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
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BIDMAS and PEMDAS is the same thing, one just use Brackets, Indices the other Parentheses, Exponents for the exact same thing.
It is a question of what words are used to describe something, English is not identical in all countries. Just compare it to if the sidewalk, pavement, or footpath is correct, they are different names for the same thing in different countries
If we just use Parentheses, Exponents, Multiplication/Division, Addition/Subtraction and look at the logic.
Having parentheses first makes sense because they is the symbol we use when the normal order of operation is incorrect. How would you represent (7+3) /10 if the division had higher priority? If it had () would be meaningless.
The next part is the exponent. It is simply more common that 2 * 3^5 is the same as 2*(3^5) compared to (2*3)^5 like if you what to write down the prime factors of a number this case it is 486
for the same reason, we give multiplication and division the same priority as addition and subtraction. It is not uncommon that you have two parts with some operation and add them there then multiple
If you purchase times like a carrot that cost 5 and 2 apples that cost 3 each the expression is 5 + 2*3 which would be 5 + (2*3) if addition is higher than multiplication You would need more parenthesis if you did it the other way around.
There is not really a correct order except for parentheses that need to be the highest for them to work. For the rest, the important part is the one that writes the expression agrees with the one that read it. There is one common standard so it is not a good reason to avoid it
You need an order of operation if the operators are between the operands (what is operating on like numbers), this is called infix notation. You can have postfix notation, commonly known as https://en.wikipedia.org/wiki/Reverse_Polish_notation where the operators are after the operations.
3 + 4 become 3 4 +
You put the number in a stack and use them on the top values in the order they come
2*(3^5) will be 2 3 5 ^ *
(2*3)^5 will be 2 3 * 5 ^
It might not be as simple to read but it has been used on some calculators especially early ones because it is simpler to implement and the number of buttons you need to press can be reduced. Handling parenthesis can be quite hard if the calculator can just show one number at a time. It was really popular with HP calculators that still support that type of operation
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