7. If 196 be divided by 14, what will the quotient be? 8. A section of land containing 1885 acres was divided into 13 farms; how many acres did each farm contain?

9. How many kegs, containing 18 gallons each, can be filled from 4 casks of wine each containing 108 gallons? Ans. 24. 10. Twenty-five men were employed in building a cotton factory, the labor of which amounted to 3125 dollars; how much did each man receive ? Ans. $125.

11. A farmer sold 21 acres of land for 210 dollars, by which he lost 42 dollars; how much did it cost him per acre?

12. A privateer in the last war took a prize worth $8050; the owners claimed $4025, the captain claimed $375, and the mate 275 dollars; the residue was divided among the sailors, 25 in number; what was each seaman's share? Ans. 135 dollars. 13. Eighteen wagons were employed to transport 810 bushels of salt; how many bushels to each wagon?

N. B.-In order to give the scholar an opportunity of exercising his judgment in finding the proper quotient figure, I have set in the quotient's place such a sum as will be produced by multiplying the true quotient by 2, and adding in the remainder. The scholar therefore need only multiply his quotient by 2, (adding in the remainder if any,) and if the product agree with the figures I have placed in the answer, he may venture to call his work right; as the following examples will show. 1. Divisor 14)156970998(Quotient x2+the Remainder. 22424430 Ans.

2. Divisor 16)1243789469 (Quot. x2+the Rem.

155473695 Ans.

3. Divisor 25)290327894(Quot. ×2+the Rem.

23226249 Ans.

4. Divisor 36)168236008(Quot. x2+the Rem.

9346460 Ans.

5. Divisor 37)463728192(Quot. x2+the Rem.

25066402 Ans.

6. Divisor 125)1067324678(Quot.x2+the Rem.

17077247 Ans.

7. Divisor 246)610194144(Quot. x2+the Rem.

4960928 Ans.

8. Divisor 416)1438024224(Quot. x2+the Rem.

6913578 Ans.

9. Divisor 2467)987654321 (Quot. x2+the Rem.

801431 Ans.

10. If a cannon-ball were to continue with the same rapid flight as when leaving a cannon's mouth, it would travel about 11516 miles in one day; how many days would it be in going from the earth to the sun, a distance of 95000000 miles?

Ans.x2+Rem. 21014 days.

11. How many firkins, each holding 45 lbs. can be filled from 45900 lbs. of lard? Ans. X2-2040. lbs.

12. On the first day of January, 1816, the public debt of the United States amounted to 123016375 dollars: Now if a man could count 75423 dollars in one day, in how many days could he count the whole debt? Ans. X2+Rem.-4724 days.

13. A wine merchant bought 14 pipes of wine, each containing 126 gallons; if he wish to put it into quarter casks, each containing 32 gallons, how many casks must he buy?

Ans.x2+Rem.=114. 14. If a steam-boat can sail in one day, 245 miles, how long will she be in passing round the earth, a distance of 25000 miles? Ans. x2+Rem. 214 days. 15. A cistern holding 4690 gallons of water, is required to be emptied; how long will a man be in pumping it dry, at the rate of 35 gallons a minute? Ans. X2 268 minutes. 16. How many lots, each containing 16 acres, can be fenced in, from a farm containing 368 acres?

Ans. X2=46. 17. There is a fountain of water containing 1237750 gallons; how long will a force pump, which discharges 250 gallons in a minute, be in emptying this fountain?

Ans. X2-9902 minutes.

18. If a township contain 64000 acres of land; how many farms, each containing 200 acres, can be laid out in it, and if each farm be inhabited by 8 persons, how many inhabitants are there in the town?

CASE SECOND.

Q. What is the second Case in Long Division?

A. When there are ciphers at the right hand of the divisor. Q. What is the RULE in this Case?

A. Cut off the ciphers in the divisor, and as many figures from the right hand of the dividend; then divide the remaining part of the dividend, by the significant figures of the divisor, as before taught, and to the remainder annex the figures which were cut off from the dividend, and you will have the

same remainder which would result from dividing by the whole divisor; if there be no remainder, after dividing, bring down the figures which were cut off from the dividend, and they will constitute the remainder.

EXAMPLES.

