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No, they're Distribution done in the Brackets step, a(b+c)=(ab+ac), now solve (ab+ac)
Nope! a(b+c)=(ab+ac). 1/a(b+c)=1/(ab+ac), but 1/ax(b+c)=(b+c)/a.
(2x3+2x5) actually, or you'll get the wrong answer when it follows a Division sign. See previous point
Nope, that's wrong. See https://www.wolframalpha.com/input?i=10%2F2%282%2B3%29 for reference.
You think Maths textbooks are wrong?? 😂
See Maths textbooks for reference 😂
Yes, the math textbook says exactly what I said, that it's a multiplication. There's no mention of it being a separate operation taking precedence. The parentheses in your example are added for clarity.
Whether you give priority to juxtapositions is an open debate with the consensus being to just use parenthesis around when writing in a single line to avoid confusion. However, there is no distribution step taking precedence, as you mentioned, and the whole debate centers around whether the writer was too lazy to add parenthesis.
Nope, they say it's Brackets...
5(36)=(5x36) <== Brackets
bc=(3x4) <== Brackets
It's part of the Brackets step. I have no idea what "separate operation" you're talking about
Nope. They are there because The Distributive Law requires them. "those who study algebra are required to make their calculations conform to these laws".
A literal Law of Maths. See textbook.
No it isn't. You won't find any Maths textbook that says that.
There is the Brackets step, including Distribution, taking precedence, as per Maths textbooks 🙄
As the textbooks mention
The only debate is by people like you ignoring what is taught in Maths textbooks.
Nowhere in your "proof" screenshots does it say anything about distribution being part of the brackets step. Distribution is a method that can help solve equations, but it isn't required. If you have 2(3+5) you're free to solve it as 2*3+2*5 or as 2*8, whichever is easiest. That is because juxtaposition means multiplication and nothing else.
Math textbooks almost universally will either use clear brackets or simply write divisions in 2 lines, which avoids the confusion altogether.
Which step is first? Brackets. What do they do first in 5(36)/9? The Brackets.
What does the other textbook do with bc? Puts it in Brackets. Which step is first in order of operations? Brackets 🙄 What do they end that page with? “those who study algebra are required to make their calculations conform to these laws”. You seriously need to work on your comprehension that I need to explicitly spell out to you what the textbooks say
The Property is. The Law is a rule which literally must be obeyed, when solving expressions, as per Maths textbooks 🙄
Yes it is! That's why it's a Law 😂
Nope, neither
1/2(3+5)=1/(6+10)
1/2x3+2x5=3/2+10 WRONG ANSWER
1/2x8=8/2=4 WRONG ANSWER
Welcome to why it must be in brackets, as per Maths textbooks 🙄
says person who can't cite any Maths textbook that says that. Nope! It means it's a Term/Product, the result of a Multiplication (or Factorisation), and nothing else...
Note that it never used the word Multiplication at all in that definition 🙄
or an obelus or slash on one line
Only people who don't remember the rules of Maths are confused about it. Students have no trouble with it.
Here is math for kids https://www.mathsisfun.com/definitions/distributive-law.html
Distributive law means you are allowed to distribute, not that you must distribute. I'm so sorry for the amount of effort you're futilely putting into this lmao. Nowhere in all your sources and screenshots is it stated you must distribute, and thus the entire argument breaks down.
Yep, that's about The Distributive Property too 🙄 Every time Multiplication gets mentioned, you know they're talking about the Property, since the Law has no multiplication in it, but The Distributive Property of Multiplication over Addition does
No, the Property does. The Law tells you that you literally must Distribute.
Because The Law says that, hence why it's a Law 🙄
says someone who can't even tell the difference between the Property and the Law 😂
Yes it does liar
Not for people who know how to read 😂
You must not distribute brother, lay it to rest lmao. It's optional. Google distributive law and find me one source saying it's imperative to distribute - there's none. You can even confirm this is true yourself with simple examples like the ones I've mentioned above.
Literally a Law of Maths, but go ahead and stay in Denial about it 😂
You think the word "must" means it's optional?? 😂
Go through Maths textbooks and find me one which says it isn't, or alternatively go through dictionaries and find me one that says "must" means "optional" 😂
He says, when I've already posted multiple textbooks which say it is 😂
I've confirmed it with Maths textbooks - you know, those things you refuse to look in because you know they prove you are wrong 😂 BTW your "example above" was about The Distributive Property, as I already pointed out to you at the time
Bro directly after what you underlined it says "if you want to remove the brackets" lol. Selective reading much? "If" means optional. You are free to solve what's inside the brackets first, before multiplying it with what's outside.
