Expert: Paul Klarreich - 12/16/2006

Question
Dear Paul,
Could you tell me a problem using parentheses, exponents, sighned numbers, and all the four operations using the order of operations? You can just give me a problem. Or if you want you can show the work. Just to tell you it is not a homework question.
Thanks!
Carly

Answer
Questioner:  Carly
Category:  Advanced Math
 
Subject:  Math
Question:  Dear Paul,
Could you tell me a problem using parentheses, exponents, signed numbers, and all the four operations using the order of operations? You can just give me a problem. Or if you want you can show the work. Just to tell you it is not a homework question.
Thanks!
Carly
...............................................
Hi, Carly,

Well, here's an expression that involves a bunch of these operations:

Evaluate:

(x^2 + 1)^2 - 2x^2
------------------
 5 - sqrt(9)

for x = 3

Assuming you are studying algebra (you didn't say) you should be learning that the fundamental idea in algebra is ORDER OF OPERATIONS in many guises.  So in the example above, you see that:

A. x^2, a power, is evaluated BEFORE addition or multiplication.
B. Operations that are grouped in parentheses are done before operations that are outside.
C. A long bar, such as a fraction line, which you see above, is a grouping symbol.  (Also a long bar that is part of a root expression is a grouping symbol.  It's hard for me to make one on the computer.)

Please note;

A. If you work that example, the answer is 41.

B. It is OK to send me a homework example, as long as you don't push it.  Don't send me your whole assignment, just a couple of examples that you can't do and I'll be happy to try.  If you do send a HW example, make sure to send the whole example with the instructions from the book.

C. Tell me just what math course you are taking; many examples can be done more than one way and I have to know which way is appropriate for you.

Look at some archived answers on this site to get an idea of the notation that is generally used.