What is the logic behind PEMDAS?

Question

I know some places use BIDMAS as well. Overall though, to someone who knows little about mathematics, why is this the correct order? What’s the exact logic behind it

In: 6

Answer 1

It is a convention that, if followed, mathematical expressions can be written in a certain way without ambiguity. There could well be other conventions but this would require the expressions to be written differently. It just happens that for most mathematics, the agreed upon convention is PEMDAS or BODMAS (just different names for the same thing).

We follow conventions all the time especially in languages. They’re mostly the product of some logic and some tradition and, as long as they’re agreed upon, they make life simpler.

One could try to speak like Yoda, “the egg, red is” and more or less be comprehensible but, for most, the conventional “the egg is red” sounds more natural and more easily comprehended.

Mathematics is somewhat more precise and unforgiving because expressions can get fairly long. So without a convention, they add to errors and ambiguities.

So if someone writes 3 * x + 5, the convention is that multiply x by three then add 5. If we reversed the priority 3 * x + 5 becomes add five to x then multiply the sum by 3. Both conventions are workable if used consistently but if the order is interchangeable arbitrarily, math would be more confusing.