Order of Operations with Parentheses

Date: 08/04/2001 at 19:00:18
From: Christie Babinski
Subject: Algebra And Order Of Operations

Dear Dr. Math,

Hello! I am having some trouble doing algebra and solving problems 
with order of operations. I am going into to seventh grade, but since 
I am in the GEM program I will be doing ninth grade math. Some of the 
problems I came across while reviewing were:

1.  3-(0-5)
2.  0+6+7+2x(0-0)
3.  (7+7)-0-6x2+7
4.  3+6-1+6

I know the answers to the problems but I still do not understand how 
to get the answers.

Thank you so much for your help.

Sincerely,
Christie Babinski

Date: 08/07/2001 at 13:49:34
From: Doctor Ian
Subject: Re: Algebra And Order Of Operations

Hi Christie,

Note that if we write

  2 + 3 * 4 + 5

by convention, we do the multiplication first:

  2 + 3 * 4 + 5 = 2 + 12 + 5

                = 14 + 5

                = 19

But what if we want to do the additions first?  Then we need to use
parentheses to indicate that:

  (2 + 3) * (4 + 5) = 5 * 9 

                    = 45

So whenever you see parentheses, the person who set up the expression
intends for you to do those operations first. And if you don't see any
parentheses, everyone assumes that you'll do multiplications and 
divisions before doing additions and subtractions. 

So, let's look at one of your problems:

  (7 + 7) - 0 - 6 * 2 + 7

We have some parentheses, so let's work on those first:

       14 - 0 - 6 * 2 + 7                  7 + 7 = 14

Now we have no parentheses, but we have a multiplication, so let's do 
that first:

          14 - 0 - 12 + 7                  6 * 2 = 12

Now we have only additions and subtractions, so let's do those left to
right:

              14 - 12 + 7                  14 - 0 = 14          

                    2 + 7                  14 - 12 = 2

                        9                  2 + 7 = 9

Can you follow the same steps to solve the rest of your problems? 

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