Under normal interpretations of pemdas this is simply wrong, but it’s ok. Left to right only applies very last, meaning the divisor operator must literally come after 2(4).
This isn’t really one of the ambiguous ones but it’s fair to consider it unclear.
Pemdas puts division and multiplication on the same level, so 34/22 is 12 not 3. Implicit multiplication is also multiplication. It’s a question of convention, but by default, it’s 16.
I don’t know what you’re on about with your distributive law thing. That just states that a*(b + c) = a*b + a*c, and has literally no relation to notation.
I wasn’t. I quoted Maths textbooks, and if you read further you’ll find I also quoted historical Maths documents, as well as showed some proofs.
I didn’t say the distributive property, I said The Distributive Law. The Distributive Law isn’t ax(b+c)=ab+ac (2 terms), it’s a(b+c)=(ab+ac) (1 term), but inaccuracies are to be expected, given that’s a wikipedia article and not a Maths textbook.
I did read the answers, try doing that yourself
I see people explaining how it’s not ambiguous. Other people continuing to insist it is ambiguous doesn’t mean it is.
If you read the wikipedia article, you would find it also stating the distributive law, literally in the first sentence, which is just that the distributive property holds for elemental algebra. This is something you learn in elementary school, I don’t think you’d need any qualification besides that, but be assured that I am sufficiently qualified :)
By the way, Wikipedia is not intrinsically less accurate than maths textbooks. Wikipedia has mistakes, sure, but I’ve found enough mistakes (and had them corrected for further editions) in textbooks.
Your textbooks are correct, but you are misunderstanding them. As previously mentioned, the distributive law is about an algebraic substitution, not a notational convention. Whether you write it as a(b+c) = ab + ac or as a*(b+c) = a*b + a*c is insubstantial.
also stating the distributive law, literally in the first sentence
Except what it states is the Distributive property, not The Distributive Law. If I call a Koala a Koala Bear, that doesn’t mean it’s a bear - it just means I used the wrong name. And again, not a Maths textbook - whoever wrote that demonstrably doesn’t know the difference between the property and the law.
This is something you learn in elementary school
No it isn’t. This is a year 7 topic. In Primary School they are only given bracketed terms without a coefficient (thus don’t need to know The Distributive Law).
be assured that I am sufficiently qualified
No, I’m not assured of that when you’re quoting wikipedia instead of Maths textbooks, and don’t know the difference between The Distributive Property and The Distributive Law, nor know which grade this is taught to.
Wikipedia is not intrinsically less accurate than maths textbooks
BWAHAHAHAHA! You know how many wrong things I’ve seen in there? And I’m not even talking about Maths! Ever heard of edit wars? Whatever ends up on the page is whatever the admin believes. Wikipedia is “like an encyclopedia” in the same way that Madonna is like a virgin.
but you are misunderstanding them
And yet you have failed to point out how/why/where. In all of your comments here, you haven’t even addressed The Distributive Law at all.
Whether you write it as a(b+c) = ab + ac or as a*(b+c) = ab + ac is insubstantial
And neither of those examples is about The Distributive Law - they are both to do with The Distributive Property (and you wrote the first one wrong anyway - it’s a(b+c)=(ab+ac). Premature removal of brackets is how many people end up with the wrong answer).
About the ambiguity: If I write f^{-1}(x), without context, you have literally no way of knowing whether I am talking about a multiplicative or a functional inverse, which means that it is ambiguous. It’s correct notation in both cases, used since forever, but you need to explicitly disambiguate if you want to use it.
I hope this helps you more than the stackexchange post?
If I write f^{-1}(x), without context, you have literally no way of knowing whether I am talking about a multiplicative or a functional inverse, which means that it is ambiguous
The inverse of the function is f(x)^-1. i.e. the negative exponent applies to the whole function, not just the x (since f(x) is a single term).
Under normal interpretations of pemdas this is simply wrong, but it’s ok. Left to right only applies very last, meaning the divisor operator must literally come after 2(4).
This isn’t really one of the ambiguous ones but it’s fair to consider it unclear.
Pemdas puts division and multiplication on the same level, so 34/22 is 12 not 3. Implicit multiplication is also multiplication. It’s a question of convention, but by default, it’s 16.
https://en.m.wikipedia.org/wiki/Order_of_operations
There’s no such thing as implicit multiplication. The answer is 1.
