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CASE III.
When there are cyphers at the right hand of the multipli-

cand, or multiplier, or both.
Rule.--Multiply by the figures only; and to the right
of the product annex as many cyphers, as are equal to
the number of cyphers in both factors.

Examples.
101200
456000

94000
200
3000

20

by

Products, 20240000 1368000000

1880000 Questions. No. Multiplicands. Multipliers. Products, 1. 621000 Х by 2900

1800900000 2. 700000 "Х by 9900

6930000000 3. 854000 by 7600

6490400000 4. 943200 by 7000

6602400000 5. 94944 by 600

56966400 6. 412342 by 550

226788100 7. 671230

by
123

82561290
8. 421233
by 120

50547960 9. 4567852 Х

19000

41110668000 Practical Questions in Multiplication. 1. A man had a farm on which he raised 360 bushels of wheat; and he had another, on which he raised 6 times as much; what quantity did he raise on both of them?

Ans. 2520 bushels. 2. A man had an estate which he divided among 9 sons as follows, viz. to the first eight, he gave 333 dol. lars each: to the ninth, he gave as much wanting 1000 dollars as to the other eight; I demand the value of the estate ; and also the ninth son's share.

Value of the estate 4328 dolls.

The 9th son's share 1664 dolls. 3. A man sheared 364 sheep, six years successively, each sheep neated 3 pounds of wool per year: how much wool had he yearly, and how much in six years?

Ans. Yearly 1092 pounds.

In six years 6552 pounds, 4. I sold 342 tons of iron at 142 dollars per ton: I deand the price of the whole.

Ans. 48564 dolls.
B

3

5. I sold 742 thousand of boards in the W. I. at 62 dollars per thousand; what did they come to ?

Ans. 46004 dolls. 6. What will 6422 quintals of fish come to at 6 dolls. per quintal ?

Ans. & 38532. 7. A man travelled 26 days, and each day, he travelled 37 miles ; what distance did he travel in the whole time ?

Ans. 962 miles,

SIMPLE DIVISION.

DEFINITION --Simple Division teaches to find how many times a smaller number is contained in a larger.

The number given to be divided, is called the dividend.
The number given to divide by, is called the divisor.

That number which expresses the number of times, that the divisor is contained in the dividend, is called the quotient, or answer.

If any thing is left after dividing, it is called the rempainder.

LONG DIVISION.

Long division is when the Divisor is more than twelve.

CASE I. RULE..Write down the dividend, on the right and left draw a curved line ; on the left hand of the dividend write down the divisor; seek how many times the divisor can be had in a competent number of the first figures of the dividend, and place the figure expressing the number of times, at the right of the dividend ; multiply the divisor by the same figure, and place the product under the first figures of the dividend, and subtract; to the remainder bring down the next figure of the dividend, and divide as before ; and thus proceed until all the figures of the dividend are brought down; if at any time when you have brought down a figure the sum is still less than

the divisor, a cypher must be placed in the quotient, and another figure must be brought down; the remainder must always be less than the divisor.

Proof.--Multiply the quotient and divisor together, to the product add the remainder (if there is any) and the sum will be like the dividend, if the work is right.

Examples
Dividend.

Dividend. Divs.16)3721491(232593 Qnto. Divs.24)3102134(129255 Quo. 32

24

[blocks in formation]

3 Rem.

14 Rem. Questions. No. Dividends. Divisors. Quotients. Rem. 1. 1432400

222

6452 56 2. 2045600

912

2242 896 3. 9400032

203
46305

117 4 9320143

4211

2213 1200 5. 7345681

5566

1319 4127 6 54321 40

2345

2316 1120 6041231 → 97 60

618 9551 CASE II. When there are cyphers at the right of the divisor,

RULE.--Cut off the cyphers, and also cut off as many figures, or cyphers from the right of the dividend; divide the remaining part of the dividend as before, and to the right of the remainder, place the figures which were cut off from the dividend.

as on

Eramples.
1. Divide 5642321 by 432000.
432|000)5642|321(13 Quo.

432

1322
1296

26321 Rem.

63-82.13

60_232 1.

No. Dividends. Divisors.
2. 764213 12000 - Ans.
3. 943217
5000 Ans. 1883217

5000
674321
11200 Ans.

111275 5. 432132

9200 = Ans. NOTE:--To divide by 10, 100, or 1000, &c. is only to cut of as many figures, or cyphers from the right of the dividend as are equal to the number of cyphers on the right of the divisor.

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Practical Questions in Division. 1. A man had an estate valued at 2474 dolls. and it was divided equally between twelve sons : I demand the share of each.

Ans. $20612 2. If a tax of 40000 dollars were to be lèvied

upon 1200 polls : I demand what one poll would pay.

Ans. $3310 3. Divide 1474 dollars equally among 25 men, so women, 17 boys, and 27 girls : after taking out 75 dollars for a present to a nephew.

Ans. $1417 4. Divide 247600 pounds of beef equally among an army of 23724 men. Ans. 10113s: lbs. 5. Sixty men at a feast, which lasted 3 days,

per day ; how much did each mai spend per day, and how much in the whole ?

Ans. $4 per day, and $12 the whole.

spent 240 dollars

6. Divide 151200 lbs. of beef equally among an army consisting of 27 regiments, each regiment 7, companies, and each company 100 men.

Ans. 8 lbs. 7. If 10500 dollars are given 'for 750 barrels of Aour ; I demand the price of one barrel.

Ans. $14. . 8. If 45 horses were sold in the West Indies for 9900 dollars, I demand the average price.

Ans. $ 220 each.

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SHORT DIVISJON. Short Division is when the divisor is less than 12. RULE.--Seek how many times the divisor is con.. tained in a competent number of the figures on the left hand of the dividend, and set the figure express... ing that number underneath, and all that is over call so many tens, annex the next figure of the div-. idend to the tens, divide as at first, and thus proceed through the whole, and the quotient will stand. under the dividend.

Examples 2)4230 3)4567 4)612340 5)12345670 "211 Ans. 1522 Ans. 153082 Ans. 246913 Ans. 6)64567C 7)123456

8)43213) 9)7643210

/ COMPOUND ADDITION. DEFINITION.-Compound Addition teaches to add different denominations together ; such as dollars, cents and mills. Tons, hundreds, quarters, pounds, &c.

RULE.Write down dollars under dollars, cents under cents; mills under mills. Tons under tons ;.

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