of the dividend as there are ciphers. These figures will be the remainder, and the rest of the dividend will be the quotient.
- 10) 2717316
- 271731 and rem. 6.
Or we may prove these results thus: from (20), 2717316 is 271731 tens and 6; of which the first contains 10 271731 times, and the second not at all; the quotient is therefore 271731, and the remainder 6 (72). Again (20), 33429 is 334 hundreds and 29; of which the first contains 100 334 times, and the second not at all; the quotient is therefore 334, and the remainder 29.
- The following examples will shew how the rule may be shortened when there are ciphers in the divisor. With each example is placed another containing the same process, all unnecessary figures being removed; and from the comparison of the two, the rule at the end of this article is derived.
| I. 1782000 ) | 6424700000 | (3605 | 1782 ) | 6424700 | (3605 |
|---|---|---|---|---|---|
| 5346000 | 5346 | ||||
| 10787000 | 10787 | ||||
| 10692000 | 10692 | ||||
| 9500000 | 9500 | ||||
| 8910000 | 8910 | ||||
| 590000 | 590000 | ||||
| II. 12300000 ) | 42176189300 | (3428 | 123 ) | 421761 | (3428 |
| 36900000 | 369 | ||||
| 52761893 | 527 | ||||
| 49200000 | 492 | ||||
| 35618930 | 356 | ||||
| 24600000 | 246 | ||||
| 110189300 | 1101 | ||||
| 98400000 | 984 | ||||
| 11789300 | 11789300 |
The rule, then, is: Strike out as many figures4 from the right of the dividend as there are ciphers at the right