Late Sunday night poser

[toml_12953]

(10-27-2024 04:10 PM)dm319 Wrote:  

(10-27-2024 02:28 AM)toml_12953 Wrote:  but the complete rule states

There are no complete rules - PEMDAS is just a mnemonic.

I've never seen the term 'implied multiplication' in any textbook or book of algebra. I believe it originated on a blog.

Instead, they have been 'terms' or 'products', which are made up of coefficients and factors.

PEMDAS applies to operators working on terms.

1÷2a means 1÷(2 x a), because 2a is a term. It has already been multiplied.

And there is historical evidence to show that this is how it has been done.

I was trying to find the historical references, but it looks like internet archive is still down, though this video* has some historical references.

Thankfully, with RPN, at least our calculators get it right for both of us.

*I don't completely agree with that video - she talks about the books 'breaking the rules' with their own examples, but you only think rules have been broken if you don't spot the terms in the expressions.

In the USA, some teachers say that 1÷2a is the same as 1 ÷ (2 * a) since the obelus (÷) groups everything on the left as a unit and everything on the right as a unit. Others say that multiplication and division are performed left to right so 1÷2a = (1 ÷ 2) * a. Go figure!