48÷2(9+3) and similar

Hurkyl

An issue of mathematical grammar circulating the internet lately has been how to read a mathematical expression like

[tex]48 \div 2 (9 + 3)[/tex]

that involves a combination of division and implied multiplication.

The standard way to read arithmetic expression (i.e. order of operations) involves dealing with parentheses first, then you do all division and multiplication operations from left to right, then all addition and subtraction operations from left to right.

So, this expression is computed as

[tex]48 \div 2 (12)[/tex]
[tex]24 (12)[/tex]
[tex]288[/tex]

It doesn't matter whether or not the multiplication is made explicit, as in

[tex]48 \div 2 \times (9+3) = 288[/tex]

or if division is represented by a slash, as in

[tex]48 / 2 (9+3) = 288[/tex]

all of these variations mean the same thing.



One thing to keep in mind is that not everybody follows the standard. Some people prefer to do implied multiplication before other multiplication and division operations. Some people prefer to do all multiplications before division with /. Some people even prefer to do addition before division with /.

So, when you are reading math from an unfamiliar source, make sure you know what convention they are adopting. And no matter what convention you prefer, you really ought to write things in an unambiguous fashion -- e.g. you should avoid

[tex]48 / 2 (9+3)[/tex]

and instead use the crystal clear

[tex](48 / 2) (9+3)[/tex]