I don’t know what you’re on about with your distributive law thing. That just states that
a*(b + c) = a*b + a*c, and has literally no relation to notation.And “math is never ambiguous” is a very bold claim, and certainly doesn’t hold for mathematical notation. For some simple exanples, see here: https://math.stackexchange.com/questions/1024280/most-ambiguous-and-inconsistent-phrases-and-notations-in-maths#1024302
No, The Distributive Law states that a(b+c)=(ab+ac), and that you must expand before you simplify.
Examples by people who simply don’t remember all the rules of Maths. Did you read the answers?
Please learn some math before making more blatantly incorrect statements. Quoting yourself as a source is… an interesting thing to do.
https://en.m.wikipedia.org/wiki/Distributive_property
I did read the answers, try doing that yourself.
I’m a Maths teacher - how about you?
I wasn’t. I quoted Maths textbooks, and if you read further you’ll find I also quoted historical Maths documents, as well as showed some proofs.
I didn’t say the distributive property, I said The Distributive Law. The Distributive Law isn’t ax(b+c)=ab+ac (2 terms), it’s a(b+c)=(ab+ac) (1 term), but inaccuracies are to be expected, given that’s a wikipedia article and not a Maths textbook.
I see people explaining how it’s not ambiguous. Other people continuing to insist it is ambiguous doesn’t mean it is.
If you read the wikipedia article, you would find it also stating the distributive law, literally in the first sentence, which is just that the distributive property holds for elemental algebra. This is something you learn in elementary school, I don’t think you’d need any qualification besides that, but be assured that I am sufficiently qualified :)
By the way, Wikipedia is not intrinsically less accurate than maths textbooks. Wikipedia has mistakes, sure, but I’ve found enough mistakes (and had them corrected for further editions) in textbooks. Your textbooks are correct, but you are misunderstanding them. As previously mentioned, the distributive law is about an algebraic substitution, not a notational convention. Whether you write it as
a(b+c) = ab + acor asa*(b+c) = a*b + a*cis insubstantial.…which isn’t a Maths textbook!
Except what it states is the Distributive property, not The Distributive Law. If I call a Koala a Koala Bear, that doesn’t mean it’s a bear - it just means I used the wrong name. And again, not a Maths textbook - whoever wrote that demonstrably doesn’t know the difference between the property and the law.
No it isn’t. This is a year 7 topic. In Primary School they are only given bracketed terms without a coefficient (thus don’t need to know The Distributive Law).
No, I’m not assured of that when you’re quoting wikipedia instead of Maths textbooks, and don’t know the difference between The Distributive Property and The Distributive Law, nor know which grade this is taught to.
BWAHAHAHAHA! You know how many wrong things I’ve seen in there? And I’m not even talking about Maths! Ever heard of edit wars? Whatever ends up on the page is whatever the admin believes. Wikipedia is “like an encyclopedia” in the same way that Madonna is like a virgin.
And yet you have failed to point out how/why/where. In all of your comments here, you haven’t even addressed The Distributive Law at all.
And neither of those examples is about The Distributive Law - they are both to do with The Distributive Property (and you wrote the first one wrong anyway - it’s a(b+c)=(ab+ac). Premature removal of brackets is how many people end up with the wrong answer).
About the ambiguity: If I write
f^{-1}(x), without context, you have literally no way of knowing whether I am talking about a multiplicative or a functional inverse, which means that it is ambiguous. It’s correct notation in both cases, used since forever, but you need to explicitly disambiguate if you want to use it.I hope this helps you more than the stackexchange post?
The inverse of the function is f(x)^-1. i.e. the negative exponent applies to the whole function, not just the x (since f(x) is a single term).
Incorrect, pemdas puts multiplication before division.
I always thought pemdas was more like P/E/MD/AS with MD and AS occurring left to right
This is how I was taught, but also people don’t really use the ÷ symbol in algebra beyond like 6th grade
Yes they do, just pick up a high school Maths textbook (in a country which uses obelus rather than colon).
And “Multiplication” refers literally to multiplication signs, of which there are none in this question.
#MathsIsNeverAmbiguous if you follow all the rules of Maths (there’s a lot of people here who aren’t).