Also, the link I posted is literally titled "distributive law", not property. You realize a law can have conditions, right?
Quick quiz for you: what's the result of 2(3+5)² ?
Yep, that's right, and removing brackets is the first step in order of operations 😂
By you apparently.
So... you're telling me that the "B" step in BEDMAS, and the "P" step in PEMDAS, is optional? I don't have to remove Brackets?? 😂 Better go back to school dude
Yep, but inside the brackets, as per the text you can see in the screenshot 😂
5(8-5)=(5x8-5x5)=(40-25)=15
5(8-5)=5(3)=(5x3)=15 <== Multiplication inside the Brackets, as per The Distributive Law
same answer both ways 😂
But has a multiply sign in it, thus proving it is the Property that they are talking about - The Distributive Property of Multiplication over Addition to call it by it's full name
You realise it literally must be obeyed, right? The condition that The Distributive Law has, is "A number or letter next to a Bracket", direct quote from the textbook, hence a(b+c)=(ab+ac), and not ax(b+c) since the a is not next to the bracket in that case
Ok bro so answer my question what's the result of the expression I wrote above?
Deflection is the word you're looking for
So... you're telling me you don't know what comes first out of Brackets and Exponents in order of operations? That's your deflection strategy??
Exponents come after brackets, so I'm curious to see how you solve that with your logic lol. It has an obvious correct solution, which is 128, but you need to distribute in the brackets step, which comes before exponents, so let's see what you do with it lmao.
That's right
Ummm, you do the brackets and then the exponent. Not sure what you find unclear about that
The one where you do the brackets before the exponent
Nope! You can only get that by doing the exponent before the brackets, which is against the order of operations rules. Or did you wrongly add a multiply sign before the brackets - that also yields a different answer
That's right, so why did you do the exponent first?
That's right. So why did you do the exponent first?
Brackets before exponents, as already established 🙄
Ok bro now find an expression solver that verifies your solution. I tried Wolfram Alpha, Google, and others, and they all return 128. So either you're wrong, or all people who make these tools professionally are wrong. Not trying to be offensive, but I know where I'm putting my money.
To be clear, the reason you're wrong is because distribution is not part of the brackets step. Brackets are solved before exponents, resulting in 2(8)². Remove the brackets and then it's 2*8²
Yep, all known to give wrong order of operations answers
Well, it's not me, so...
That's right. Welcome to programmers writing Maths apps without checking that they have their Maths right first. BTW, in some cases it's as bad as one of their calculators saying 2+3x4=20! 😂
To be clear, I am correct, because Distribution is part of the Brackets step, as we have already established...
Yes
No, you haven't finished solving the Brackets yet, which you must do before proceeding...
Nope! We have already established that you cannot remove the brackets if you haven't Distributed yet...
So what we actually get is...
2(8)²=(2x8)²=16²
and now that I have removed the Brackets, I can now do the exponent,,,
16²=256
Welcome to you finding the answer to 2x(3+5)² - where the 2 is separate to the brackets, separated from them by the multiply sign - rather than 2(3+5)², which has no multiply sign, and therefore the 2 must be Distributed
Lmao citing yourself and assuming you're correct and smarter than everyone who programs solvers, even those who are known to be respectable and used extensively in academia. Nothing's been established cause you've cited sources that don't support your argument, and repeating them again and again won't make it different. Good day bro, continuing this is useless.
Nope! I cite Maths textbooks here, here, here, here, here, here, here, a calculator here, need I go on? 🙄 There's plenty more of them
That's hilarious that you think random programmers know more about Maths than a Maths professional 😂
As I already stated, everyone knows the complete opposite of that about them. It's hilarious that you're trying to prop up places that give both right and wrong answers to the exact same expression as somehow being "respectable". 😂 And you'll see at the end of that thread - if you decide to read it this time - the poof that academia does not use it (because they know it spits out random answers)
BWAHAHAHAAH! Like?? 😂
That's right, the Maths textbooks are still as correct about it as the first time I cited them.
Well it is when you don't bother reading the links, which you've just proven is the case
I've read everything you've posted, but the problem is you're interpreting the texts in such a way that they support your flawed argument, conveniently ignoring what they're actually saying, such as "if" statements.
