Under pemdas divisor operators must literally be completed after multiplication. They are not of equal priority unless you restructure the problem to be of multiplication form, which requires making assumptions about the intent of the expression.
Okay, let me put it in other words: Pemdas and bodmas are bullshit. They are made up to help you memorise the order of operations. Multiplication and division are on the same level, so you do them linearly aka left to right.
Pemdas and bodmas are not bullshit, they are a standard to disambiguate expression communication. They are order of operations. Multiplication and division are not on the same level, they are distinct operations which form the identity when combined with a multiplication.
Similarly, log(x) and e^x are not the same operation, but form identity when composited.
Formulations of division in algebra allow it to be at the same priority as multiplication by restructuring it as multiplication, but that requires formulating the expression a particular way. The ÷ operator however is strictly division. That’s its purpose. It’s not a fantastic operator for common usage because of this.
There are valid orders of operations, such as depmas which I just made up which would make the above expression extremely ambiguous. Completely mathematically valid, order of ops is an established convention, not mathematical fact.
I agree that pemdas is a bad acronym for teaching exactly because it can be misunderstood as multiplication coming before division and addition coming before substraction, when it’s not the case.
Luckily we don’t have that acronym where I grew up. We learned “dot before line” (as our division and multiplication symbols involve dots while the addition and substraction symbols only involve lines).
Dpemas would be a fully valid mathematical order of operations. As would only left to right. Or right to left. Or only parenthesis.
The ambiguity remains due to the ambiguity of division operators in single line phrasing and implied multiplication, not because of the shape of the operator lol
Under pemdas divisor operators must literally be completed after multiplication. They are not of equal priority unless you restructure the problem to be of multiplication form, which requires making assumptions about the intent of the expression.
Okay, let me put it in other words: Pemdas and bodmas are bullshit. They are made up to help you memorise the order of operations. Multiplication and division are on the same level, so you do them linearly aka left to right.
Pemdas and bodmas are not bullshit, they are a standard to disambiguate expression communication. They are order of operations. Multiplication and division are not on the same level, they are distinct operations which form the identity when combined with a multiplication.
Similarly, log(x) and e^x are not the same operation, but form identity when composited.
Formulations of division in algebra allow it to be at the same priority as multiplication by restructuring it as multiplication, but that requires formulating the expression a particular way. The ÷ operator however is strictly division. That’s its purpose. It’s not a fantastic operator for common usage because of this.
There are valid orders of operations, such as depmas which I just made up which would make the above expression extremely ambiguous. Completely mathematically valid, order of ops is an established convention, not mathematical fact.
This comment is the epitome of being confidently wrong on the internet.
For one misinterpretation? Are you sure about that?
There was 3 misinterpretations - see my reply to them.
I made a hashtag for people #LoudlyNotUnderstandingThings :-)
No, they’re not.
Yes, they are.
In other words, they are the inverse operation of each other - welcome to why they have the same precedence.
It’s a mathematical fact.
Except they are and you are literally demonstrating why PEMDAS is shitty acronym.
We’re agreed that order of operations is a poorly taught subject and pemdas would benefit from revision.
I agree that pemdas is a bad acronym for teaching exactly because it can be misunderstood as multiplication coming before division and addition coming before substraction, when it’s not the case.
Luckily we don’t have that acronym where I grew up. We learned “dot before line” (as our division and multiplication symbols involve dots while the addition and substraction symbols only involve lines).
However as I demonstrated an order of operations in which mult is before div is valid.
In this case your dot before line still would result in the above expression being ambiguous, as well.
You didn’t demonstrated that and it’s not.
We are also taught left to right, so no.
Dpemas would be a fully valid mathematical order of operations. As would only left to right. Or right to left. Or only parenthesis.
The ambiguity remains due to the ambiguity of division operators in single line phrasing and implied multiplication, not because of the shape of the operator lol
Not literally. It’s only a mnemonic, not the actual rules.
Yes, they are. Binary operators have equal precedence, and unary operators have equal precedence.