Question

Dear Mitch,

I really always hate doing subtraction problems where you have to borrow from one number and add the little one like my teacher calls regrouping, so this girl who's a teenager from down the block and stays with us on wensdays until my parents come home showed  me a different way to do it that she says is called equal addition that she learned from her Europe friend.  I never heard of it but it's easier.  And so before I ask my teacher if I can use it my mother said to find out if it always works.  Can you tell me, does it?  Just so you know what im talking about, it goes like this:

  54 you put a 1 in front of the 4, then instead of making the 5 into

 -37        a 4 you make the 3 into a 4

So you get

  5 14          

   1 7

Answer

Dear __________ (You forgot to give me your name!?!),

Good news!

Yes, it always works!

When we do regular math problems like the one you're writing about, we answer them using what we call "algorithms".  Algorithms is just a fancy name for a remembered method that we know we can rely upon to give us the right answer once we apply that method to our problem.  By the way, problems using algorithms are easier for most people than word problems, and MUCH easier for most people than what we call 'problem solving' where you have to figure out WHICH OPERATION to do before you start doing anything (like do you want to do addition or subtraction or multiplication or division?... And in what order should you do the operations? And on which numbers?)

Yes, for problems like the one you gave, it's just a matter of using the right algorithm.  And, using these math terms, the question you ask is this:  Does a different algorithm (from Europe(?)) work as well as the one your teacher taught you, which you know is correct but you like less.

And the answer is YES.  The method that your friend showed you is called the "Equal addition algorithm", and it is taught in many parts of the world.  Some people, like you, find it a little easier, because one of the steps involves addition instead of subtraction (when you add a one to the ten's column of the number on the bottom – which is the number being subtracted from the top one, instead of subtracting a one from the tens column of the top number, which is the number you are subtracting the smaller one from).

By the way, the method your teacher taught you that you call "borrowing" and your teacher calls "regrouping" is officially called "Decomposition" or "Renaming".  The reason that this method that you learned outside of school works as well is that the end result for the problem in both cases is that you get a number in the tens column that – when you do the subtraction – has you end up with the bottom number being one less than it would be before you borrowed a one, or added a one to the number being subtracted from it.

What we call the 'net result' or the 'answer', is an answer that is one less in the tens column than it would be if you forgot to add a one or subtract a one from the right place. Here is one more example of how it works:

   -36

Using your old way you make it into:

 4 14

-3  6

 1  8

 And using your new way (new "algorithm!!) you make it into:

   514

- 4 6 

  1 8 

Hope that helps,

Mitch