1. ทำไมต้องเวทคณิต และ การยันความถูกต้อง

(Casting Out Nines)

0
20 2 + 0 = 2
305 3+ 0 + 5 = 8
29 2+9 = 11 1 + 1 = 2
399 3+9+9 = 21 2 + 1 = 3

(Casting Out Nines)

09

20 2
29 9

4990 +ระ79376r== 1436rr6

4ก

65451 + 48769 = 114220

35567 + 11828 = 47295

4127 - 2376 = 1751
65451 - 48769 = 16682
35567 - 11828 = 23729

4127 36 = 148572
65451 11 = 719961
11828 362 = 4281736

24572 5 = 4914 2

24572 = 4914 5 + 2



(Casting Out Elevens)

634 6 + 3 + 4 = 13 1 + 3 = 4
643 6 + 4 + 3 = 13 1 + 3 = 4
436 4 + 3 + 6 = 13 1 + 3 = 4
463 4 + 6 + 3 = 13 1 + 3 = 4
364 3 + 6 + 4 = 13 1 + 3 = 4
346 3 + 4 + 6 = 13 1 + 3 = 4

58457 11

5314 ,, , 11
11 ) 5 8 4 5 7 7 5+4 8+5 = 3= r ,

55
34
33
15
11
47
44
3=r

58457 11

58457 11 = 58457
11
=58457 5(10000) 8(1000) 4(100) 5(10) 7
11 11
= 5(9999 1) 8(1001 1) 4(99 1) 5(11 1) 7
= 5(9999) 5 8(1001) 118 4(99) 4 5(11) 5
11 11 11 11 11 11 11 11 7
11
= 5 8 4 5 7= 3
11 11 11 11 11 11

(Casting Out Elevens)

4990 + 9376 = 14366
65451 + 48769 = 114220
35567 + 11828 = 43795

4127 - 2376 = 1751
65451 - 48769 = 16682
35567 - 11828 = 23729

4127 36 = 148572
65451 11 = 719961
11828 362 = 4281736

24572 5 = 4914 2

24572 = 4914 5 + 2



6745215 4891538

67 45215

4891538

111021131 89997

89997 111 0 21131
10003 100 03
20 006
3 0009
30009
1233
54830

111021131 89997 1233 54830
89997

1.
spreads diversity

1. Ekadhikina Purvena 9. Chalana-Kalanabyham

2. Nikhilam Navatashcaramam Dashatah 10. Yaavadunam

3. Urdhva-Tiryagbyham 11. Vyashtisamanstih

4. Paraavartya Yojayet 12. Shesanyankena Charamena

5. Shunyam Saamyasamuccaye 13. Sopaantyadvayamantyam

6. (Anurupye) Shunyamanyat 14. Ekanyunena Purvena

7. Sankalana-vyavakalanabhyam 15. Gunitasamuchyah

8. Puranapuranabyham 16. Gunakasamuchyah