You’re implicitly reading 2x as one variable, but not implicitly reading 2(2+2).
The answer is 1, per standard notation. If you put an explicit multiplication, only then would it be 16. Frankly, I’ll trust my Japanese calculator’s maths over Americans who butcher language as well :p
Really though there is a bit of academic debate on the subject. Wikipedia even has a section on it.
Incidentally, I just found another juicy rabbit hole: the UK version of the acronym is BODMAS (Brackets, Order, etc) and is widely attributed to Achilles Reselfelt. However, it seems that this person doesn’t even exist! There was a recent reddit thread on it, and as a result the textbook they tried asking about it ended up removing the reference. In any case, the earliest known version of that acronym is from 1945. Suffice it to say, though, orders of operation have been around far longer than the acronym, so it doesn’t really make sense to apply a strict interpretation of the new simplified learning tool when the nuance was established long before.
What many people don’t realize is that the “rules” we teach are only an attempt at DESCRIBING what mathematicians did for a long time without explicitly stating what rules they were following. They do not PRESCRIBE what inherently must be done, a priori. In just the same way, English grammar came long after English itself, and has sometimes been taught in a way that is inconsistent with actual practice, in an attempt to make the language seem perfectly rational.
Correct, you’re reading 2x as one variable, and you’re not reading 2(2+2) as one variable. That is the proper way of reading it. 2(2+2) is not one variable, and should not be read as such; it is a sequence of operations, and should be read with that in mind.
The answer is not 1 per any correct rules of mathematical calculation. If your calculator is giving you 1, you have a bad calculator that is incapable of performing this kind of operation.
Dude you really are being stubborn. You clearly haven’t studied maths beyond grade school level.
In academia, even in America, either implicit multiplication is considered first before explicit multiplication and division, or, as per the American Physical Society, multiplication always comes first.
If you’d read even just the wikipedia article you would have realised this.
You’re taking what you were taught in school as if it were gospel. Do yourself a favour and fact check. What they teach in school is often simplified so that more people can understand the basics.
In no level of mathematics is a calculation written as above correctly solved as 1. You’re attempting to extrapolate from the natural reading of variable handling a mythical order of operations that applies in every instance. This is false.
Multiplication and division are essentially the same operation expressed differently, and they occur at the same level of priority. The only reason we evaluate things like 2x before other multiplication or division operations to the left is because the natural reading of variable components like this makes sense, and we implicitly treat it as (2x).
There is no separation of multiplication types in the order of operations.
According to the American Mathematical Society and the American Physics Society, the answer is absolutely 1.
I’m not making any extrapolation here, I’m following practices that have been standard for far longer than the PEDMAS acronym - which you are attempting to retroactively apply.
Implicit multiplication, or juxtaposition, comes before division and explicit multiplication. It’s just harder to teach kids that when they’re starting out - they keep it to a simple acronym. But that’s the way it goes, like I say, you wouldn’t split 2x across the denominator in exactly the same way you wouldn’t split 2(2+2).
You’re implicitly reading 2x as one variable, but not implicitly reading 2(2+2).
The answer is 1, per standard notation. If you put an explicit multiplication, only then would it be 16. Frankly, I’ll trust my Japanese calculator’s maths over Americans who butcher language as well :p
Really though there is a bit of academic debate on the subject. Wikipedia even has a section on it.
Incidentally, I just found another juicy rabbit hole: the UK version of the acronym is BODMAS (Brackets, Order, etc) and is widely attributed to Achilles Reselfelt. However, it seems that this person doesn’t even exist! There was a recent reddit thread on it, and as a result the textbook they tried asking about it ended up removing the reference. In any case, the earliest known version of that acronym is from 1945. Suffice it to say, though, orders of operation have been around far longer than the acronym, so it doesn’t really make sense to apply a strict interpretation of the new simplified learning tool when the nuance was established long before.
This link perhaps explains it better:
Correct, you’re reading 2x as one variable, and you’re not reading 2(2+2) as one variable. That is the proper way of reading it. 2(2+2) is not one variable, and should not be read as such; it is a sequence of operations, and should be read with that in mind.
The answer is not 1 per any correct rules of mathematical calculation. If your calculator is giving you 1, you have a bad calculator that is incapable of performing this kind of operation.
OK, you’re just ignoring me, and the wealth of evidence I’ve provided that contradicts what you’re saying. Goodbye.
You’ve given no evidence, you’ve given bullheaded insistence on an incorrect answer.
Check the links in my previous comment, look it up on Wikipedia. The jury is very much out. You’re the one being bullheaded here.
The last link is well worth a read.
No, the jury is not out, you’re attempting to read from common convention regarding variables an order of operation that doesn’t exist.
Dude you really are being stubborn. You clearly haven’t studied maths beyond grade school level.
In academia, even in America, either implicit multiplication is considered first before explicit multiplication and division, or, as per the American Physical Society, multiplication always comes first.
If you’d read even just the wikipedia article you would have realised this.
You’re taking what you were taught in school as if it were gospel. Do yourself a favour and fact check. What they teach in school is often simplified so that more people can understand the basics.
In no level of mathematics is a calculation written as above correctly solved as 1. You’re attempting to extrapolate from the natural reading of variable handling a mythical order of operations that applies in every instance. This is false.
Multiplication and division are essentially the same operation expressed differently, and they occur at the same level of priority. The only reason we evaluate things like 2x before other multiplication or division operations to the left is because the natural reading of variable components like this makes sense, and we implicitly treat it as (2x).
There is no separation of multiplication types in the order of operations.
According to the American Mathematical Society and the American Physics Society, the answer is absolutely 1.
I’m not making any extrapolation here, I’m following practices that have been standard for far longer than the PEDMAS acronym - which you are attempting to retroactively apply.
Implicit multiplication, or juxtaposition, comes before division and explicit multiplication. It’s just harder to teach kids that when they’re starting out - they keep it to a simple acronym. But that’s the way it goes, like I say, you wouldn’t split 2x across the denominator in exactly the same way you wouldn’t split 2(2+2).