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Q&A #4952


Decomposition in math subtraction

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From: Gail (for Teacher2Teacher Service)
Date: Oct 25, 2000 at 23:41:58
Subject: Re: Decomposition in math subtraction

I believe that "decomposition algorithm" refers to the standard algorithm
used in many American schools for subtraction.  Decomposing means breaking
down, and that is what is done when you subtract, in a way.

Here is a step leading up to that algorithm that might help you understand
what is happening:

When you want to subtract 987 and 123, what you are really doing is
subtracting each place value separately.    So you could look at the problem
this way:               or this way:

 987            9 hundreds   8 tens   7 ones
-123           -1 hundred    2 tens   3 ones
 ____           ______________________________

that is pretty easy to solve.

But what about this one:  907  123.     Now there is a problem you can't
subtract easily in the tens so you have to "regroup" what you have:

 907     9 hundreds   0 tens   7 ones     8 hundreds  10 tens   7 ones
-123    -1 hundred    2 tens   3 ones    -1 hundred    2 tens   3 ones
____    _____________________________   ______________________________

That works because 8 hundreds 10 tens and 7 ones is the same thing as 9
hundreds 0 tens and 7 ones.

Here is another:  6007 - 451

 6 thousands 0 hundreds 0 tens 7 ones  5 thousands 10 hundreds 0 tens 7 ones
-            4 hundred  5 tens 1 ones    -          4 hundred  5 tens 1 ones
_____________________________________   ____________________________________


But that still doesn't fix all the places for us, so lets "regroup" again:

5 thousands 10 hundreds 0 tens 7 ones   5 thousands 9 hundreds 10 tens 7 ones
-            4 hundred  5 tens 1 ones    -          4 hundred   5 tens 1 ones
_____________________________________   ____________________________________


That works because 5 thousands 9 hundreds 10 tens 7 ones is the same thing as
6 thousands 0 hundreds 0 tens 7 ones.

If you take it one step at a time, it should be easier for your daughter to
figure out.  You might want to try writing the numbers out by place values
for a while, and then going back to the "shorthand" method we learned in
school.

If you think she is still having trouble with this "regrouping", there are
some chip trading games that can help her feel more comfortable with that
skill.   Just write back and let us know.  Good luck!  :-)

 -Gail, for the T2T service


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