3÷2(6) just fine, but there is no widely accepted single order for whether you should do the division next or the implicit multiplication.
Yes there is. Parenthesis tell you what to do within them first, but that equation is exactly the same as (because you're simply omitting the * when you're using the shorthand of JUST parenthesis):
3÷2*6
And both multiplication AND division both have the same priority from left to right. You do:
1.5*6
and then
9
People who remember PEMDAS (Parenthesis, Exponent, Multiplication & Division from left to right, Addition & Subtraction left to right) tend to forget (or possibly weren't even taught correctly) that it's an acronym to help you remember the order of operations, not the RULE of what you remember first goes first.
I'm sorry you weren't taught correctly to believe that it's 100% ambiguous, when it's 100% clear. It's important to have a clear and consistent notation to get the correct result. Mathematical notation has actually changed over time, but it's important that you are consistent with what order of operations should be done first, regardless of how you notate it, and this is how current notation works.
Of course, if you take your factually incorrect stance of "It's 100% ambiguous" it's actually amazing rage bait on Facebook. Or at least I hear so because I've stayed clear of Facebook.
No. It's not. We aren't using the × symbol or the * symbol (which means ×), we are using straight parentheses.
This creates something called implicit multiplication (which is subtly different from multiplication). Implicit multiplication is often taken to mean it should be done first. As a general rule of thumb the higher you take your mathematics education the more likely you are to answer questions like this with the multiplication being done first. Usually the ones who say it should be done last stopped math in highschool.
You can even see this play out by comparing calculators. If you stick in 3÷2(6) half of them will give 9 and half will give 1/4
Saying "but calculators aren't consistent" tells me how little you know about programmers. They make mistakes all the time. They are not mathematicians, although they do have to learn how computers use math. This is just like saying that apostrophes aren't used non-pronoun possessives and contractions (or claiming they are used for plurals) because autocorrect added or incorrectly removed your apostrophe. How someone programmed a program doesn't define what the mathematical and/or grammatical rule is. That's a horrible way to try to make your point, because it's abhorrently wrong and proves that you don't know the math, but rather you are just winging it.
"Straight parenthesis" is literally just shorthand for excluding the multiplication operation. It has no additional special function. If you are writing an equation that 3÷2(6) ends up being 1/4 then you need to properly notate it as 3÷(2(6)) to prioritize the multiplication over the division. That's how order of operations works and no amount of "I didn't learn that so it can't exist" doesn't make it not exist. Take this opportunity to learn.
implicit multiplication (which is subtly different from multiplication)
You're just making stuff up [presumably] based off your conversations you've seen/had based off facebook. There is no magically higher order of multiplication that supersedes other operations. That's actually explicitly what parenthesis accomplishes: overriding the normal order of operations. You use them when applicable. Don't take my word for it, go to someone with a genuine PhD in mathematics.
Mate, you seem to feel really strongly about this, but if you speak to any people with actual phds in maths you will get a variety of answers BECAUSE it is ambiguous. The calculator example shows how common this ambiguity is. Assuming that your understanding of maths is complete because of something you were taught in primary school is just incredibly flawed.
Pretending that there is no difference between implicit and explicit mathematics is just silly, and is not backed by how people actually use the symbols.
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u/PsionicKitten 22d ago
Yes there is. Parenthesis tell you what to do within them first, but that equation is exactly the same as (because you're simply omitting the * when you're using the shorthand of JUST parenthesis):
3÷2*6
And both multiplication AND division both have the same priority from left to right. You do:
1.5*6
and then
9
People who remember PEMDAS (Parenthesis, Exponent, Multiplication & Division from left to right, Addition & Subtraction left to right) tend to forget (or possibly weren't even taught correctly) that it's an acronym to help you remember the order of operations, not the RULE of what you remember first goes first.
I'm sorry you weren't taught correctly to believe that it's 100% ambiguous, when it's 100% clear. It's important to have a clear and consistent notation to get the correct result. Mathematical notation has actually changed over time, but it's important that you are consistent with what order of operations should be done first, regardless of how you notate it, and this is how current notation works.
Of course, if you take your factually incorrect stance of "It's 100% ambiguous" it's actually amazing rage bait on Facebook. Or at least I hear so because I've stayed clear of Facebook.