Even this textbook that you yourself posted goes against what you're saying if you just bother to look at it outside of your tunnel vision:
Notice something?
You've read every textbook, and looked at the calculator answer? Yeah nah, you clearly haven't.
Says person who can't come up with any textbooks that support their argument. 😂 BTW if you had looked at the calculator, you would've seen it does it exactly as I have described - 6/2(1+2)=6/2(3)=6/(2x3)=6/6=1, not, you know, 6/2(1+2)=3(3)=9, which is your flawed argument
Says person ignoring this "if" statement which says you literally must distribute if you want to remove the brackets.
No it doesn't! 😂
Yes, you ignored the Distribution in the last step 😂 I have no idea what you think is significant about the first 2 steps, other than you were trying to draw attention away from the Distribution in the last step
Here's another one (different authors) that does the same thing, which you would've seen if you had actually read all the textbooks I posted, but they explicitly spell out what they're doing as they're doing it...
Yep I have looked at all you've posted, I say you're wrong because what you've posted says things that are true, but you're reading them wrong. For example your last image clearly says a number next to a bracket means the content of the bracket must be multiplied with said number. Nowhere there does anybody speak of distribution taking precedence over other operations. In fact, nowhere in all sources I can find does it say so. Wonder why all screenshots you post use convoluted wording and wonder why you pop up everywhere arguing the same thing and keep getting downvoted? At some point you need to understand that if one old-ass calculator and selective reading of cherry picked passages is all the proof you have, when all modern calculators and algebra solvers go against you, maybe it's time to reconsider.
Juxtaposition taking precedence over other multiplications I can understand and it's an arguable point. Distribution being a mandatory step and taking precedence over even exponents is just silly and unfortunately wrong.
Also another thing: you're a math teacher as you've said, and consistently ask if I think "random programmers" know more about algebra than you. What I say to that is I've met plenty of teachers who are wrong about things in their own fields, for one. And also, people defining the rules of all those algebra solvers aren't the programmers, as you'd know if you looked a bit into product development. It's domain experts, who also define tests and receive feedback on the software's performance and errors. I'm sure (lol) you've sent feedback to them, and they probably looked at it and decided you're wrong. As well all have.
says the person who is actually reading them wrong, who is unable to cite any example of me reading it wrong
the content of the bracket - you just quoted that yourself and still completely missed what that means 😂
BRACKETS has precedence over everything 😂 So here we have an example of you reading it wrong
And can you find any source which says Multiplication takes precedence over Brackets? No. Another example of you reading it wrong
They don't use "convoluted wording"! 🤣
"the contents OF THE BRACKETS should be multiplied"
"everything IN THE BRACKET should be multiplied by that number"
Yet another example of you reading it wrong 😂
The only person downvoting me is the person replying, whereas the others are getting downvoted by others as well 🙄
My brand new Casio calculator gives the same answer! 😂 They all do now, except for Texas Instruments - the only one stubbornly still doing it wrongly
Sure, I'm "cherry picking" the sections of textbooks about Distribution. Do you want me to post something random about a different topic? 😂 BTW, noted that you haven't come up with any textbooks that agree with you
And it is indeed proof.
Agree with me (except for Texas Instruments)
Written by programmers who have forgotten the rules of Maths, and as pointed out by many people in forums.
And yet, here you are not reconsidering 🙄
Because BRACKETS - ab=(axb) BY DEFINITION 😂
And is also the exact same rule 🙄
There's a reason it's called The Distributive Law
BRACKETS taking precedence over Exponents is "silly"?? 🤣🤣🤣
BRACKETS taking precedence over Exponents is "unfortunately wrong"?? 🤣🤣🤣
You think they're wrong you mean, person who is saying Brackets before Exponents is "wrong" 🤣🤣🤣
Yes they are! That's why they give wrong answers 😂 I told one he was wrong and he went and fixed it, being the one who had programmed it that way 🙄
I know they are because I have spoken directly to them 😂 Maybe try asking some yourself, before making completely wrong statements
No it isn't, as proven by personal experience. You know who uses domain experts? calculator manufacturers. 😂 They have considerably more riding on it being right or not.
You know there's a whole bunch of programmers who don't bother even defining tests to begin with, right??
Yep!
