Similar remarks apply when addition and subtraction enter into a computation. The order in which the numbers are taken is indifferent; and, in place of the respective numbers, their difference may be used, adding it when the sum of the additive numbers is the greater, and subtracting it when the sum of the subtractive numbers is the greater.

When the number to be divided or diminished will not run into fractions by the process, it will always save time to divide before multiplying, or to subtract before adding.

Exercises for the Slate or Black-board.

1. A merchant bought, in the spring, goods to the amount of $106,409, and on the first of January following found he had sold to the amount of $74,326; what amount of goods was left unsold? Ans. $32,083.

Suggestive Questions.-What do we want to know here? Is it the sum of these two numbers, or their difference? or is either of those numbers to be taken a certain number of times, or to be divided into a number of equal portions?

all?

2. A merchant bought 340 pieces of cotton. In every piece there were 26 yards. How many yards were there in Ans. 8840 yards. Suggestive Questions.—What is required here? In every piece 26 yards. How many in all? Is it the sum, difference, product, or quotient?

3. A merchant making an inventory of his stock, finds he has cotton cloth to the value of $356, linen $152, broadcloth $575, cassimere $264 75, silk goods $254 25, ginghams $125, calicoes $240, and various small articles to the amount of $336.56. What is the whole value of the stock?

Ans. $2303 56. 4. A man died leaving an estate worth $21,156 to be equally divided among his six children. How much would they have apiece? Ans. $3,526.

5. A merchant, on New Year's day, sent his clerk to collect debts and make some purchases. He received from John Stokes $265, from William Budd $375, from Jacob Jones $526, and from Thomas Strickland $623. The clerk then bought at one of the cotton mills 360 yards of cotton cloth, at 6 cents per yard; 525 yards of calico, at 10 cents per yard; 240 yards of gingham, at 183 cents. He also bought at a

woollen manufactory 200 yards of broadcloth at $2.25, 140 yards at $275, 75 yards at $4, and 63 yards at $5; and be-. fore he reached home he also bought 33 yards of carpeting at 60 cents. He paid over the balance to his employer, who divided the cents equally between his two little boys; the dollars he divided equally among his four daughters as a NewYear's present. How much did each of his children receive? Ans. $50 to each daughter, and 5 cents to each boy.

The above question embraces Addition, Subtraction, Multiplication and Division. The amount of money received by the clerk must first be ascertained. Secondly, the cost of each article that he purchased, and the total amount of the purchases. Thirdly, the difference between the receipts and payments will show what money he paid his employer. Lastly, the cents being divided into two parts, and the dollars into four, will show how much each child received. The addition and subtraction may be one operation.

6. A lady who had 19 five dollar bank notes in her pocketbook, and five dollars in silver change in her purse, went out one morning to make some purchases. She bought 7 lbs. of beef, at 6 cents per lb.; a fish for 25 cents; a piece of corned beef for 30 cts.; a cabbage for 4 cts.; a peck of potatoes 8 cts.; a pound of sausages 10 cts.; a bunch of celery 10 cts. Having sent these articles home, she called at a store, where she made the following purchases: 8 yds. of calico, at 18 cts.; 8 yds. of mousseline de laine, at 25 cts.; 2 linen handkerchiefs, at 621 cts.; a yard of linen, 75 cts.; 8 yds. cotton cloth, at 18 cts.; a pound of tea, 75 cts.; a loaf of sugar, weighing 9 lbs., at 15 cts.; 4 lbs. of raisins, at 10 cts.; a dozen of eggs, 8 cts. At a bookstore she paid $3 for her yearly subscription to a magazine, and bought some new books to the amount of $4. She next called on a poor widow, who had lately lost her only daughter, and presented her with $2. Lastly, she stopped at the tinsmith's, where she bought a watering-pot for $1, 6 tin pans, at 25 cts. each, and a dipper for 25 cents. How much money had she remaining when she got home?

Ans. $77.50.

7. A merchant in Burlington, Vt., received 17 packages of goods from Boston, each weighing 72 lbs. The total freight by railroad was of a cent per lb., the cartage to his store was 25 cts. for the whole. What was the whole expense of carriage from Boston to his store? Ans. $4.33.

cwt. of wool, at $401 Ans. $7187.

meadow land, which He kept 63 head of and sold, besides, 621

8. The same merchant bought 17 What was the whole cost? per cwt. 9. A farmer mowed 781 acres of yielded on an average 23 tons per acre. cattle through the winter on the hay, tons. How much hay did he make in the whole, and how much did each of the cattle consume on an average through the winter? [That is, how much hay did he cut? How much did he sell? How much did all his cattle eat? How much did each of them eat?] Ans. to the last question, 2 tons. 10. What do 9 pieces of cloth, of 28 yards each, come to, at $3.374, or $33, per yard? Ans. $86511.

11. A captain of a vessel has on board 205 bales, each paying $125, or $14, freight; 275 packages, each paying 87 cents, or $3; 150 tons of other goods, each ton paying $12 625, or $12§; and 6 passengers, each paying $75. What does the whole freight and passage money amount to? Ans. $2840 62. 12. A man who owned of a ship sold of his share. What share of the vessel did he sell, and what share did he keep? Ans. to last question, 13. The net profits of the vessel for one year after this sale was $32000. How much was each of the above shareholders entitled to receive? Ans. $9000 and $3000. 14. I have 765 pieces of cloth, and am about to put them up into bales of 15 pieces each. How many bales will there be? Prove by trial. 15. How many days are there in 24,480 minutes?