1. Divisor 14600)37548659732(Quotient x2+Remainder.

5143784 Ans.

2. Divisor 375000)7849345678 (Quot. x2+Rem.

262540 Ans.

3. Divisor 433000)53729614529 (Quot. x2+Rem.

624701 Ans.

4. Divisor 16730000)1230450670890(Quot. x2+Rem.

5. Divisor 1200)103789467(
6. Divisor 900)123478625(
7. Divisor 8000)3746789000(
8. Divisor 40)37678925(

9507984 Ans.

9. A general, commanding an army of 44000 men, received 5676320 dollars to be equally divided among them, so long as each man could receive a dollar, and whatever was left, the general was to have for his share; what was each soldier's part, and how much remained for the commander?

Ans.

Each soldier's share $129. The general's share $320. 10. What number multiplied by 3600 will produce 457200?

Ans. 127.

11. If, in a town containing 25000 inhabitants, a tax of 75000 dollars be assessed, to be paid equally by each person, how many dollars will each pay?

12. If a certain quotient be 437000, and the dividend be 587765000, what is the divisor? Ans. 1345. 13. Suppose a pond to contain 984960000 cubic feet of water, and a sluice-way to discharge 4500 cubic feet in a minute, how many minutes will it take to draw the pond dry?

CASE THIRD.

Ang. 218880 minutes.

Q. What is the third Case in Long Division?

A. When the divisor is an unit with any number of ciphers annexed, as 10, 100, 1000, 10000, &c.

Q. What is the RULE in this Case ?

A. Cut off as many figures from the right hand of the div idend as there are ciphers in the divisor, and the figures at the

left hand of the cut-off will be the quotient, and those at the right hand, the remainder.

1. Divide 4873 by 10.

EXAMPLES.

2. Divide 398763 by 100.

3. Divide 408721436 by 1000.

4. Divide 6543167102 by 10000.

Ans. 487, and 3 remains.
Ans. 3987, 63 rem.

5. If 100 acres of land cost 15600 dollars; what is that an acre?

6. If 10 horses cost 450 dollars, what was the price of each horse?

7. If 100 barrels of flour cost 800 dollars, what is that per barrel?

8. If 1000 barrels of beef cost 14000 dollars, how much is that per barrel?

9. If a hound run 150 miles in 10 hours, how much is that an hour?

SUPPLEMENT TO MULTIPLICATION AND

DIVISION.

Q. How will you express any part of a unit or one, as one half, one third, or two thirds?

A. By a term called a Fraction.

Q. How is a fraction expressed, or written?

A. By two figures, one placed above the other, with a line drawn between them, thus: represents one half: represents one third: represents two thirds, &c.

Q. What does the lower figure of a fraction always show? A. It shows how many parts the unit or whole number is divided into.

Q. What dose the upper figure show?

A. It shows how many of these parts are meant to be included in the fraction; (thus means that the unit is divided into 4 parts, and that 3 of these parts are meant by the fraction also, when I say I own of a ship, I mean that the ship is divided into 8 shares, and that I own 5 of those shares.)

Q. By what name are the figures which form a fraction, distinguished from each other?

A. The figure above the line is called the numerator: that below the line, is called the denominator.

Q. From what do fractions arise, and how are they produced?

A. All fractions arise from division. When any number is divided by another, and there is a remainder, that remainder is a numerator, and the divisor is a denominator; and then a fraction is produced; as 28 divided by 6 leaves a remainder of 4; this 4 is the numerator of a fraction, and the divisor 6, is the denominator: thus, 4, showing that if 28 be divided into 6 parts, each part will be 44 that is, 4 units, and of a unit. Q. What is such a number as 44 called?

A. It is called a mixed number.

Q. What is the definition then of a mixed number? A. It is a whole number, joined with a fraction, as 5, 71, 6}, 144, 284, &c.

CASE FIRST.

Q. What is the first Case ?

A. It is when the Multiplier is a mixed number, as 6}, 241, 314, &c.

Q. What is the RULE in this Case ?

A. Multiply by the whole number as in Multiplication; then divide the multiplicand by the lower figure, or denominator of the fraction, and add this quotient to the product, and the sum will be the answer.

Q. How would you multiply by a simple fraction, as,, , &c.?

A. Divide the multiplicand by the lower figure of the fraction, and the quotient will be the answer.