Convention of order of operations

In summary, the conversation discusses the PEMDAS order of operations convention and its significance. It questions whether math would be the same or different if we changed the convention, but ultimately concludes that the convention is convenient and any changes would not be significant. An alternative notation, reverse Polish notation, is mentioned but is not widely used.
  • #1
Mr Davis 97
1,462
44
To what extent is the PEMDAS order of operations convention, and to what extent is this convention significant? For example, how would math change if we stipulated that ##1+2*3 = 3*3 = 9##? Would it be the same or would it be completely different?
 
Mathematics news on Phys.org
  • #2
You'd have to write things differently; e.g. 1 + (2*3) = 1 + 6 = 7. I tend to think the present convention is convenient but I could well be biased. I can't see any fundamental changes happening if we switched to a different convention: important changes would only occur if some expressions became impossible or very awkward to write--or suddenly much easier--and I can't think of any that would be.

Of course, if we did switch, it would be like suddenly having to drive on the other side of the road and reading mathematics written before the change would be like reading a foreign language.
 
Last edited:
  • #3
Mr Davis 97 said:
To what extent is the PEMDAS order of operations convention, and to what extent is this convention significant? For example, how would math change if we stipulated that ##1+2*3 = 3*3 = 9##? Would it be the same or would it be completely different?
If you want to have a look what happened last time we discussed this ...
https://www.physicsforums.com/threads/biggest-science-or-math-pet-peeve.885541/
(I don't remember where exactly in this thread PEDMAS started, but once it did, you barely couldn't get rid of it.)
 
  • #4
Change to reverse Polish notation!

((1+2)*3 ⇒ 1⊥2+3*, 1 + (2*3) ⇒1⊥2⊥3*+) (the ⊥ sign is just used to indicate "enter")
 
  • Like
Likes alan2 and berkeman
  • #5

Cute. (But several decades after it was introduced on calculators, RPN doesn't seem to have really caught on for some reason.)
 

FAQ: Convention of order of operations

What is the convention of order of operations?

The convention of order of operations is a set of rules that determines the sequence in which mathematical operations should be performed. It is used to ensure a consistent and unambiguous interpretation of mathematical expressions.

What are the rules of the convention of order of operations?

The rules of the convention of order of operations are as follows: 1) Perform operations within parentheses first, 2) Perform multiplication and division from left to right, 3) Perform addition and subtraction from left to right.

Why is the convention of order of operations important?

The convention of order of operations is important because it allows for a standardized way of solving mathematical expressions, ensuring that the same result is obtained regardless of who is solving the problem. It also eliminates ambiguity and confusion when evaluating complex expressions.

Are there exceptions to the convention of order of operations?

There are certain situations where the convention of order of operations may not apply, such as when using exponential or logarithmic functions. In these cases, it is important to follow the specific rules for evaluating those types of functions.

How can I remember the convention of order of operations?

A common mnemonic device to remember the convention of order of operations is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. Another helpful tip is to remember that multiplication and division have the same priority, as do addition and subtraction, and should be performed from left to right.

Similar threads

Replies
1
Views
2K
Replies
14
Views
1K
Replies
5
Views
1K
Replies
2
Views
929
Replies
20
Views
5K
Replies
45
Views
4K
Replies
1
Views
3K
Replies
4
Views
331
Back
Top