Afaik the order of operations doesn’t have distributive property in it. It would instead simply become multiplication and would go left to right and would therefore be 16.
If you agree that parenthesis go first then the equation becomes 8/2x4. Then it’s simply left to right because multiplication does not take precedence over division. What’s the nuanced talk? That M comes before D in PEMDAS?
In this more sophisticated convention, which is often used in algebra, implicit multiplication is given higher priority than explicit multiplication or explicit division, in which those operations are written explicitly with symbols like x * / or ÷. Under this more sophisticated convention, the implicit multiplication in 2(2 + 2) is given higher priority than the explicit division in 8÷2(2 + 2). In other words, 2(2+2) should be evaluated first. Doing so yields 8÷2(2 + 2) = 8÷8 = 1. By the same rule, many commenters argued that the expression 8 ÷ 2(4) was not synonymous with 8÷2x4, because the parentheses demanded immediate resolution, thus giving 8÷8 = 1 again.
If you agree that parenthesis go first then the equation becomes 8/2x4
No, it becomes 8/(2x4). You can’t remove brackets unless there’s only 1 term left inside. Removing them prematurely flips the 4 from being in the denominator to being in the numerator, hence the wrong answer.
No it doesn’t? You treat parenthesis as it’s own variable or equation. X/Y*Z. X is 8. Y is 2. And z is 2+2, or 4. Why did you add brackets to the 2? They were never there from the first equation. You can’t just multiply Y to Z and ignore X.
I put back the brackets that you had prematurely removed when you wrote 8/2x4. You can’t remove brackets unless there is only 1 term left inside. 2(4)=(2x4)=(8)=8. When you removed the brackets prematurely you flipped the 4 from being in the denominator to being in the numerator, hence the wrong answer.
Considering how conflicting and confident we are that we are both correct, clearly there’s an issue with order of operations and how brackets work. Otherwise this wouldn’t be such a debating issue. We were taught that 2(2) is the same as 2x2.
It’s not in debate in any Maths textbooks, which is something none of the people claiming ambiguity ever reference.
We were taught that 2(2) is the same as 2x2
It’s the same as (2x2), which is 1 term, not 2x2, which is 2 terms, which is why you can’t prematurely remove the brackets. See worked example in this textbook…
OK, so in that picture you sent, the bottom part of it where it says you multiply the brackets by the number preceding it. Take that and put it to the right of the devision equation.
If you just put those numbers into brackets you’ll also have to put 8/2 in brackets as well. Then it’s (8/2)x(2+2). The answer is 16. Your way the answer is 1. Which is wrong.
Yes, the answer to that is 16, which isn’t the same as 8/2(2+2) (since you added a multiply to it and changed the expression).
you’ll also have to put 8/2 in brackets as well
No, 8/2 is two terms. I see you didn’t read the link about Terms then. If you put 8/2 into brackets, then you just changed the expression, and thus also the answer. According to your logic - add more brackets to the left - 4+8/2(2+2)=(4+8/2)(2+2)=32
The problem is that there’s no “external” parentheses to really tell us which is right:
(8 / 2) * 4or8 / (2 * 4)The amount of comments here shows how much debate this “simple” thing generates
When there are no parentheses, you process left to right on the same tier of operations. That’s how it’s always been processed.
Afaik the order of operations doesn’t have distributive property in it. It would instead simply become multiplication and would go left to right and would therefore be 16.
The Distributive Law applies to all bracketed terms that have a coefficient. It’s literally the first step in solving brackets.
If you agree that parenthesis go first then the equation becomes 8/2x4. Then it’s simply left to right because multiplication does not take precedence over division. What’s the nuanced talk? That M comes before D in PEMDAS?
Finally someone in here who knows math. Thank you.
deleted by creator
My observation was mainly based on this other comment
https://programming.dev/comment/5414285
No, it becomes 8/(2x4). You can’t remove brackets unless there’s only 1 term left inside. Removing them prematurely flips the 4 from being in the denominator to being in the numerator, hence the wrong answer.
No it doesn’t? You treat parenthesis as it’s own variable or equation. X/Y*Z. X is 8. Y is 2. And z is 2+2, or 4. Why did you add brackets to the 2? They were never there from the first equation. You can’t just multiply Y to Z and ignore X.
Exactly! 2(2+2) is a Term subject to The Distributive Law
But it isn’t. It’s X/YZ.
I put back the brackets that you had prematurely removed when you wrote 8/2x4. You can’t remove brackets unless there is only 1 term left inside. 2(4)=(2x4)=(8)=8. When you removed the brackets prematurely you flipped the 4 from being in the denominator to being in the numerator, hence the wrong answer.
Yes they were. The original equation is 8/2(2+2).
Considering how conflicting and confident we are that we are both correct, clearly there’s an issue with order of operations and how brackets work. Otherwise this wouldn’t be such a debating issue. We were taught that 2(2) is the same as 2x2.
It’s not in debate in any Maths textbooks, which is something none of the people claiming ambiguity ever reference.
It’s the same as (2x2), which is 1 term, not 2x2, which is 2 terms, which is why you can’t prematurely remove the brackets. See worked example in this textbook…
OK, so in that picture you sent, the bottom part of it where it says you multiply the brackets by the number preceding it. Take that and put it to the right of the devision equation.
If you just put those numbers into brackets you’ll also have to put 8/2 in brackets as well. Then it’s (8/2)x(2+2). The answer is 16. Your way the answer is 1. Which is wrong.
Yes, the answer to that is 16, which isn’t the same as 8/2(2+2) (since you added a multiply to it and changed the expression).
No, 8/2 is two terms. I see you didn’t read the link about Terms then. If you put 8/2 into brackets, then you just changed the expression, and thus also the answer. According to your logic - add more brackets to the left - 4+8/2(2+2)=(4+8/2)(2+2)=32
The Distributive Law tells us it’s the latter.