Except for the ones who did change it. The ones who claimed I was wrong, quoted Google - who have also been told they're wrong by many people -and not Maths textbooks 🙄
says person who did nothing of the sort, and lied about such things as "all modern calculators " being against me (they aren't, if you had actually tried some), Exponents having precedence over Brackets, etc.
Here you go:
Please post a source that gives a different answer to this expression, I'll wait.
There's of course programmers that implement their own projects, but for big monetized products that's no longer the case. I'm in the software industry myself and have worked extensively in product development.
Sure bro you have multiple downvotes in many posts, I'm sure it's the person you're arguing with logging in with multiple accounts lol.
Yep, that's an old Casio model, Mr. "All modern calculators", proving yet again that you can't back up your own statements 😂
No need to wait - just scroll back through this thread and look at all the sources I already posted 🙄
You know none of the calculators you're referring to are commercial right? They're all free to use, and that tells you how much effort was put into them. The only e-calc I've ever seen give a correct answer is MathGPT, which is indeed commercial now (I tried it before it went commercial), so we have a commercial e-calc giving the correct answer, and all the free ones giving the wrong answer 😂
So am I in case you didn't notice 😂
I've never seen more than 2 on any, Mr. Needs To Exaggerate Because Has No Actual Evidence Of Being Right 😂
You realize a calculator doesn't need to be a dedicated hardware, right? Windows calculator, MacOS calculator, Android calculator, and all web-based calculators count as well.
You have no clue what you're talking about. Wolfram Alpha is a commercial product (with a free-tier as is usual nowadays) and uses the same engine as Mathematica, which is used extensively in industry, academic institutions, and government agencies.
None of your sources has exponents in them, and that's very convenient for your mistake of mixing up juxtaposition and your invented rule.
Btw, ask yourself this as well: why would your invented interpretation of distributive law be necessary at all? It brings no benefit to the table at all. Juxtaposition arguably does, because it allows shorter notation, but your invention doesn't.
Please find a calculator that gives a result different to 128 for the expression
2(3+5)². You won't be able to, because it's the only correct answer. If you don't post a reproducible example of a solver anywhere coming to a different solution, I'll consider your argument defeated and ignore further engagement from your part. Have a nice day!You realise the calculator manufacturers have much more riding on their calculators being correct, right? 😂
Nope. Programmed by... programmers, who aren't earning any money from the calculator, and put the corresponding amount of effort into it.
says someone who just claimed that e-calcs count as much as actual, buy from a store, calculators 🤣
Also well known to give wrong answers
Nope! Academia warns against using it
In other words, you're admitting to trying to deflect from what's in Maths textbooks! 😂
It's the same rule, duh! Here it is in a textbook from more than 100 years ago when everything was still in brackets...
We've since then dropped the brackets from Factors which are a single Term. i.e. (a)(b+c) is now a(b+c), and (a)(b) is now ab. BTW would you like to explain how "my invented rule" appears in a textbook from more than 100 years ago? 🤣
It's not invented, it's required as the reverse rule to Factorising, duh 😂 And I don't need to ask myself - as usual, all you have to do is look in Maths textbooks for the reason 😂
Being able to reverse the process of Factorising brings no benefit to the table?? 🤣
It's the same thing duh 🤣 ab=(a)(b), a(b+c)=(a)(b+c) notice how they are the same thing, expanding BRACKETS?? 🤣
Maybe you've forgotten about FOIL...
Now, think carefully about this, what happens when b=0, and what happens when d=0, you got it yet?? 🤣
AKA Factorised Terms and Products 😂
Again, explain how "my invention" appears in textbooks that are more than 100 years old. I'll wait 🤣
Have you noticed yet that everything you think is correct is actually wrong as per Maths textbooks?? 🤣
says person who has been comprehensively defeated by Maths textbooks and is now trying to deflect away from that 🤣
I'll take that as an admission that you're wrong then, having been unable to debunk any Maths textbooks. See ya
Like how the 5 in the first image isn't?
BWAHAHAHAHAHA! And how exactly do you think they got from 5(17) to 85 without distributing?? 🤣 Spoiler alert, this is what they actually did...
5(17)=(5x17)=85
They do that throughout the book, because they think it's so trivial to get from 5(17) to 85, that if you don't know how to do it without writing (5x17) first, then you have deeper problems than just not knowing how to Distribute 😂
5(17) means they didn't distribute 5(3+14) into 5*3+5*14.
