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.

84. EXERCISES.

Dividend.Divisor.Quotient.Remainder.
96944720612
1756183136562
237964841300001836484
14002564187174840
3103144207878393900
393904064768895717874
22876792454961430467215314410

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.

85. Take any two numbers, one of which divides the other without remainder; for example, 32 and 4. Multiply both these numbers by any other number; for example, 6. The products will be 192 and 24. Now, 192 contains 24 just as often as 32 contains 4. Suppose 6 baskets, each containing 32 pebbles, the whole number of which will be 192. Take 4 from one basket, time after time, until that basket is empty. It is plain that if, instead of taking 4 from that basket, I take 4 from each, the whole 6 will be emptied together: that is, 6 times 32 contains 6 times 4 just as often as 32 contains 4. The same reasoning applies to other numbers, and therefore we do not alter the quotient if we multiply the dividend and divisor by the same number.

86. Again, suppose that 200 is to be divided by 50. Divide both the dividend and divisor by the same number; for example, 5. Then, 200 is 5 times 40, and 50 is 5 times 10. But by (85), 40 divided by 10 gives the same quotient as 5 times 40 divided by 5 times 10, and therefore the quotient of two numbers is not altered by dividing both the dividend and divisor by the same number.