The uniqueness of the number nine (Part 1)

The uniqueness of the number nine

(Part 1)

We are very familiar with operations such as count plus surgery, less, times and to share.

These operations are quite helpful in observing the beauty of figure 9. We will describe in the following description.


Try search results from 63 x 99.

How do we solve it?


One way to calculate the 63 x 99 is the multiplicative composite. However, there are other ways to calculate the product of two numbers, are as follows:

Because 99 = 100-1,

So 63 x 99 = 63 (100-1)

= (63 x 100) - (63 x 1)

= 6300-63

= 6237


To multiply 999 x 27 can be completed as follows:

Because 999 = 1000-1

So 999 x 27 = (1000-1) x 27

= 2700-27

= 26 973


Furthermore, how is the result of, for example, 52 x 999? Try doing this with such techniques.

If the description, examples and problems above have been understood, then we will exploit the uniqueness of the other nine digits.


In integer division by the number 9, there are things that are very unique. Let's look at an example.


Example 1:

If 12 divided by 9, then the result is 1 and the remaining 3.

If the numbers 1 and 2 added together then the result is 1 + 2 = 3 (the rest of the division by 9).


Example 2:

If 78 divided by 9, then the result is 8 and the remainder is 6.

If the numbers 7 and 8 are added then the result is 7 + 8 = 15. Furthermore, if the numbers one and five added together then the result is a + 5 = 6 (the rest of the division by 9).


Example 3:

If 878 is divided by 9, then the result is 97 and the remainder is 5.

If the numbers 8, 7 and 8 are added then the result is 8 + 7 + 8 = 23. Furthermore, if the numbers two and three added together then the result is 2 + 3 = 5 (the rest of the division by 9).


From these examples it can be concluded "Every integer is divided by 9, then the rest is the sum of the numbers over and over that there is a number that is divided on it until obtaining a number from 0 to 8".