Sorry, mate, TLDR.
I skimmed through it, I'm glad you learned some new concepts, still find it hilarious that you're then trying to turn it around and pretend like I didn't understand something, but it's all good fun.
Enjoy your newfound knowledge and maybe work on not being so prickly.
Which would explain why you don’t know The Distributive Law, which is taught in Year 7
Me: consistently using the Distributive Law throughout the thread.
You: "Which would explain why you don’t know The Distributive Law, which is taught in Year 7"
How does that work again?
No, just evidence to back up your claims, but of course you don’t have any
I showed you two, you showed yourself one - how many more do you need?
You know reading things again doesn’t change what’s written right??
True, but reading again carefully would change what you thought was written, friend.
still say, do all addition first
OK, here's a challenge for you - quote the bit that says "do all addition first".
Well, apparently you are, since there are no Maths textbooks listed in the sources
Awww, you're so cute! You think all maths knowledge only comes from school textbooks! <3
Let’s go to the screenshot… (...) Nope, see screenshot of you saying they are the same
Ah, so you don't know what "context" is. Got it. I'll try to keep things easier to understand for you going forward.
Now you’re just rehashing the same already-debunked rubbish. The whole point of the mnemonics is for those who don’t understand, just follow these steps
In which case they will often make mistakes, as shown by the "9 minus whatever plus something" equation I did. Again, I get that you're only on your "day two on the Internet" so you're not aware of it, but these kinds of equations cause people A LOT of trouble.
Don't get me wrong - I get what you're saying. That if the people who don't understand the order of operations understood the Distributive Law, then their lack of understanding of the order of operations wouldn't matter. But, I hope, you get where this line of thinking fails, right?
Did that already with the textbooks and worked examples. Maybe you need to read it slowly?
Ah, so you're saying that a site teaching maths is wrong, and your proof is the fact that you don't understand how sentences work? Cool, cool.
Nope. Again let’s go to the screenshot…
Which proves what, in your mind...?
AS doesn’t reinforce doing A before S?
A is not before S. A is equal to S in the order of operations. As proven here, here, here or here, which also conveniently mentions the two different mnemonics in PEMDAS and BODMAS (where, I'm sure your keen eye will notice, the D and M are flipped).
Here's a short quote from the second to last source:
Multiplication and division can be done together. In other words, it doesn’t matter if you do division or multiplication first, but they must be done after parentheses and exponents and before addition and subtraction. (...) Addition and subtraction also work together. You can do subtraction first, or you can do addition first. They are part of the same step, however, they can only be done after items in parentheses, exponents, and any multiplication and division.
So, there's that.
Yep, you’ve got none. You thought Wikipedia counted as a Maths textbook
No, I thought you were capable of checking the sources on the bottom of the article. My bad. But now I also understand that you wouldn't consider actual mathematical research as sources, because it needs to be a school book for you. I hope the university article links above will be good enough?
I knew it all along - you were the one saying that the brackets matter in PE(MD)(AS), which we’ve now comprehensively debunked 😂
You have an extremely weird fixation on brackets, friend. The only thing we've debunked is your understanding of mathematical fundamentals and reading skills. :(
No they weren’t! You have such a short memory, no wonder you ended up contradicting yourself! 🤣 Let’s go to the screenshot…
Oh no! You caught me on misremembering one of the couple of examples I gave you! NOOOOOO! My life is RUINED!
So now, again, why did you start talking about 1 + 3 if the examples were 2 - 2 and 2 / 2?
you can deflect again 😂
Awww... You can't answer these questions? I mean, I'm not surprised considering what you've shown so far but I was hoping you'd at least try.
Let’s go to the screenshot, again…
And where are the brackets, friend? Do your keen eyes see (2-2) or whatever, or 2+(-2)?
But, as I see you'll just never let go of this misconception of yours, here you are:
1.7 Negative numbers and the use of brackets
Rules of negative numbers
The rules for using negative numbers can be summarised as follows:
Addition and subtraction
- Adding a negative number is the same as subtracting a positive 50 + (-30) = 50 – 30 = 20
- Subtracting a negative number is the same as adding a positive 50 – (-30) = 50 + 30 = 80
You can see the exact same notation as I used, in the exact same context. When you read the rest of that Level 1 introductory lesson, you'll also learn that you can actually ONLY use brackets to denote negative numbers, like so: 2 + (2), which would equal to 2 - 2. Incredible, I know!
Nope. your point that brackets matter in PE(MD)(AS) is still wrong, as proven 😂
I mean... Come on - brackets DO matter in PEMDAS, they're the very first item on the list (Brackets == Parentheses). You're getting all confused here.