Ans. 17.

16. A farmer threshed grain 7 days: the first day 121 bushels: the 2d, 181; the 3d, 241; the 4th, 30%; the 5th, 32; the 6th, 443; the 7th, 15. He paid his workmen in grain. To one man he gave 31 bushels, to another 2; he returned to his neighbor what he had last borrowed of him to go to mill, which was 78 bushels; and he sent 10 bushels to mill to be ground for his stock, and 5 for family use. The next day he sold half of what was left, and the day following sent half of the remainder to the store in payment of the balance of his account. How much was then left in his granary?

Ans. 37 bushels. 17. If 18 grains of silver make a thimble, and 12 dwts. make a teaspoon, how many, of each an equal number, can be made from 15 oz. 6 dwts. of silver?

Ans. 24.

18. A man divided 75 cents among his three sons. As often as he gave the eldest 7 cents, he gave the second 5, and the third 3. How many cents did each receive? Prove by trial.

19. A carpenter bought 16 pieces of timber, each 16 inches square, and 13 feet long. What was the number of cubic feet, and what was the cost, at 12 cents per cubic foot?

Ans. to last question, $463.

20. A mason undertook to build a bridge for $300. He hires six laborers to assist him, to each of whom he pays 62 cents per day, and their board, which he calculates to cost 25 cents each, for every working day. The work was finished in 40 days. How much did he get for his labor and superintendence, calculating his board at the same rate as that of his Ans. $80.

men?

21. Bought 16 bales of cotton. Four of them weighed each 1024 lbs.; 6 weighed each 998 lbs.; and the remainder 1054 lbs. each. What was their cost at 61 cents per lb.?

Ans. $1025 50.

22. What are the solid contents of a wall 75 feet long, 3 feet 9 inches thick, and 24 feet 2 inches high; and how many bricks did it take, if (including the mortar) they occupied 9 inches in length, 4 in width, and 2 in depth?

Ans. to last question, 116,000.

23. There is a room 16 feet long, 14 feet broad, and 11 feet high. A mason engages to plaster it for 20 cents per square yard, the doors and windows being counted the same as an unbroken wall. What will be the amount of his bill, including the ceiling? Ans. $19.644.

Suggestion. In order to solve such questions correctly, the pupil should realize the statements, by looking around the room in which he is placed. Thus, let him ask himself How many long sides of the room? What are their dimensions? How many short sides? their dimensions? What are the dimensions of the ceiling? What, then, are the dimensions of the whole room? How many square feet in a square yard?

24. What will be the cost of a floor-cloth for an entry which is 34 feet long, and 10 feet wide, in which the stairs occupy a space of 14 feet by 3 feet 9 inches, making an allowance of of a yard for waste in cutting, at $1.12 per square yard? Ans. $36.

25. How many cubic feet of earth will fill a dock 120 feet long, 75 feet broad, and 10 feet deep? A man has engaged

to fill it for 15 cents a load, his cart being 8 feet long, 4 feet broad, and 1 foot 6 inches deep. What will be the expense, supposing the heaping of the loads will balance the settling of Ans. $281 25. 26. What must be the depth of a square vessel 1 foot 6 inches broad, and 2 feet 4 inches long, that shall hold 8 feet cubic measure? Ans. 2 feet, 33 inches.

the earth?

27. Three brothers emigrate to the western country. The eldest buys 640 acres at $2.25 per acre; the second buys 240 acres for $600; the third bought as much land as both his brothers for $1100. How much had the eldest to pay; how much did the second pay per acre; how much land did the third buy, and at what price per acre; and how much land had the three brothers?

Ans. $1440; $250; 880 acres, at $1.24+; 1760 acres. 28. A carpenter hewed 25 pieces of timber 8 inches square and 36 feet long; 16 pieces a foot square and 42 feet long; 23 pieces 18 inches by 20, and 26 feet long; 12 of 10 inches square and 32 feet long; and 15 pieces of 8 inches square and 18 feet long. What will be the amount of his bill at 64 cents per cubic foot ? Ans. $200-433.

29. What will be the cost of painting two rooms, including walls, ceilings and floors, at 7 cents per square yard? Their height is 12 feet 4 inches; the length of one is 32 feet, and its breadth 24; the length of the other is 24 feet and the breadth 16 feet 6 inches. No allowance to be made for doors or windows. Ans. $36 627.

30. A workman engaged to plaster a house at 21 cents per square yard, of which the following are the dimensions: on the first floor there are two rooms, each 20 feet by 18, and 11 feet high, and an entry 10 feet by 36, of the same height. In each room, one of the ends, 18 feet wide, is not to be reckoned, as compensation for doors, windows and fireplace; in the entry neither end is to be reckoned, as compensation for doors and windows. On the second floor there are two rooms the same size as those below, on which a similar allowance is to be made; the entry is the same size as below, excepting that a room 10 feet square is taken off one end; neither end of the upper entry is to be counted, as compensation for doors and windows in the entry. What will be the amount of the plasterer's bill? Ans. $152.04. 31. The Hoosac Mountains are two degrees west of Boston.