Regrouping and Subtracting

Date: 03/29/2001 at 19:56:35
From: Annette
Subject: Math - Regrouping tens as ones and Subtracting ten and ones

I have no clue how to do this.  

37 - 9        Do you need to regroup?    Subtract the ones
                                         Subtract the tens
                                         How many are left?

Please help me.  I did not have this in school...

Date: 03/30/2001 at 12:26:29
From: Doctor Nbrooke
Subject: Re: Math - Regrouping tens as ones and Subtracting ten and 
ones

Good morning, Annette, and thanks for writing to Dr. Math.

I imagine that you're writing to help your son or daughter with his or 
her math assignment. Tom Lehrer wrote a song about the very problem 
you're having, so I'll pass those lyrics along to you, with a little 
bit of running commentary to help you out along the way.

Tom Lehrer: That Was the Year That Was
10. New Math
http://members.aol.com/quentncree/lehrer/newmath.htm   

Some of you who have small children may have perhaps been put in the 
embarrassing position of being unable to do your child's arithmetic 
homework because of the current revolution in mathematics teaching 
known as the New Math. So as a public service here tonight, I thought 
I would offer a brief lesson in the New Math. Tonight, we're gonna 
cover subtraction. 

This is the first room I've worked for a while that didn't have a 
blackboard, so we will have to make do with more primitive visual 
aids, as they say in the ed biz. Consider the following subtraction 
problem, which I will put up here: 342 minus 173. 

 342
-173
----
   ?

Now, remember how we used to do that: But in the new approach, as you 
know, the important thing is to understand what you're doing, rather 
than to get the right answer. Here's how they do it now: 

You can't take three from two,
Two is less than three,
So you look at the four in the tens place.
Now that's really four tens
So you make it three tens,
Regroup, and you change a ten to ten ones,
And you add 'em to the two and get twelve,
And you take away three, that's nine.
Is that clear? 

    3   12 
 3 (4) (2)
-1  7   3
----------
        9

(Pretend that the numbers in parentheses are crossed out.)
   
Now instead of four in the tens place
You've got three,
'Cause you added one,
That is to say, ten, to the two,
But you can't take seven from three,
So you look in the hundreds place. 
From the three you then use one
To make ten ones...
(And you know why four plus minus one
Plus ten is fourteen minus one?
'Cause addition is commutative, right!)...
And so you've got thirteen tens
And you take away seven,
And that leaves five... 

Well, six actually...
But the idea is the important thing! 

     13
  2  (3) 12 
 (3) (4) (2)
- 1   7   3
-----------
      6   9

Now go back to the hundreds place,
You're left with two,
And you take away one from two,
And that leaves...? 

Everybody get one?
Not bad for the first day! 

     13
  2  (3) 12 
 (3) (4) (2)
- 1   7   3
-----------
  1   6   9

Hooray for New Math,
New-hoo-hoo Math,
It won't do you a bit of good to review math.
It's so simple,
So very simple,
That only a child can do it! 

-------------------------------------------------------------------

So now let's work your problem with our newfound knowledge.

 37 
- 9
---
  ?

You can't take nine from seven, so we have to borrow 10 ones from the 
tens place:

  2  17
 (3) (7)
-     9
--------
     
Now we subtract 9 from 17 to get 8.  

  2  17
 (3) (7)
-     9
--------
      8

There are no tens to subtract, so you subtract 0 from 2 to get the 
tens digit of your answer:

  2  17
 (3) (7)
-     9
--------
2 8

I hope this helps.  Feel free to write back.

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