As to the notation of "PE(MD)(AS)" - you may be surprised to learn, but brackets used in the context of language don't mean the same thing as brackets used in the context of maths, which means that the "(MD)" doesn't somehow mean I was suggesting these should be considered to... always be in brackets? Like, I don't even know what you were trying to say here.
says person who proved it was wrong 😂
Again, it's OK to have a vivid imagination, but you're just making yourself look silly when you talk about it with others as if it's fact.
Nope! You claimed it was entirely different if you did that. Again, let’s go to the screenshot…
Yes, I agree, the way I worded that was poor. Setting pronumerals to 1 is the same as just removing them from the notation completely.
says the person actually trying to do that, as proven by the screenshots 😂
It's OK, you already understood the core concept of what I meant, I firmly believe that we can get you to understand the whole thing within a week! :)
So you want to keep it here, because the other is full of screenshots proving you wrong and you want to ignore them?? 🤣🤣🤣
Again with the reading comprehension issues? No, friend, I'm suggesting you keep responding where we were already talking, instead of here.
I know that you finally understood what I was talking about, as shown by your replies in the other comment, but it's OK to keep it all to a single thread.
says person who has no evidence whatsoever
Yes, because I finished third grade in primary school. Do you also expect evidence of gravity?
And the questions I did ask you didn’t answer anyway
Go back and read the comments again. I know they're getting lengthy, but I'm sure if you put your mind to it, you can find the answers.
Which proved you were wrong
Yeah, if you ignore what the text says and just assume it does what you want, then sure, it proves me wrong. However, if you actually read the letters on the screenshot, you'll find that it does not, in fact, prove me wrong, it does the opposite.
Well, here you go proving you have a severe comprehension problem anyway… 😂
Oh wow, so you're also incapable of scrolling down to the sources part of the article...?
Yep, gives the same result, but does not say that the number and it’s inverse are the same thing 😂
Yeah, speaking of reading comprehension - I never said anything like that. I said that, in terms of the order of operations, addition/subtraction and multiplication/division are equal, because they can be inverted (subtraction into addition of negative numbers, division into multiplication of fractions) to achieve, as you observed, the exact same result. Which means that - if you ensure that children learn and understand that concept, you can skip subtraction and division from the mnemonics, because children will understand that - again, in terms of order of operations - division = multiplication, and subtraction = addition.
Which also wasn’t a Maths textbook
OK, how about this: let's do what grown up mathematicians do: prove that what I linked to is wrong.
Which they never are (...) Nope, no-one thinks that
One more time: welcome to the Internet, I'm sure you'll find many surprises here, but overall it's a pretty great place.
Addition first for 9-3+2 is +(9+2)-3=+11-3=8 same correct answer as left to right, which is why the textbook teaches you to do it that way
I like how you're doing exactly what I'm talking about while still saying I'm incorrect.
Which you’re demonstrated repeatedly that you don’t, and here we are
OK, sure, quote one example equation I did here that proves I'm not understanding these concepts. :)
Which is a totally valid thing to do, as is taught by the textbook
But is not reinforced by the mnemonic itself. Reading comprehension, remember?
Which is also a valid thing to do. That’s the whole point, it does not matter which order you do addition and subtraction 😂
I'm glad I was able to explain this to you. You go ahead and pretend like you're explaining it to me, I'm just happy you finally managed to understand that.
And when they do calculate the addition first, they get an answer of 8, as I just proved a few comments back 😂 Add all the positive numbers, then subtract the total of all the negative numbers. This is so not complicated, and yet you seem to have trouble understanding it
See above.
From an example of how 2+2 and 1+3 aren’t the same thing, even though they equal the same value, which you are now trying to avoid addressing because you know it proves you are wrong 😂
Why are you bringing 1 + 3 into the mix when the examples were 2 + 2 and 2 * 2? What are you trying to say here?
I’m starting to wonder if you do, given you think 2/2 is the same thing as 2x½ - one has a fraction, the other doesn’t, but you think they are the same thing 🙄
I'm going to ask you a couple of questions so you can research that and then pretend to explain them to me, like you did above:
2 / 2?2 * ½?says person not remembering that they brought it up to begin with… 😂
There's no confusion from my side. I understand how brackets work and that was a perfectly valid use - for readability's sake.
says person who thinks doing addition first for 9-3+2 is 4
Now you're just inventing things I never said. That's not nice.
Not for 2-2 they don’t. Go ahead and cite one. I’ll wait
It wasn't 2 - 2, tho. Or did you fail to read that correctly too?
Which proves my point that you can do addition and subtraction in any order, given you just admitted that 2-2 and -2+2 give the same result 😂
Again, I'm glad you're slowly getting to the point I was making. It's weird how you're still phrasing it like I was somehow wrong, but I'm just happy you learned something.
