Why is addition easier than subtraction?

Here is one explanation:

"Addition is easier than subtraction for me. The reason is that 
addition is symmetric or commutative. (See the Dr. Math Glossary of 
Properties and select "commutative": 
   http://mathforum.org/dr.math/faq/faq.property.glossary.html   .)  

For example:

  1 + 2

is the same thing as:

  2 + 1

Subtraction is NOT symmetric:

  1 - 2

is NOT the same as:

  2 - 1"

from

http://mathforum.org/library/drmath/view/57873.html

Wow, a great explanation. My daughter the Science Teacher, calls that
gobbledy-gook.

I suspect, though, it might actually be because kids learn to count UP
first, which is what is involved in learning the concepts of addition,
but do not usually learn to count DOWN, which is what is involved in
learning the concepts of subtraction.

If I look at web sites about teaching children addition and
subtraction, there are different ways that subtraction is approached.

When there are a number of ways to work a problem, it takes more
mental work than if only one way is available (or, in some cases, than
if only one way is taught). More generally, since there are several
ways to solve a subtraction problem but just one way to solve an
addition problem, subtraction is more difficult to master.

From the web sites, it appears that, in teaching subtraction, you can
use counting down, counting back up, sometimes making choices between
the two, and sometimes recasting subtraction as a mystery addition
problem.

I've seen differences like this:

Addition is simpler because it is "symmetric," that is, if you are
adding 3 and 8, it makes no difference (other than time) whether you
start with 3 and count up 8 or start with 8 and count up 3. In either
case, the process is the same.

With subtraction, there is more than one process you can use. For "11
- 8", you can start at 11 and count down to 8 (keeping track of both
two series at the same time, "10, 9, 8", and "1, 2, 3" - with the
latter generally done by moving fingers and then counting them later).
You can also count up from 8 to 11. At least one site recommends using
one of these methods for some problems and the other method for other
subtraction problems.

In other cases, some sites recommend recasting the problem as an
addition problem, that is, recast "11 - 8" as "8 + ? = 11." I suppose
that this is used after a child knows that addition facts and hasn't
learned all the subtraction facts.

 One educational site evaluated mental strategies in addition and
subtraction and states:

"The Addition and Subtraction Strategies domain exemplifies the
emphasis in Number on the development of an increasingly sophisticated
repertoire of mental strategies."

"2. Count on
Counts on from one number to find the total of two collections.

3. Count back/count down to/count up from
Given a subtraction situation, chooses appropriately from strategies
including count back, count down to and count up from."

I take point 2 as referring to addition and there being only one
method in learning the concept. I take point 3 as referring to
subtraction and there being several ways to go about subtraction. The
statement implies that there are times when each of these ways can be
more efficient in doing mental subtraction than the other ways.

I suspect that Dr. Math was referring more to learning addition and
subtraction facts, that is, when you learn "3 + 8," you don't have to
worry about learning "8 + 3." On the other hand, knowing "11 - 3" is
not the same as knowing "3 - 11." Though knowing the answer to "11 -3"
will let you get to the answer to "11 - 8," you have to go through
some some mental steps to do so. You don't have to do anything like
this for "3 + 8" vs. "8 + 3."

In summary, addition has one main process "count up" and order isn't
important. Subtraction can be solved several ways and order is
important.

Here are three of the sites I looked at:

http://www.redshift.com/~bonajo/mmathsubtract.htm

http://www.mathcats.com/grownupcats/ideabankaddition.html

http://www.sofweb.vic.edu.au/eys/num/ENRP/wholeschdes/STANDTARGETS2a.HTM

Subtraction should be viewed only as the difference between two numbers.

This way the difference can easily be viewed as a positive quantity.

I don't believe personally there are any more than 2 real numbers (1 and 0).
There is only addition; no subtraction, division or multiplication.

5 is only a name for 1+1+1+1+1.
The difference between -2 and 1 is three ones.
I guess it could be a little confusing that 1+(-2)is -1 but that is addition,
not subtraction,heh heh heh.
2 times 3 is only (1+1) * (1+1+1) or really just (1+1+1)+(1+1+1).
Division is really multiplication and thus really addition.
Once you grasp this intuitively numbers are fun instead of scary.

I could be wrong and don't ask me to explain imaginary numbers.

Now I am confused.

addition seems to be natural for us.  we are wired for simple
arithmetics.  as an educator, i know of two brain disorders that a
manifested  by a patent lack of mathematical skills, acalculia and
discalculia.  this implies that, most of us, need only practice to
learn to do addition.  Subtraction is just a reverse form of addition.
 The brain may take a bit longer to adjust to this point of view.  for
example, 7-4=3 is the same as asking,"4 plus what number is 7."