Yes, the fundamentals the same, higher orders come first. BUT...
-Multiplication comes before division in some forms, like PEMDAS. In the example I use, this changes the answer.
-When you apply an operation, you should specify what it is operating on. In all of these acronyms, addition comes before subtraction, but with a different example:
2 - 2 + 2
The minus sign only applies to the middle term, by convention. It is the equivalent of "adding negative two". You can quickly see that this expression is equal to 2.
But if you use one of these acronyms, you end with this expression evaluating to -2. I would say it is almost universally accepted that 2 is the correct answer, and -2 is incorrect. Basically, all these acronyms end up being useless waste of time.
I don't know if I conveyed this the first time, but, as a lover of pure mathematics, this is something that does not have application in life or in study. It's an utterly useless waste of time. There is never a case where someone give you numbers like this, where it is not clear what order the numbers should be applied in.
Multiplication comes before division in some forms, like PEMDAS. In the example I use, this changes the answer
If you have both multiplication and division then you do them left to right. PEMDAS doesn't mean multiplication first, nor does BEDMAS mean division first. It's PE(MD)(AS) and BE(DM)(AS) where the bracketed parts are done left to right.
you should specify what it is operating on
Left associativity means it always operates on the following term. i.e. terms are associated with the sign on their left.
The minus sign only applies to the middle term, by convention
By the rule of left associativity.
But if you use one of these acronyms, you end with this expression evaluating to -2
No it doesn't. How on Earth did you manage to get -2?
all these acronyms end up being useless waste of time
No they're not, but I don't know yet where you're going wrong with them without seeing your working out.
If you have both multiplication and division then you do them left to right. PEMDAS doesnβt mean multiplication first, nor does BEDMAS mean division first. Itβs PE(MD)(AS) and BE(DM)(AS) where the bracketed parts are done left to right.
You are adding more rules to protect a convention that doesn't work and doesn't mention them to begin with. If all that matters is higher orders first, then why bother having an acronym? Just say "Brackets, then higher orders". Bam. Solved it with less words than any of the acronyms.
Left associativity means it always operates on the following term. i.e. terms are associated with the sign on their left.
As someone who studied mathematics, computer science, and engineering in university, I certainly don't you to tell me how to do bare bones arithmetic. I know operators apply to the numbers to their right. Everyone does. You jumped right on by the point.
With 2/2*2, you don't know if it is 2*2/2, or 2/(2*2). When you are dividing by numbers, you put them all in the denominator. If I had to put it in a line, I would at least do 2/(2)*2, to show what is in the denominator. If it is ambiguous, you have done it incorrectly.
By the rule of left associativity.
BY CONVENTION, as I said. You don't have to repeat what I said a second time.
No it doesnβt. How on Earth did you manage to get -2?
wow. geez. I wonder.
If you can't follow the steps guided for such a simple example, maybe we just shouldn't have this conversation. It's not like you could have tried in your head different orders to combine 3 numbers.
You are adding more rules
I'm stating the existing rules.
If all that matters is higher orders first
I don't even know what you mean by that. We have the acronyms as a reminder of the rules, as I already said.
I know operators apply to the numbers to their right.
If you know that then how did you get 2-2+2=-2?
With 2/22, you donβt know if it is 22/2, or 2/(2*2)
Yes you do - left associativity. i.e. there's no brackets.
When you are dividing by numbers, you put them all in the denominator
Only the first term following a division goes in the denominator - left associativity.
BY CONVENTION, as I said. You donβt have to repeat what I said a second time.
I didn't. You said it was a convention, and I corrected you that it's a rule.
Itβs not like you could have tried in your head different orders to combine 3 numbers.
addition first
2-2+2=4-2=2
subtraction first
2-2+2=-2+2+2=-2+4=2
left to right
2-2+2=0+2=2
3 different orders, all the same answer