The exact same thing as an expression written without pronumerals 😂 I see you’re still not understanding how pronumerals work then
Considering that's exactly what I did, how do you see that as me not understanding pronumerals? I'm asking out of sheer curiosity at this point.
and thus proving again that they can be done in any order 😂 It’s so hilarious watching you prove yourself wrong (...) [and the rest of the comment]
You're so cute when you're trying to turn this whole argument on its head after realising how silly your initial points were! <3
You do you, friend. Whatever makes you feel better about your ignorance.
Don't worry, friend! One day you'll look back at this and think "damn, I really was an idiot back then!"
It's not that "murder is cheap", it's that many countries figured out that holding a person indefinitely in prison doesn't do anything for their rehabilitation, only puts money in the prison's owner's pocket.
The point of most European prisons is to get the prisoner to understand and repent their crime, teach them some useful skills, and send them back to be a productive member of society. The point of US prisons is to just eliminate a person from public life in revenge.
The Polish lullabies include a song about a royal family (king, page, princess) who live in happiness and love until they get eaten by a cat, a dog, and a mouse. Only after singing about this massacre does the parent do a big reveal that they were made out of sugar, gingerbread, and marzipan, respectively ("Był sobie król"/"Once there was a king")
You can say that as much as you want and you’ll still be just as wrong.
That's the thing - I'm not wrong.
Noted that, yet again, you are unable to cite any Maths textbooks that agree with you
Yet again? You never asked for citations. I also didn't have to, as you did it for me with your screenshot.
But here you go:
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x^−1^, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. Dividing 1 by a real number yields its multiplicative inverse. For example, the reciprocal of 5 is one fifth (1/5 or 0.2) (...) Multiplying by a number is the same as dividing by its reciprocal and vice versa.
Here's another source if you're allergic to Wikipedia.
Again, the mnemonics are for people who don’t understand, which would be people like you! 😂
Again, the mnemonics, when taught without appropriate context, cause confusion in people like you, who think that the order of operations is set to: Multiplication → Division → Addition → Subtraction, instead of being (M or D, start from the left) → (A or S, start from the left).
Again, the mnemonics, when taught without appropriate context, cause people to think that 9-3+2 is 4, when the actual result is 8, because they think that they have to calculate the addition first.
What’s the result of 2+2? What’s the result of 1+3? Are 2+2 and 1+3 the same? No! 😂 2 apples + 2 oranges = 4 pieces of fruit. 3 apples and 1 orange = 4 pieces of fruit. Is 2 apples and 2 oranges the same as 3 apples and 1 orange? 😂 Anything else you want to embarrass yourself about not understanding?
WTF are you talking about? Where did you get the 1 and 3 from? Also... Do you not know what fractions are...?
You’re the one who brought it into the conversation - you tell me!
You're so very, very confused by all of this...
You’ll find most people find that less readable. Welcome to why textbooks never use them
I can see why you are finding them less readable - you have absolutely fundamental lacks in understanding of maths. And, sorry to burst your bubble, but maths textbooks all over the world use brackets all the time.
Just making it less readable
Not if you understand what they mean. Which is why they're confusing for you, I guess.
which haven’t changed at all in all that time 😂 2-3 has never and still does not require brackets, same as when Arithmetic was first written.
Now that I know that you have a fundamental lack of understanding how maths works, I apologise for using the brackets earlier. Let's try this: you can write 2 - 2 as -2 + 2, or - a slightly less legible version - as 2 + -2. You'll get the same result, and this inversion is a perfectly "legal" mathematical operation. Which shows you how addition and subtraction are equal.
and everyone was taught that the order of DM/MD does not matter. If it did then one of them would not exist
One more time, let me welcome you to the Internet, I'm sure you'll have a great time here!
Already posted a screenshot of one. You really need to work on your comprehension
We were not talking about monomials.
Set all the pronumerals to 1, and guess what you have - the exact same thing 😂 I see you don’t understand how pronumerals work either
If you set the pronumerals in addition/subtraction problems to 1, you would have something entirely different. And if you want to do 2x - 2x where x = 1, then your own posted fragment explains that you only need to calculate the arithmetic difference between the total postive/negative coefficients.
The arithmetic difference between -2 + 2 and 2 - 2 is the same, proving - again - that subtraction is equal to addition of a negative.
Which is my point. Which you are proving.
BTW you still have not cited any textbook whatsoever that agrees with anything that you have said
I didn't have to, you did it for me.
Yep, 1a-2a+3a-4a=a((1+3)-(2+4)). Now set a=1 and guess what you have? 😂
Now do -(2+4) + (1+3) and guess what you have?
You know the textbook just literally told you it is, right?? 😂
I already suggested this: read it again, but slower.
Oh, I realised that a long ago, but it's actually a kind of "mental exercise" for me. :) Cheers!
Whatever makes you feel better. :)