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 _figures_[12] from the right of the dividend as there are _ciphers_ at the right of the divisor. Strike out all the ciphers from the divisor, and divide in the usual way; but at the end of the process place on the right of the remainder all those figures which were struck out of the dividend. [12] Including both ciphers and others. 84. EXERCISES. Dividend. | Divisor. |Quotient.|Remainder. 9694 | 47 | 206 | 12 175618 | 3136 | 56 | 2 23796484 | 130000 | 183 | 6484 14002564 | 1871 | 7484 | 0 310314420 | 7878 | 39390 | 0 3939040647 | 6889 | 571787 | 4 22876792454961 | 43046721 | 531441 | 0 Shew that 100 × 100 × 100 - 43 × 43 × 43 I. ------------------------------ = 100 × 100 + 100 × 43 + 43 × 43. 100 - 43 100 × 100 × 100 + 43 × 43 × 43 II. ------------------------------ = 100 × 100 - 100 × 43 + 43 × 43. 100 + 43 76 × 76 + 2 × 76 × 52 + 52 × 52 III. -------------------------------- = 76 + 52. 76 + 52 12 × 12 × 12 × 12 - 1 IV. 1 + 12 + 12 × 12 + 12 × 12 × 12 = ----------------------. 12 - 1 What is the nearest number to 1376429 which can be divided by 36300 without remainder?--_Answer_, 1379400. If 36 oxen can eat 216 acres of grass in one year, and if a sheep eat half as much as an ox, how long will it take 49 oxen and 136 sheep together to eat 17550 acres?--_Answer_, 25 years.