did not take away 13 more than once at a time, in order that the method might be as simple as possible. But if I know what is twice 13, 3 times 13, &c., I can take away as many thirteens at a time as I please, if I take care to mark at each step how many I take away. For example, take away 13 ten times at once from 156, that is, take away 130, and afterwards take away 13 twice, or take away 26, and the process is as
- 156
- 130 10 times 13.
- 26
- 26 2 times 13.
- 0
Therefore 156 contains 13 10 + 2, or 12 times.
Again, to divide 3096 by 18.
- 3096
- 1800 100 times 18.
- 1296
- 900 50 times 18.
- 396
- 360
- 36
- 36
- 0
Therefore 3096 contains 18 100 + 50 + 20 + 2, or 172 times.
- You will now understand the following sentences, and be able to make similar assertions of other numbers.
450 is 75 × 6; it therefore contains any number, as 5, 6 times as often as 75 contains it.
| 135 | contains 3 more than | 26 | times; therefore, |
|---|---|---|---|
| Twice 135 | ” 3 ” | 52 | or twice 26 |
| 10 times 135 | ” 3 ” | 260 | or 10 times 26 |
| 50 times 135 | ” 3 ” | 1300 | or 50 times 26 |
| 472 | contains 18 more than | 21 | times; therefore, |
| 4720 | contains 18 more than | 210 | times, |
| 47200 | contains 18 more than | 2100 | times, |
| 472000 | contains 18 more than | 21000 | times, |
| 32 | contains 12 more than | 2 | times, and less than 3 times. |
| 320 | ” 12 ” | 20 | times, ” ” 30 times. |