These textbooks unambiguously disagree.
That's right, they Distributed the 5(17) into (5x17), and your point is?
With you, yes, and your point is?
The first textbook only gets 5(17) by not doing what the second textbook says to do with 5(3+14).
First image says 'always simplify inside,' and shows that.
Second image says 'everything inside must be multiplied,' and shows that.
You're such an incompetent troll that you proved yourself wrong within the same post.
Because the first textbook is illustrating do brackets from the inside out, which the second textbook isn't doing (it only has one set of brackets, not nested brackets like the first one). They even tell you that right before the example. They still are both Distributing. You're also ignoring that they actually wrote 5[3+(14)], so they are resolving the inner brackets first, exactly as they said they were doing. 🙄 The 5 is outside the outermost brackets, and so they Distribute when they reach the outermost brackets. This is so not complicated - I don't know why you struggle with it so much 🙄
And then says to Distribute, and shows that 🙄 "A number next to anything in brackets means the contents of the brackets should be multiplied".
Yep, that's right, same as I've been telling you the whole time 😂
Ah, no, you did, again - you even just quoted that the second one also says to Distribute! BWAHAHAHAHAHAHAHA! 😂 I'll remember that you just called yourself an incompetent troll going forward. 😂
I think I know what you're missing - perhaps intentionally 🙄 - in a(b+c), c can be equal to 0. It can be any number, not just positive and negative, leaving us with a(b)=(axb), which is also what I've been saying all along (not sure how you missed it, other than to deliberately ignore it)
Nope! I've said a(b+c)=(ab+ac) is correct.
You mean I know that, because it disobeys The Distributive Law 🙄 The expression you're looking for is 2x(3+5)², which is indeed not subject to Distribution, since the 2 is not next to the brackets.
Instead I've stuck to one actual law of Maths, a(b+c)=(ab+ac).
The Distributive Law, including c=0 🙄 Not sure why you would think c=0 is somehow an exception from a law
No, the rules of Maths is the point
Says person who thinks c=0 is somehow an exception that isn't allowed,🙄but can't cite any textbook which says that
Dude you're not even hitting the right reply buttons anymore. Is that what you do when you're drunk? It'd explain leading with 'nope! I've said exactly what you accused me of.'
You keep pretending distribution is different from multiplication:
And then posting images that explicitly say the contents of the brackets should be multiplied. Or that they can be simplified first. I am not playing dueling-sources with you, because your own sources call bullshit on what you keep hassling strangers about.
Yes I am
Is that why you think I'm hitting the wrong buttons?
I have no idea what you're talking about. Maybe stop drinking
No pretending - is is different - it's why you get different answers to 8/2(1+3) (Distribution) and 8/2x(1+3) (Multiplication) 😂
B 8/2(1+3)=8/(2+6)=8/8
E
DM 8/8=1
AS
B 8/2x(1+3)=8/2x4
E
DM 8/2x4=4x4=16
AS
That's right.
The "contents OF THE BRACKETS", done in the BRACKETS step , not the MULTIPLICATION step - there you go quoting proof that I'm correct! 😂
That's right, you can simplify then DISTRIBUTE, both part of the BRACKETS step, and your point is?
B 8/2(1+3)=8/2(4)=8/(2x4)=8/8
E
DM 8/8=1 <== same answer
AS
No, because you haven't got any 😂
says person failing to give a single example of that EVER happenning 😂
I'll take that as an admission of being wrong then. Thanks for playing
This is your own source - and it says, juxtaposition is just multiplication. It doesn't mean E=mc^2^ is E=(mc)^2^.
Throwing other numbers on there is like arguing 1+2 is different from 2+1 because 8/1+2 is different from 8/2+1.
inside brackets. Don't leave out the inside brackets that they have specifically said you must use - "Parentheses must be introduced"! 🤣 BTW, this is a 19th Century textbook, from before they started calling them PRODUCTS 🙄
No, it means E=mc² is E=mcc=(mxcxc)
I have no idea what you're talking about 🙄
You've harassed a dozen people to say only 5*3+5*14 is correct, to the point you think 2(3+5)^2^ isn't 2*8^2^.
If you'd stuck to one dogmatic answer you could pretend it's a pet peeve. But you've concisely proven you don't give a shit - the harassment is the point. Quote, posture, emoji, repeat, when you can't do algebra right.