What Do Parentheses Mean?

Date: 08/15/2002 at 23:52:45
From: Jeffrey
Subject: Algebra

Dear Dr. Math,

I was working on some algebra questions and the problems had 
parentheses in them. I didn't know you had to multiply to find the 
answer. Can you help me find ways to figure out what the parentheses 
mean?

Date: 08/16/2002 at 14:00:05
From: Doctor Peterson
Subject: Re: Algebra

Hi, Jeffrey.

I suppose you mean something like

    2(3+4) = 2*7 = 14    [here "*" is the multiplication sign]

or

    (x-1)(x-2) = 0       [here "x" is a variable, and the equation
                          is true if x is either 1 or 2]

In such cases, the parentheses themselves don't tell you to multiply; 
they just mean that what's inside is to be treated as a single value, 
as when you first add 3+4 to get 7 before doing anything to it. But 
when two things (other than two numbers) are placed side by side in 
an algebraic expression, that means they are multiplied:

    xy

means the product of the variables x and y, while

    x(y+1)

means the product of x and y+1. When you are working only with 
numbers, rather than variables, the only way you can put two things 
side by side is when one or both are in parentheses, since

    12

has to mean twelve, not 1 times 2. So often the first time you see 
this notation for multiplication, it involves parentheses.

Here is a brief discussion of what parentheses are for:

   Brackets
   http://mathforum.org/library/drmath/view/58445.html 

and here is a little more detail:

   Explaining Order of Operations
   http://mathforum.org/library/drmath/view/57199.html 

If you have any further questions, feel free to write back.

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