Brackets

Date: 01/29/2001 at 23:40:29
From: James
Subject: Brackets

I had a test and on it there was a question about brackets. I would 
like you to explain to me how these brackets [] work. 

Thanks! (In advance.)

Date: 01/30/2001 at 08:54:53
From: Doctor Peterson
Subject: Re: Brackets

Hi, James.

I'm going to assume you are referring to the ordinary use of brackets, 
where they mean the same thing as parentheses, "()". There are special 
ways they are used in more advanced fields, but you probably are not 
doing that.

You can read about this in our FAQ on "Order of Operations":

  http://mathforum.org/dr.math/faq/faq.order.operations.html   

Brackets are a way to modify the order in which you would ordinarily 
evaluate an expression, when you want to say something that can't be 
written the usual way. For example, suppose I want you to add the 
numbers 1 and 2, then multiply the result by 3. If I wrote

    1 + 2 * 3

(using "*" as the multiplication sign), it would mean that you would 
multiply 2 and 3 first, then add 1, since the rules say to multiply 
first. But if I "package" the expression "1 + 2" together in such a 
way that you are required to evaluate it first and then treat it as a 
single number, then you will do what I want. That's what brackets are 
for. When I write

    [1 + 2] * 3

it means to first turn everything inside the [...] into a single 
number, then multiply by 3. The answer will be 9.

That's what it's all about, in general. If you have some problems you 
can't figure out using this basic explanation, send them to us so we 
can explain any details I've missed. It might help if you could show 
us how you tried to solve the problems, so we can see where you need 
help.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/