💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @ SmartmanApps @programming.dev

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591

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2 yr. ago

Division is usually written in fractions

Division and fractions aren't the same thing.

fractions which has an implied set of parenthesis

Fractions are explicitly Terms. Terms are separated by operators (such as division) and joined by grouping symbols (such as a fraction bar), so 1÷2 is 2 terms, but ½ is 1 term.

8/2(2+2) could be rewritten as 8×1/2×(2+2)

No, it can't. 2(2+2) is 1 term, in the denominator. When you added the multiply you broke it into 2 terms, and sent the (2+2) into the numerator, thus leading to a different answer. 8/2(2+2)=1.

Except TI calculators also give the wrong answer when a bracketed term has a coefficient.

Yeah, that's exactly the problem with TI calculators - ignoring the rules of Maths.

My calculator gets 1

That is the correct answer.

TI calculators disobey The Distributive Law and give the wrong answer when a bracketed term has a coefficient.

but the phone is actually correct

No, it's actually wrong.

8 / 2 * 4

It's 8/(2x4). You can't remove brackets unless there is only 1 term left inside.

There's no multiplication in this question - multiplication refers literally to multiplication signs - only division and brackets, and addition within the brackets. So you have to use The Distributive Law to solve the brackets, then do the division, giving you 1.

you’re just a tutor and not actually a teacher?

Both - see the problem with the logic you use?

Let me know when you decide to consult a textbook about this.

I'm an Australian teacher who has also taught the U.K. curriculum (so I have textbooks from both countries) and, based on these comments you mention, have also Googled some U.S. textbooks, and I've yet to see any Maths textbooks that teach it "the other way". I have a very strong suspicion that it's just a lot of people in the U.S. claiming they were taught that way, but not actually being true. I had someone from Europe claim the way we (and the U.K.) teach it wasn't taught there (from memory it was Lithuania, but I'm not sure now), so I just Googled the curriculum for their country and found that indeed it is taught the same way there as here. i.e. people will just make up things in order not to admit they were wrong about something (or that their memory of it is faulty).

a single sentence of a wikipedia article without me handfeeding it to you

And I told you why it was wrong, which is why I read Maths textbooks and not wikipedia.

I’m sorry for your students

My students are doing good thanks

As far as you can tell. Really. Like it’s an oblique implication

Indeed there was an oblique implication in me saying "as far as I can tell", but you seemed to miss it (I was wording it in a polite way, rather than being downright rude like a lot of people in here seem to have no trouble with at all, but water off a duck's back...).

your original point was off-topic

The OP was about an e-calculator giving the wrong answer, so I don't see how explaining why it's doing that is off-topic (in your view).

Good day

Bye now.

The notation is not intrinsically clear

It is to me, I actually teach how to write it.

The only confusion I can see is if you intended for the 4 to be an exponent of the 3 and didn't know how to do that inline, or if you did actually intend for the 4 to be a separate numeral in the same term? And I'm confused because you haven't used inline notation in a place that doesn't support exponents of exponents without using inline notation (or a screenshot of it).

As written, which inline would be written as (2^{3)4, then it's 32. If you intended for the 4 to be an exponent, which would be written inline as 2\}34, then it's 2^81 (which is equal to whatever that is equal to - my calculator batteries are nearly dead).

we don’t have a standard

We do have a standard, and I told you what it was. The only confusion here is whether you didn't know how to write that inline or not.

Exactly! It’s in math textbooks, in both ways!

And both ways are explained, so not ambiguous which is which.

I’m talking about how you said (A)B for A=3 B=-6 equals -3

No, that's not what I said, since that's not what you said. You didn't write (A)B where A=3 and B=-6, you wrote (3)-6, which is 3-6 (the brackets are redundant as they are 2 terms separated by an operator), which is -3. If you intended this to be interpreted as a single term then you should've written (3)(-6), which is -18. Alternatively, if you had written (3)6, that would be equal to 18, but you wrote (3)-6, which is 2 terms separated by a minus. You wrote (A)-B, not (A)B (or (A)(B)), and so I read it as (A)-B.

The syntax can be ambiguous.

No, it's not. Now that I know what you mean, you just failed to write it the way you apparently intended - you didn't follow the syntax rules for multiplying by a negative.

but the concept of distribution does not exist within in RPN

So what you're really saying, as far as I can tell, is brackets themselves don't exist in RPN.

evaluating a parenthetical gets the same result as distribution

Except when it doesn't, which is my original point.

