why in algebra class they teach the order of operations (PEMDAS) in that order. Is this just an arbitrary standard everyone agreed on or was it the result of higher math only making sense when equations are done in that order?

Question

Title

In: 1362

Answer 1

It’s not entirety a random choice. Parentheses, for example, kinda have to go first. If they appear anywhere else in the order they function as a deprioritizing tool, and this gives you fairly convoluted equations if you need to group certain terms, where you rapidly need to start adding multiple parentheses to ensure the terms are treated as a group. Similarly exponents kinda need to come next (again as they function as a group, or you start to need a lot of parentheses to get them to work.

It’s also not really arbitrary that addition/subtraction and multiplication/division are equal in precedence as division is just multiplication of the inverse of the number you are dividing by (Eg 5/3 is 5 x 1/3. They’re the same functions so it makes sense they are equal in precedence.

Although you could argue the division should be after multiplication as it *could* be taken to mean to include multiple terms before and after- and when writing by hand this is how it is commonly used:

A**x** + B

——————-

C**x** + D

When writing on screens you’d normally have to format it:

(A**x** + B) / (C**x** + D)

But on balance there are a *lot* of cases where you’d have to add in parentheses to treat division like this, so it makes more sense to use parentheses to group terms when needed, albeit this gives rise to the debate over “implicit multiplication” where terms are assumed grouped for multiplication when they’re adjacent to each other without an actual sign.

Eg:

Y = 1/3**x**

Where if x = 2 you’d wind up with 1/6 instead of 2/3 – this is common notation in engineering and science, but not in grade school, which results in those viral math problems you see floating about about the order of operations.