Posted on 12/28/2024 8:35:57 AM PST by Jonty30
I am getting a lot of people who say the answer is 9, but you can get 9 from 6/2(1+2) if you separate the 2 from the 2(1+2), which seems incorrect to me. I view the 2(1+2) as a complete phrase within the mathematical question, so I think it needs to be solved before you move left to right.
6/2(1+2) = 6/2(3) = 6/6 = 1 But there are a lot of people who want to write the question as 6/2 x (1+2), which is the only way you will get 9.
The order of operations, that is, the order in which the operations in an expression are usually performed, results from a convention adopted throughout mathematics, science, technology and many computer programming languages. It is summarized as:
Parentheses
Exponentiation
Multiplication and division
Addition and subtraction
This means that to evaluate an expression, one first evaluates any sub-expression inside parentheses, working inside to outside if there is more than one set. Whether inside parenthesis or not, the operation that is higher in the above list should be applied first. Operations of the same precedence are conventionally evaluated from left to right.
Reminds me of the old joke:
“Let’s eat Grandma!”
Does that mean you’re inviting Grandma to dinner?
Or suggesting Grandma is dinner?
Absence of the comma leads to ambiguity.
This expression as written is a deliberate attempt to be ambiguous unnecessarily.
I’m not a mathematician. But an engineer who’s been through a lot of math both theoretical and practical. No one yet has died or been injured from my calculations. I would interpret the correct answer as “1”.
But, I would question the source of the equation to understand the intention. And if the correct answer is meaningful, reprimand them for the ambiguity.
As written, I see it as a polynomial fraction. The / separates numerator from denominator. The denominator is a binomial expansion. Simplification Leads to 6/6 or 1.
No there’s definitely ambiguity. Partly because it’s being written in line. OP seems to think it’s:
6
___
2(1+2)
That would give his answer. That’s where the ambiguity is, is the dividing line just over the 2 over over the expression 2 could be part of?
100% correct and most of these pinheads know you are correct, but being on FR, they want to see how many angels can dance on the top of their pinheads.
40 plus posts to show they once took a math course and still remember something about it.
Your separation using the / is correct and with that fact, the rest takes care of all the BS that was spouted about this could be or that could be...
Which is the root of all these discussions that happen on social media. They do a really bad job of writing the equation, then people read it differently, and they come up with different answers. The smart way to write it in 1 line for the answer you get is:
6/(2x(1+2))
The smart was to write it for the answer most are getting is:
6/2X(1+2)
The worst possible way to write it for either answer is the one you found. It’s just there to confuse.
Nuts. Now the cat is out of the bag.
💯%
Or make the correct answer 3/4!
I doubt that you will find any Math textbook (regardless of date of print) where these "newer rules" are not taught. Orders of operations have not changed.
The problem is that students don't learn "orders of operations" - they only learn PEMDAS.
PEMDAS, when strictly applied is incorrect. "Orders of operations" when applied as taught will always be correct and unambiguous.
1) parentheses, and ALL other grouping symbols
2) multiplication and division left to right in order
3) addition and subtraction left to right in order
Retired Algebra Teacher - BS in Mathematics
for everything past "/" to be considered a "denominator" an additional set of parentheses are required.
Try any TI calculator
3/4. Don’t you have Facebook?
Strictly speaking, you are correct.
I misread. Answer is 1.
My first answer was to the problem posed in the headline. The second answer was to the problem as stated in the body.
“Retired Algebra Teacher - BS in Mathematics”
I have an MEd, made straight As in math, and had a perfect score on my AP calculus exam. If credentials matter.
What I was taught, right or wrong, was that multiplication was done before division. Addition and subtraction order does not matter. The outcome is the same. Parentheses are obvious.
I don’t recall seeing math problems like this in college, but through high school, I would have assumed the multiplication is first even though it comes after the division. That certainly might be wrong. You may be correct.
I tried to find an authoritative answer to the question and found this:
https://jeff560.tripod.com/operation.html
“In A History of Mathematical Notations (1928-1929) Florian Cajori writes (vol. 1, page 274), ‘If an arithmetical or algebraical term contains ÷ and ×, there is at present no agreement as to which sign shall be used first.’”
Apparently, there is no final authority on notation and order of operations, and this has been debated for more than a century.
So, I’d recommend that anyone teaching or testing this topic should define which standard is being used.
As someone who has written computer code involving math operations for many years, I’d say that the rules are very well defined at the coding level for whatever language is being used. It cannot be otherwise.
ChatGPT gave the same answer you did. However, I asked for a citation and it gave me Wikipedia. And Wikipedia actually said the standard is not agreed on:
https://en.wikipedia.org/wiki/Order_of_operations
Mixed division and multiplication
There is no universal convention for interpreting an expression containing both division denoted by ‘÷’ and multiplication denoted by ‘×’. Proposed conventions include assigning the operations equal precedence and evaluating them from left to right, or equivalently treating division as multiplication by the reciprocal and then evaluating in any order;[10] evaluating all multiplications first followed by divisions from left to right; or eschewing such expressions and instead always disambiguating them by explicit parentheses.[11]
10. Chrystal, George (1904) [1886]. Algebra. Vol. 1 (5th ed.). “Division”, Ch. 1 §§19–26, pp. 14–20.
Chrystal’s book was the canonical source in English about secondary school algebra of the turn of the 20th century, and plausibly the source for many later descriptions of the order of operations. However, while Chrystal’s book initially establishes a rigid rule for evaluating expressions involving ‘÷’ and ‘×’ symbols, it later consistently gives implicit multiplication higher precedence than division when writing inline fractions, without ever explicitly discussing the discrepancy between formal rule and common practice.
11. Cajori, Florian (1928). A History of Mathematical Notations. Vol. 1. La Salle, Illinois: Open Court. §242. “Order of operations in terms containing both ÷ and ×”, p. 274.
When this simple question was posited I had no idea it would uncover such a complex issue.
Thanks for adding to the discussion because it forced me to dig deeper and learn something new.
“The order of operations... results from a convention adopted throughout mathematics, science, technology and many computer programming languages... Operations of the same precedence are conventionally evaluated from left to right.”
Meant to include you in my previous post:
https://freerepublic.com/focus/chat/4286860/posts?page=56#56
I learned Please Excuse My Dear Aunt Sally.
Thank you.
“...a warning in making one’s intent clear.”
So many problems occur due to miscommunication. Some are deadly. Same goes for math problems. The one thing with these stupid math equation questions is that people are doing math just for the sake of math.
The intent of the equation would perhaps be clear in the real world, which is what math is really for.
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