CASE II.

To divide by any number with ciphers annexed.

Cut off the ciphers from the divisor, and the same number of digits from the right hand of the dividend; then divide the remaining figures as in the last case, and the quotient is the answer; and what remains written before the figures cut off is the true remainder.

To divide by an unit with ciphers annexed.

Cut off as many figures from the right hand of the dividend, as there are ciphers in the divisor, and the figures on the left hand of the separation will be the quotient, and those on the right hand the remainder.

To divide by a composite number, that is, a number, which is produced by the multiplying of two or more numbers.

Divide the dividend by one of those numbers, and the quotient thence arising by another, and so continue; and the last quotient will be the answer.

NOTE. To find the true remainder, we multiply the last remainder by the last divisor but one, and, to the product, add the next preceding remainder; we multiply this sum by the next preceding divisor, and to the product add the next preceding remainder; and so on, till we have gone through all the divisors and remainders to the first.

This rule will be better understood by the pupil, after he has become acquainted with fractions.

1. Divide 47932 by 72.

9)47932
8)5325-7

EXAMPLES.

As 72 is equal to 9 times 8, we first divide the dividend by 9, and the quotient, thence arising by 8; and to find the true remainder, we multiply the last remainder, 5, by the first 665-5-52 divisor, 9; and to the product add the first remainder, 7; and find the amount to be 52.

2. Divide 5371 by 192.

4)5871

6)1342

3

8)223-4

27 7

We find 192 equal to the product of 4 times 6 times 8. 4 X 6 X 8 = 192. We therefore divide by these factors, as in the last example. To find the true remainder, we multiply the last remainder, 7, by the last divisor but one, 6; and to the product add the last remainder but one, 4; this sum we multiply by the first divisor, 4; and to the product add the first remainder, 3; and find the amount to be 187.

187

1. What number multiplied by 1728 will produce 1705536 ?

2. If a garrison of 987 men are supplied with of beef, how much will there be for each man? 3. In one dollar there are 100 cents, how 697800 cents?

Ans. 987.

175686 pounds Ans. 178 lbs. many dollars in Ans. $6978.

4. In one pound there are 16 ounces, how many pounds are in 111680 ounces? Ans. 6980 lbs. 5. A dollar contains 6 shillings, how many dollars are in 5868 shillings? Ans. $978. 6. The President of the United States receives a salary of $25,000; what does he receive per month? Ans. $2083}. 7. A man receiving $96 for 8 months' labor; what does he receive for 1 month? Ans. $12.

8. The distance from Haverhill to Boston is 30 miles; and if a man travel 6 miles an hour, how long will he be in going this distance ? Ans. 5 hours.

9. The annual revenue of a gentleman being $8395, how much per day is that equivalent to, there being 365 days in a year? Ans. $ 23. 10. The car on the Liverpool railroad goes at the rate of 65 miles an hour; how long would it take to pass round the globe, the distance being about 25,000 miles ? Ans 384 hours. 11. How much sugar at $15 per cwt. $ 405 ?

may be bought for Ans. 27 cwt.

12. In 6789560 shillings how many pounds, there being 20 shillings in a pound? Ans. 339478 pounds. 13. The Bible contains 31,173 verses; how many must be read each day, that the book may be read through in a year?

Ans. 85 verses.

14. In 123456720 minutes how many hours?

Ans. 2057612 hours.

15. A gentleman possessing an estate of $ 66,144, bequeathed one-fourth to his wife, and the remainder was to be divided between his 4 children; what was the share of each ?

Ans. $12,402.

16. A man disposed of a farm, containing 175 acres at $87 per acre; of the avails he distributed $1234 for charitable purposes; $197 was expended for the purchase of a horse and chaise; the remainder was divided between 6 gentlemen and 8 ladies, and each lady was to receive twice as much as a gentleman; what was the share of each ?

Ans. $ 627 for a gentleman, and $1254 for a lady. 17. If there are 160 square rods in an acre, how many acres are in 1086240 square rods? Ans. 6789 acres.

18. If 144 square inches make one square foot, how many square feet in 14222160 square inches? Ans. 98765 feet.

19. What number is that, which being multiplied by 24, the product divided by 10, the quotient multiplied by 2, 32 subtracted from the product, the remainder divided by 4, and 8 subtracted from the quotient, the remainder shall be 2? Ans. 15. 20. What is the difference between half a dozen dozen, and six dozen dozen ?

Ans. 792.

By this weight are weighed gold, silver, and jewels.

NOTE."The original of all weights, used in England, was a grain or oorn of wheat, gathered out of the middle of the ear; and, being well dried, 32 of them were to make one pennyweight, 20 pennyweights one ounce, and 12 ounces one pound. But in later times, it was thought sufficient to divide the same pennyweight into 24 equal parts, still called grains, being the least weight now in common use; and from hence the rest are computed."