Dialogue on 2-Color Numbers (1)

Part 1:
2-Color Numbers

Ni Suiti was in the veranda when her granddaughter Si Nessa come to tell her experiences when she went  to Numberland brought by her aunt Mak Retitia. She told Ni Suiti that the Numberland is a wonderful land. In one region of the island he found out that in there there are colorful numbers.

Si Nessa: Grandma, I have never known that numbers in the amazing Numberland where numbers have colors.

Ni Suiti:   Do you mean that we can find numbers with the same value but  has different colors?

Si Nessa: Yes, but more interesting is their properties. When two numbers meld into another number then they become another colored number.

Ni Suiti:  What is the color of the new number?

Si Nessa: They get a new color or stay in their original color according to the way they meld: addition or multiplication.

Ni Suiti:  What is the rules for color change for the addition?

Si Nessa:  If the colors are similar, the result is similar color

Ni Suiti:  So, red one plus red three is red five.

2 + 3 = 5
Black two plus Black one is Black three.
2 + 1 = 3
But what if we add two numbers of
different colors?

Si Nessa: It yields a duet which is a pair of numbers of different colors

Ni Suiti:  How many kinds of colored number are there in Numberland?

Si Nessa: I was in two colored number region of the land. They call it Bichromic province which is populated by two kind of number: Black and Red. But there are many other regions which is occupied by numbers with more than two colors. I have never been there.

Ni Suiti:  Now what is the multiplication rules of of two colored numbers?

Si Nessa: That's really simple. Black number does not change the color of the number it multiply. Red number change it.

This rule can be simplified to:
Similar colors are multiplied to Black
Different colors are multiplied to Red.

Ni Suiti:  That means
Black 2 times Red 3 is equal to Red 6
2 X 3 = 6
and Red 2 times Black 3 is equal to Red 6
2 X 3 = 6
and Red 2 times Red 3 is equal to Black 6
2 X 3 = 6

Si Nessa:  That's correct. But Dichromatic province is more populated by pairs of numbers of different colors called duets.

Ni Suiti:  I wonder what are the rules of duet melding

Si Nessa:  If it is addition, then any colored number of the first duet will add to the member of the other duet of the same color. In short: Equal colored number add up the same color

Ni Suiti: 
You mean
2 + 3 +
1 + 2 =
3 + 5

Si Nessa:  You are right grandma.

Ni Suiti:  Now how can we multiply two duets?

Si Nessa: We multiply every colored number of the first duet to every colored number of the second duet and add all the results up. In short: Add up all possible multiplications

Ni Suiti: 
(1 + 2) X (3 + 2) =
=1 X 3 + 1 X 2 + 2 X 3 + 2 X 2 =
=      3 +       2 +        6 +       4 =
= 7 + 8
 
Si Nessa: Right again Grandma

Ni Suiti:  What about negative numbers

Si Nessa: They're all has the same rules.

Ni Suiti:  So we can have Red minus 2 = minus Red 2 = - 2

Si Nessa: Good Grandma!

Ni Suiti: So we will make a colored number dissapear if we add it to its negative.
Red 3 + Red minus 3 =
Si Nessa: Yes. That's the magic of colored numbers
.
Ni Suiti: In summary,
For single color number addition of similar color singlet yields similar colored singlet.
Different color numbers add to a duet.
Adding colorful number duets is adding their members colorwise.
Multiplying by black singlet does not change color.
Multiplying by red singlet changes the color.
Mutiplying duets is adding all the multiplication of of their colored members.
Si Nessa:  Good Grandma. But, sorry I have to go home now. Because I have to prepare my self for tomorrow Journey to the another province of the Numberland: the Bichromic Two. Bye, now.