You apply natural reading to 2x because that looks and reads like a single number, and so you take it as a whole. This is convention only, and is implicitly reading it as (2x).
The same is not the case for 2(2+2). There is no variable in that, and it is accurately and correctly understood as 2×(2+2).
There is no order of operations which states that removal of the multiplication sign occurs prior to multiplication and division, and nothing outside the parentheses has any bearing on resolving the parentheses order of operations.
The answer to this is 16. Reading this and getting any other answer is misunderstanding it.
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.
You apply natural reading to 2x because that looks and reads like a single number, and so you take it as a whole. This is convention only, and is implicitly reading it as (2x).
The same is not the case for 2(2+2). There is no variable in that, and it is accurately and correctly understood as 2×(2+2).
There is no order of operations which states that removal of the multiplication sign occurs prior to multiplication and division, and nothing outside the parentheses has any bearing on resolving the parentheses order of operations.
The answer to this is 16. Reading this and getting any other answer is misunderstanding it.
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.