4. An even number added to or subtracted from an even number, or an odd number to or from an odd number, produces an even number.
5. An odd number added to or subtracted from an even number produces an odd number.
6. The digits of the nine times multiplication table added together make either 9 or 18 (twice 9), thus:—
| 9 | × | 1 | = | 9 | ||||||
| 9 | × | 2 | = | 18 | or | 8 | plus | 1 | = | 9 |
| 9 | × | 3 | = | 27 | or | 7 | „ | 2 | = | 9 |
| 9 | × | 4 | = | 36 | or | 6 | „ | 3 | = | 9 |
| And so on to | ||||||||||
| 9 | × | 11 | = | 99 | or | 9 | plus | 9 | = | 18 |
Then so on again up to 9 times 24, each table making 9, with the exception of 9 times 22 =198=8+9+1=18. Indeed, the digits, added together, of the product of any number multiplied by 9, will be found to be 9 or a multiple thereof.
7. The digits 1 to 9 may be placed to form 362880 combinations; this number divided by 9 gives 40320; these figures added together make 9.
8. If two numbers are divisible by any one number, their sum and their difference will also be divisible by the same number.
9. If two numbers divisible by 9 be added together, the sum of the figures will be either 9 or a multiple of 9.