New Math (in base 16 instead of 8)

by Tom Lehrer, meddled with a bit by KT



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 going to 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:

   3 4 2
 - 1 7 3

Now remember how we used to do that. Three from two is nine; carry the one, and
if you're under 35 or went to a private school you say seven from three is six,
but if you're over 35 and went to a public school you say eight from four is
six; carry the one. So we have 169, 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 them to the two and get twelve,
And you take away three, that's nine.
Is that clear?

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 have thirteen tens,
And you take away seven,
And that leaves five...

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

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

Everybody get one?
Not bad for the first day!

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!

Now that actually is not the answer that I had in mind, because the book that I
got this problem out of wants you to do it in base sixteen. But don't panic. Base
sixteen is just like base ten really - if you have four hands, each missing a finger. 
Shall we have a go at it? Hang on.

You can't take three from two,
Two is less than three,
So you look at the four in the sixteens place.
Now that's really four sixteens,
So you make it three sixteens,
Regroup, and you change a sixteen to sixteen ones,
And you add them to the two,
and you get one-two base sixteen,
Which is eighteen base ten,
And you take away three, that's fifteen,
And in base sixteen that's F.

Now instead of four in the sixteens place
You've got three,
'Cause you added one,
That is to say, sixteen, to the two,
But you can't take seven from three,
So you look at the two hundred fifty-sixes.

"Two hundred fifty-six? How did two hundred fifty-six get into it?" I hear you scream at the top of your lungs.
Well, two hundred fifty-six is sixteen squared, don't you see?
(Well, you ask a silly question, and you get a silly answer.)

From the three you then use one
To make sixteen ones,
And you add those ones to the three,
And you get one-three base sixteen,
Or, in other words,
In base ten you have nineteen,
And you take away seven,
And seven from nineteen is twelve,
Which in base sixteen is B.

Well, C actually, but like I said...

Now go back to the two hundred fifty-sixes,
And you're left with two,
And you take away one from two,
And that leaves...?

Now, let's not always see the same hands.
One, that's right!
Whoever got one can stay after the show and clean the erasers.

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!

Come back tomorrow night. We're gonna do fractions.
Now I've often thought I'd like to write a mathematics text book someday because I have
a title that I know will sell a million copies. I'm gonna call it Tropic Of Calculus. 





base 10:
   3 4 2
 - 1 7 3
   1 6 9

base 8:
     11 10
   2 13 12
  /3 /4 /2
 - 1  7  3
   1  4  7

base 16:
     19 18
   2 13 12
  /3 /4  2
 - 1  7  3
     12 15
   1  C  F