Order of operations - what is 6÷2(1+2) ?

[Wes Loewer]

I am finding this whole discussion rather humorous as it all boils down to which convention you are using, like spelling color or colour.

The Prime completely eliminates this issue in Textbook entry by always using a horizontal fraction bar. Problem solved! Everyone is happy!
Every multi-line calculator should do this.


Some have indicated that we use juxtaposition when writing by hand. I encourage my students to avoid using / for division unless there is only one value after it, like 2/3 or 1/x. If a student writes "1/2x", I might interpret it as 1/(2x). But "1/2 x" with a space might be interpreted as (1/2)x. But when you write with pencil and paper, spaces can vary in size. At what point do you switch meanings?

1/2x
1/2 x
1/2 x
1/2 x
1/2 x
1/2 x

Therefore, I avoid using / except for the unambiguous cases.


Even the symbol can be problematic. I had one former engineer tell me that he would say that
a + b ÷ c + d = a + (b ÷ c) + d
but
a + b / c + d = (a + b) / (c + d)
because he took the / to be a text replacement of the horizontal fraction bar.