Table of Contents

Introduction
Section I - Multiplication of “One” Numbers
One Number Tango - Multiplication of “One” Numbers with other “One” Numbers
Halloween Scarum Technique
The Magic Number
The Galaxy of Nines
The Descending/Ascending Scale of Nines
Multiplying by 9: The 9-Xpress
Multiplication by other Nine Numbers: 99, 999, etc.
Squaring Nine Numbers: The Nifty Nine Square Technique
Nuclear Nine Technique

Introduction

As I have said in many of my articles that treat the interconnection of mathematics and
faith, God really does not play dice with the universe but rather reveals His magnificent
presence in the realm of this most intriguing discipline called math. Indeed if you have
read Wiz Kid: A Mind-Blowing Exploration into Short-Cut Arithmetic, the first in the
series, then you know that there are amazing things you can do with numbers once you
understand some their fundamental properties. And since all of mathematics hinges on
numbers, either directly or indirectly, knowing tricks in working with them can give you
a huge advantage toward mastering this most difficult subject.

Mostly for this reason, I created the Wiz Kid series of educational ebooks. Although you
can study and learn the cool tricks in this component of the series without being familiar
with the first one, it certainly behooves you to read and learn the techniques laid out in
the first ebook. You will then have a tremendous grasp of the power of numbers and the
computations involving them. Who knows? You may even become a mathematician!
Scary thought.

In this component, we are going to learn some interesting properties of certain numbers.
These properties will afford you the ability to perform many complex computations
seemingly without effort. To this day, I am still amazed at how powerful these arithmetic
techniques are and the results that they produce. I believe without hesitation that once
you see them too, you will be convinced as well of their awesome power.

Section I - Multiplication of “One” Numbers

The first special numbers that we will treat are called “one numbers.” Now let’s see
whether you can guess why we have called them by this name. If you said it’s because
they have something to do with the number one, then you are correct. As you may
remember, the number one is a very special number. In fact, mathematicians consider 1,
one of five of the most important numbers in mathematics. One of the beautiful
properties of 1 is that it is the multiplicative identity; that is, if you multiply the number 1
with any other number, you always get back the given number. Thus 1 x 8 = 8, 1 x 158 =
158, and so on. What this first section will deal with are the following three topics:

I) The squaring of “one” numbers;
ii) The multiplication of “one” numbers together; and
iii) The multiplication of “one” numbers with other general numbers.

Now what are these amazing “one” numbers? What we call “one” numbers here in the
Wiz Kid Universe are simply numbers made up entirely of 1's. The simplest “one”
number is 1. The next “one” number is 11, then 111, then 1111 and so on. So what’s so
special about these numbers, you ask? Well “one” numbers are fascinating indeed. A
rare and very unique species of numbers. And what makes them so special goes back to
a property in multiplication that we’ve covered before, and which doubtless you’ve heard
of, but probably never really remembered because it didn’t make much sense at the time
or didn’t seem that important. The property is called the Identity Property of
Multiplication.

Oh, I know you’re saying: “Here we go again with those mathematical terms and
definitions. All that stuff confuses me.” That’s okay. Remember, here in the Wiz Kid
Universe, we take fear and great mystery out of math and put the fun back in. We bake a
great “math cake” so to speak—one that everyone enjoys. So get ready to have some
enjoyment!

As mentioned before, the identity property is a very special quality of the number 1. Any
number multiplied by 1 does not change or lose its identity. In other words the number
stays the same. Thus multiplying by 1 does not require any effort or skill whatsoever.
For example,

1 x 68 = 68
1 x 897 = 897
1 x 7856 = 7856

You see in the examples above, the numbers 68, 897, and 7856, when multiplied by 1,
did not change: they did not lose their identity. And thank God for that. We wouldn’t
want anyone of them to have an identity crisis or something. After all, numbers have
feelings too.

Anyway, this special property of the number 1, allows us to become a multiplication
magician. And I’m going to show you some things that going to dazzle your minds. So
let’s go!

First, we’re going to look at squaring “one” numbers. Remember that squaring a number
means multiplying it by itself. Thus 11 x 11 is 11 squared, which we usually write as
112, the little 2 or superscript being called the exponent or power of the number 11. By
the way, for those of you who are wondering, the term square comes from the geometric
figure of a square. The square of a number represents the area of the square, since we
calculate this measure by multiplying the two side lengths together. Thus 11 squared is
the area of a square with side length of 11.

Now what if I told you that you could square any “one” number and that you could do it
faster than using a calculator? Skeptical? Good. Well watch and learn.

“ONE NUMBER SQUARE RULE”

To square any “one” number, write the product (the result of the
multiplication) as the numbers 1,2,3... up to the number of 1's in the
“one” number, and then back down...3,2,1 from the highest number you
counted up to.

Hearing those words may not make this perfectly clear, so let’s look at some examples.
Suppose I wanted to square 11. This number has two 1's. So the product is going to be
121, in which case I count up to 2 and then back down from 2 to 1. Suppose I wanted to
square 111. This number has three 1's, so I’m going to count up to—you got it—3 and
then back down from 3 to 1, without repeating the 3, of course. Thus the product is
12321. Now how about multiplying 111,111 x 111,111? I bet you never thought it could
be this easy! How many 1's? Six. So what do we count up to? Six. And what do we
count back down from without repeating? Six. Exactly. So the answer is 12345654321.

Adding commas to make the number more readable, we have 12,345,654,321 or twelve
billion three hundred and forty-five million six hundred and fifty-four thousand three
hundred twenty-one. WOW!!! In fact, the above rule works as usual all the way up to
squaring 111,111,111 which is one hundred eleven million one hundred eleven thousand
one hundred eleven. I don’t think you have to preoccupy yourself with anything bigger
than this number, but for those diehard curious-minded of you, you can use the third rule
we’re going to learn on “one” number techniques, or you can use a slight modification of
the rule we’ve just learned, to do this multiplication.