30. The former process, written with the signs of (23) is as follows:

1834 = 1 × 1000 + 8 × 100 + 3 × 10 + 4
2799 = 2 × 1000 + 7 × 100 + 9 × 10 + 9

Therefore,

1834 + 2799 = 3 × 1000 + 15 × 100 + 12 × 10 + 13

But

13 = 1 × 10 + 3
12 × 10 = 1 × 100 +2 × 10
15 × 100 =1 × 1000 +5 × 100
3 × 1000 =3 × 1000  Therefore,
1834 + 2799 =4 × 1000 +6 × 100 +3 × 10 + 3
=4633.

31. The same process is to be followed in all cases, but not at the same length. In order to be able to go through it, you must know how to add together the simple numbers. This can only be done by memory; and to help the memory you should make the following table three or four times for yourself:

1 2 3 4 5 6 7 8 9
12345678910
234567891011
3456789101112
45678910111213
567891011121314
6789101112131415
78910111213141516
891011121314151617
9101112131415161718

The use of this table is as follows: Suppose you want to find the sum of 8 and 7. Look in the left-hand column for either of them, 8, for example; and look in the top column for 7. On the same line as 8, and underneath 7, you find 15, their sum.

32. When this table has been thoroughly committed to memory, so that you can tell at once the sum of any two numbers, neither of which exceeds 9, you should exercise yourself in adding and subtracting two numbers, one of which is greater than 9 and the other less. You should write down a great number of such sentences as the following, which will exercise you at the same time in addition, and in the use of the signs mentioned in (23).