| 47963 | 6, 15, 17, 23, 31, 3″ 4′; |
| 1598 | 11, 12, 21, 22, 31, 3″7′; |
| 26316 | 9, 17, 24, 27, 32, 4″1′; |
| 54792 | 10, 14, 20, 21, 2″8′; 7, 9, 1′3′. |
| 819 | |
| 6686 | |
| 138174 |
In verifying additions, instead of the usual way of omitting one line, adding without it, and then adding the line omitted, verify each column by adding it both upwards and downwards.
Subtraction. The following process is enough. The carriages, being always of one, need not be mentioned.
- From 79436258190
- Take 58645962738
- 20790295452
8 and 2′, 4 and 5′, 7 and 4′, 3 and 5′, 6 and 9′, 10 and 2′, 6 and 0′, 4 and 9′, 7 and 7′, 9 and 0′, 5 and 2′. It is useless to stop and say, 8 and 2 make 10; for as soon as the 2 is obtained, there is no occasion to remember what it came from.
Multiplication. The following, put into words, is all that need be repeated in the multiplying part; the addition is then done as usual. The unaccented figures are carried.
| 670383 | |
| 9876 | |
| 4022298 | 18′, 49′, 22′, 2′, 42′, 4′0′, |
| 4692681 | 21′, 58′, 26′, 2′, 49′, 4′6′, |
| 5363064 | 24′, 66′, 30′, 3′, 56′, 5′3′, |
| 6033447 | 27′, 74′, 34′, 3′, 63′, 6′0′. |
| 6620702508 |
Verify each line of the multiplication and the final result by casting out the nines. ([Appendix] II. p. 166.)
It would be almost as easy, for a person who has well practised the 8th exercise, to add each line to the one before in the process, thus:
| 670383 | |
| 9876 | |
| 4022298 | 8; 21 and 9 are 30′; 59 and 2 |
| 50949108 | are 61′; 27 and 2 are 29; 2 |
| 587255508 | and 2 are 4′; 49 and 0 are 49′; |
| 6620702508 | 46 and 4 are 5′0′. |