The problem is that there's no "external" parentheses to really tell us which is right: (8 / 2) * 4 or 8 / (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.
Afaik the order of operations doesnβt have distributive property in it
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.
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 Γ·. Under this more sophisticated convention, the implicit multiplication in 2(2 + 2) is given higher priority than the explicit division in 8Γ·2(2 + 2). In other words, 2(2+2) should be evaluated first. Doing so yields 8Γ·2(2 + 2) = 8Γ·8 = 1. By the same rule, many commenters argued that the expression 8 Γ· 2(4) was not synonymous with 8Γ·2x4, because the parentheses demanded immediate resolution, thus giving 8Γ·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.
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.
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.
The Distributive Law tells us it's the latter.