7th. A man sells a farm containing three hundred and fourteen acres, for twenty-five dollars per acre; what does the whole farm amount to? 7850 dol. Ans.

5. A boy had 16 peaches, which he sold at 2
cents each. What did he get for them?
6. A person being asked his age, said that he
was 3 times as old as his brother, who was 9
years old
Required his age?

7. In one dollar there are 6 shillings. How
many in 13?

8. A person bought 12lbs. of candles, at 2 shillings a pound. How many shillings did they cost him?

9. A person owned 3 houses, for each of which he received 120 dollars per year. What did the rents of the 3 houses amount to per year?

10. In one dollar there are 72 pence. How many are there in 4 dollars ?

II. A man hired a horse and chaise for 12 dollars a week, and kept them 9 weeks. What ought he to pay for the use of them? 12. What cost 18 cords of wood, at 7 dollars per cord?

SIMPLE DIVISION

Teaches to find how often one number is contained in another, each of which must be of only one denomination; or, to separate any number or quantity, into any number of equal parts. Division consists of four parts, viz.

1st.

The Dividend, or number to be divided.

2d. The Divisor, or number to divide by.

3d. The Quotient, which is the answer to the question, and shows the number of times the divisor is contained in the dividend.

4th. The Remainder,* which is of the same name with the dividend, and is always less than the divisor.

PROOF. Multiply the divisor and quotient together, and add in the remainder, (if there be any,) to the product, which, if the work be right, will be a sum equal to the dividend.

RULE. Having properly stated the question, first inquire how many times the divisor is contained in a certain number of the first left hand figures of the dividend, (which figures alone must be a sum at least equal to the divisor,) which being ascertained, place the figure in the quotient: then multiply the divisor by the quotient figure, and set the product directly under that portion of the dividend which you divided, and subtract it therefrom; to the right hand of the remainder, bring down the next figure of the dividend, and inquire how many times the divisor is contained in that number; when found, place the figures in the quotient as before, and multiply the divisor by it, and set the product under the last divided num

*The Remainder is very uncertain, there being sometimes one, and sometimes none. NOTE. The remainder, after dividing, is always the numerator to a proper fraction, the divisas being the denominator. This fractional part belongs to the quotient.

ber; subtract as before, and to the remainder bring down the next figure of the dividend; thus proceed, till every figure of the dividend is brought down.

Note. If, after a figure is brought down, the number be less than the divisor, place a cipher in the quotient, and bring down another figure.

EXAMPLE.

In the above example, I first inquire how many times twentyfour there are in seventy-eight, which I find to be three; I then place 3 in the quotient, and multiply the divisor 24 by it, and place the product 72, under 78, the number divided; I then subtract 72 from 78, and find the remainder to be 6; I then bring down the next figure of the dividend, which is 1, and inquire how many times 24 there are in 61, which being found, I place the figure in the quotient as before; I proceed in the same manner till every figure of the dividend is brought down. Then, to prove the work, I multiply the quotient and divisor together; and, to the product, add the remainder 16; the sum, being equal to the dividend, shows the work is right.

CASE II. When there are ciphers at the right hand of the divisor, cut them off: likewise cut off the same number of figures from the right hand of the dividend, and proceed to divide as in the first case.

Note. The figures which were cut off from the dividend, must be placed at the right hand of the remainder.

CASE III. To divide by 10, 100, 1000, 10000, &c. cut off so many figures from the right hand of the dividend as there are ciphers in the divisor; the figures cut off will be the remainder, and the left hand figures will be the quotient.

Short Division is, when the divisor does not exceed 12; and is performed in the usual way, only the several steps pursued by the assistance of figures in other cases, are omitted in this, and the work wrought entirely by the mind.

RULE. Separate the divisor from the dividend in the usual way; then draw a line under the dividend, and inquire how many times the divisor is contained in one or more figures of the dividend, which, being found, place the first quotient figure directly under the unit figure of that portion of the dividend which you divide; then, mentally, multiply the divisor by the quotient figure, and subtract the product from the divided number; to the remainder bring the next figure of the dividend, and inquire how many times the divisor is contained in that number; when found, proceed as before. Thus continue, till every figure of the dividend is divided.

Note. If there be a remainder after all the figures of the dividend are divided, strike a short line at the right hand of the quotient, at the end of which place the remainder..

19 Answer.

1st. Divide six thousand, seven hundred and sixty-four, by nineteen. 356 Answer. 2d. Divide six thousand, seven hundred and sixty-four, by three hundred and fifty-six. 3d. If five hundred and fifty-five dollars be divided equally among fifteen men, what will each have? 37 dols. Answer. What is the third part of 3669 ? 5th. What is the fourth part of 87856?

4th.

6th.

7th.

8th.

1223 Answer. 21964 Answer.

What is the twenty-fourth part of 2688 ? 112 Ans.
What is the half of 98570?

49285 Answer.

What is the hundred and fiftieth part of 2550?

17 Answer.. 9th. A gentleman bought 387 acres of land, for which he gave 8514 dollars. What did it cost per acre? 22 dols. Ans. 10. A gentleman dying, left 16536 dollars, to be divided in the following manner, viz-To his widow he gave one third part; and the remainder was to be divided equally among four children; what did each have?

COMPOUND ADDITION

Teaches to find the total sum of two or more numbers, which consist of several denominations.

RULE 1st. Each denomination must be placed directly under that which is of the same name; that is, farthings must be placed under farthings, pence under pence, shillings under shillings, &c.

ŘULE 2d. Carry for so many, in every denomination, as make one,* in the next higher denomination.

PROOF. In order to prove any sum in Compound Addition, proceed in the same manner as in Simple Addition.

Before the learner begins to work questions in lawful money, it would be well to commit to memory the following Tables.

This may be illustrated by the following observation. As there are four farthings to one penny, it is evident that there are as many pence in any number of farthings as there are times Cour in that number.