Which Property?

Date: 10/11/2005 at 16:52:33
From: Falon
Subject: how do you tell what properties belong to what math problem

I am working on a problem that is asking "name the property shown by
each statement".  The problem is "55+6 is equal to 6+55".  Is that a
commutative property?

I get confused when I see this kind of problem because I get the
properties mixed up.

Date: 10/11/2005 at 23:24:09
From: Doctor Peterson
Subject: Re: how do you tell what properties belong to what math problem

Hi, Falon.

You're right about that example.  What you need to do is to look at 
the expressions on the two sides and ask WHAT CHANGED?

If the change is a change in the ORDER of two numbers (say, two 
numbers that are being added together), then the commutative property
is being used.  For example:

  3(4+5) = 3(5+4)     (only change is 4+5 to 5+4)
    ---      ---

If the change is a change ONLY in the location of PARENTHESES around a
pair of the SAME operation, the associative property is being used.
For example:

  3+(4+5) = (3+4)+5   (only change is in where the parentheses are)
    -   -   -   -

If the change is from something times a sum to the sum of two products
(changing the order in which BOTH addition and multiplication are
done), it is the distributive property:

  3(4+5) = 3*4 + 3*5  (rather than first adding 4 and 5, we first
    ---    ---   ---   multiply each of them by 3)

There are other properties, but these are the most easily confused.

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


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