of one item and 30 of the other, you would place one order for precisely that.

[Padge]

34 minutes ago, unapologetic pedant said:

PEMDAS is the only one of the five where that would be a plausible explanation. The other four have all been cited by posters who have gone through the English education system.

We don't teach four variants of multiplication tables or the English alphabet. Unsurprisingly, everyone has a common recollection of those.

 

None that weren't specifically aimed at testing knowledge of operational precedence.

 

They would say 4 + 30. And a two-letter algebraic expression representing the equivalent of the number 30 in a textbook maths question would be one term not two.

In the real world, if you ordered 4 of one item and 6 of another item, then repeated the order 5 times, you'd be somewhat miffed to receive one lot of the 4 and 5 lots of the 6.

If you wanted 4 of one item and 30 of the other, you would place one order for precisely that.

Wrong on every count.

To not realise that is either dumb or deliberately argumentative.

I don't remember fighting in the Battle of Hastings, that does not mean it didn't happen or only exists in someone else's imagination.

Edited January 1, 2024 by Padge

[unapologetic pedant]

1 hour ago, Padge said:

Wrong on every count.

Asserting that something is wrong is not proof that it is wrong.

The only point in my post that is verifiably incorrect was the line about repeating an order 5 times. Shades of the dispute over use of "threepeat".

1 hour ago, Padge said:

To not realise that is either dumb or deliberately argumentative.

If I had wanted to be vacuously argumentative, I would have been speculating on the inspiration for your a=b magnum opus. First thought was that you must have been on the grog.

 

1 hour ago, Padge said:

I don't remember fighting in the Battle of Hastings, that does not mean it didn't happen or only exists in someone else's imagination.

Nowhere have I suggested that anyone is imagining BEMDAS or its variants. Just not convinced of its utility or that the principles it denotes were taught universally in the form of an acronym. 

[Tommygilf]

https://vm.tiktok.com/ZGeM9sDqS/

Question 3 of Edexcel's non calculator November 2022 maths paper.

[gingerjon]

1 hour ago, Tommygilf said:

https://vm.tiktok.com/ZGeM9sDqS/

Question 3 of Edexcel's non calculator November 2022 maths paper.

Some men just want to watch the world burn.

[unapologetic pedant]

On 21/01/2024 at 10:29, Tommygilf said:

https://vm.tiktok.com/ZGeM9sDqS/

Question 3 of Edexcel's non calculator November 2022 maths paper.

20 ÷ (3 + 2) is the question.

I was all set to completely ignore the brackets and carry out 20 ÷ 3 + 2. Then the nice man said "BIDMAS/BODMAS" and Hey Presto, everything became clear. All hail BIDMAS/BODMAS!

[JohnM]

Ok. BODMAS sorted. 

Up next: Reverse Polish Notation.

https://en.m.wikipedia.org/wiki/Reverse_Polish_notation

[The Hallucinating Goose]

37 minutes ago, JohnM said:

Ok. BODMAS sorted. 

Up next: Reverse Polish Notation.

https://en.m.wikipedia.org/wiki/Reverse_Polish_notation

I just read the first paragraph of that and my brain exploded. I think I'll leave this one to someone else!

[JohnM]

Way back in 1989 my then boss used an HP pocket scientific calculator, which is when I first (and last!) heard about RPN. 

[JonM]

On 09/02/2024 at 08:58, JohnM said:

Way back in 1989 my then boss used an HP pocket scientific calculator, which is when I first (and last!) heard about RPN. 

Still used in quite a bit of low level computing - the Java virtual machine is all RPN, for example.

[JohnM]

That's the EU for you! What's wrong with Reverse BRITISH notation?

[tonyXIII]

On 09/02/2024 at 10:58, JohnM said:

Way back in 1989 my then boss used an HP pocket scientific calculator, which is when I first (and last!) heard about RPN. 

I thought RPN was mostly used in Texas Instruments calculators, not Hewlett Packard.

Of course, I am probably wrong.

[gingerjon]

Right. Who's to blame for this?

[unapologetic pedant]

4 hours ago, gingerjon said:

Right. Who's to blame for this?

Archimedes

[JohnM]

9 minutes ago, unapologetic pedant said:

Archimedes

So not Achilles Reselfelt after all?