When I was in school, year 7 was primary school

Oh really? My apologies then. I've only ever heard Year 7 called high school or middle school, never primary school. What country is that in?

multiplication by juxtaposition. Which I’m fairly sure for me at least was in year 6

I've seen some Year 6 classes do some pre-algebra (like "what number goes in this box to make this true"), but Year 7 is when it's properly first taught. Every textbook I've ever seen it in has been Year 7 (and Year 8, as revision).

Also, it's not "multiplication by juxtaposition", since it's not multiplication - it's The Distributive Law - which is Distribution - and/or Terms - which is a product, which is the result of a multiplication.

No, the idea of specifically codifying BIDMAS comes from the early 1900s

The order of operations rules are older than that - we can see in Lennes' letter (1917) that all the textbooks were already using it then, and Cajori says - in 1928 - that the order of operations rules are at least 300 years old (which now makes them at least 400 years old).

If you're talking about when was the mnemonic BIDMAS made up, that I don't know, but the mnemonics are only ways to remember the rules anyway, not the actual rules.

I don’t know why you’re going throughout this thread

I'm a Maths teacher, that's what we do. :-)

a rigid primary school application of BIDMAS will lead you to the wrong answer

Only if the bracketed term has a coefficient (welcome to how Texas Instruments gets the wrong answer), which is never the case in Primary School questions - that's taught in Year 7 (when we teach The Distributive Law).

juxtaposition actually comes before explicit multiplication... I think that’s what you mean when you keep saying “it’s called terms”

Terms come before operators, and we never call it juxtaposition, because The Distributive Law is also what people are calling "strong juxtaposition" (and/or "implicit multiplication"), but is a separate rule, so to lump 2 different rules together under 1 name is where a lot of people end up going wrong. There's a Youtube where the woman gets confused by a calculator's behaviour and she says "sometimes it obeys juxtaposition and sometimes it doesn't" (cos she lumped those 2 rules together), and I for one can see clear as day the issue is it's obeying Terms but not obeying The Distributive Law (but she lumped them together and doesn't understand these are 2 separate behaviours).

Terms and multiplication by juxtaposition can work together

But that's my point, there's no such thing as "multiplication by juxtaposition". A Term is a product, which is the result of a multiplication.

If a=2 and b=3 then...

axb=2x3 - 2 terms

ab=6 - 1 term

In the mnemonics "Multiplication" refers literally to multiplication signs, and nothing else. The Distributive Law is done as part of solving Brackets, and there's nothing that needs doing with Terms, since they're already simplified (unless you've been given some values for the pronumerals, in which case you can substitute in the values, but see above for the correct way to do this with ab, though you could also do (2x3), but absolutely never 2x3, cos then you just broke up the term, and get the wrong answer - brackets can't be removed unless there is only 1 term left inside. People writing 2(3)=2x3 are making the same mistake).

Ummm, I was agreeing with you??

Anyways, I'm a Maths teacher who has taught this topic many times - what would I know?

2+2 first because P. That’s 4.

P is 2(2+2)=(2x2+2x2)=(4+4)=8

Then 8/2 because it’s left of 4(4).

If you do 8/2 when you still have brackets, then you just did division before brackets and disobeyed order of operations rules. You also broke the rule of Terms, since 2(4) is a single term.

Don’t take my word for it.

I see you didn't read my thread then. I have a section on calculators, which points out that WolframAlpha does it wrong. i.e. they also break the rule of Terms.

multiple always happens first. But apparently it’s what’s left side first

Multiplication and division are equal precedence (and done left to right) if that's what you're talking about, but the issue is that a(b+c) isn't "multiplication" at all, it's a bracketed term with a coefficient which is therefore subject to The Distributive Law, and is solved as part of solving Brackets, which is always first. Multiplication refers literally to multiplication signs, of which there are none in the original question. A Term is a product, which is the result of a multiplication, not something which is to be multiplied.

If a=2 and b=3, then...

axb=2x3 - 2 terms

ab=6 - 1 term

You can define your notation that way if you like

Nothing to do with me - it's in Maths textbooks.

without knowing the conventions the author uses, it’s ambiguous

Well they should all be following the rules of Maths, without needing to have that stated.