Reason why
"n" x 10 = "n0" for any "n"
Here let us consider the reason why
5 x 10 = 50, 23 x 10 = 230, etc.
First, let us begin by the case of "1".
(Case of 1) 1 x 10 = 10
| 1 x 10 | = 1 x (9 + 1) | (D1)
|
| = 1 x 9 + 1 x 1 |
|
| = 9 x 1 + 1 x 1 |
|
| = 9 + 1 |
|
| = 10 | (D1)
|
How about the case of "2" ?
(Case of 2) 2 x 10 = 20
| 2 x 10 | = (1 + 1) x 10 | (S1)
|
| = 1 x 10 + 1 x 10 |
|
| = 10 + 10 | (Case of 1)
|
| = 10 + (9 + 1) | (D1)
|
| = (10 + 9) + 1 |
|
| = 19 + 1 | (D2)
|
| = 20 | (D3)
|
How about the case of "3" ?
(Case of 3) 3 x 10 = 30
| 3 x 10 | = (2 + 1) x 10 | (S1)
|
| = 2 x 10 + 1 x 10 |
|
| = 20 + 10 | (Case of 2)
|
| = 20 + (9 + 1) | (D1)
|
| = (20 + 9) + 1 |
|
| = 29 + 1 | (D2)
|
| = 30 | (D3)
|
Let us note that here appears the same pattern of reasoning.
By repeating this process, we can reach the following :
(Case of "n") "n" x 10 = "n0"