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the divisor, a cypher must be plac ed 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.

Dividend.

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Divs.16)3721491(232593 Quo. Divs.24)3102134(129255 Quo.

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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.

Examples.

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

432

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60-2321 111205 Ans. 469 468932

9200

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.

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. $206

2. If a tax of 40000 dollars were to be levied upon 1200 polls: I demand what one poll would pay. Ans. $33,400

3. Divide 1474 dollars equally among 25 men, 30 women, 17 boys, and 27 girls: after taking out 75 dollars for a present to a nephew.

Ans. $14

4. Divide 247600 pounds of beef equally among an army of 23724 men. Ans. 101939 lbs.

5. Sixty men at a feast, which lasted 3 days, spent 240 dollars per day; how much did each man spend per day, and how much in the whole?

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

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 flour; 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..

SHORT DIVISION.

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 dividend to the tens, divide as at first; and thus proceed through the whole, and the quotient will stand under the dividend..

Examples.

2)423(3)4567( 4)61234( 5)1234567(

211 Ans. 1522 Ans. 153082 Ans. 2469133 Ans. 7)12345( 8)43213)

6)64567(

9)764321(

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;

hundreds under hundreds; pounds under pounds, &c. always observing to write every denomination under that of the same name; begin to add in the lowest denomination mentioned; find the sum of that denomination; divide the sum by the number which it takes of this denomination, to make one of the next higher; set down the remainder, and carry the quotient to the next denomination; find the sum of the next and proceed as before through all the denominations; observing to set down the whole sum of the last denomination.

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Practical Questions in Money.

1. Add together $21,71 cts.; $63,42 cts. ; $84,96 cts. Ans. $170,09 cts.

*Some have objected to having the answers put to these questions; but the author is of opinion that they can do no harm, but will abundantly facilitate the labour of the instructor; if the scholar should attempt to copy without adding up the columns, the book can be taken from him; and if he does copy the two, or three first questions, it will be impossible to copy the practical questions.

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2. A. owes me $91, 64 cts. 7m.; B. $102,75 cts. ; and C. $21,42 cts. ; what do they all owe me ?

Ans. $215,81 cts. 7 m.

and D.

3. A. owes B. 891, 73 cts.; C. 112,41 cts.; and D. $119, 91 cts. I demand what he owes to B. C. Ans. $324,05 cts.

4. A. has a demand upon B. for $642,20 cts.; upon C. for $219; and upon D. $750,94 cts. ; I demand the sum of his dues. Ans. $1612,14 cts. 5. A farmer sold 3 yokes of oxen; for one yoke he received $105; one $117,75 cts.; and one $95,55 cts.; what did they all come to ? Ans. $318,30 cts.

6. What is the value of 3 ships, valued as follows, viz. one $4750; one $6742; and one $7891? Ans. $19383,

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By this weight is weighed gold, silver, &c.

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16.

Practical Questions in Troy Weight.

1. A man has two wedges of gold, one weighing 25 lb. 3 oz. 12 pwt. and the other weighing 1 lb. 11 oz. 12 pwt. 7 gr.; I demand the weight of the two wedges. Ans. 27 lb. 3 oz. 4 pwt. 7 gr.

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2. What is the weight of the following silver articles, viz. one spoon weighing 1 lb. 10 oz. 19 pwt.; one tankard weighing 4 lb. 6 oz. ; one basin weighing 1 lb. 10 oz. 19 pwt. ?

Ans. 8 lb. 3 oz. 18 pwt.

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