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EXAMPLES BY LONG DIVISION.

1. Divide £16 17s. 3d.

- by 13.

£ S. d. £ 8. d.

qr.

2. Divide 28 rd. 5 yd. 2 ft. by 21.

rd. yd. ft. rd. yd. ft. in.

13) 16 17 3(1 5 11 1 21)28 5 2(1 20 31.

[blocks in formation]

3. Divide £16 17s. 3d. 1qr. by 5; by 7; by 13.
4. Divide 1105 gal. 3 qt. 1 pt. 3 gi. by 3; by 16.

5. Divide 15 m. 4 fur. 34 rd. 4 yd. 2 ft. 8 in. by 4; by 8; by 32.

6. Divide 118 yd. 3 qr. 2 na. by 35.

7. Divide 54 A. 2 R. 36 sq. rd. 11 sq. yd. 2 sq. ft. 8 sq. in. by 2; by 4.

8. Divide 125 lb. 11 oz. 15 dwt. 18 gr. by 8; by 7; by 15.

68. MISCELLANEOUS EXAMPLES IN COMPOUND NUMBERS. 1. If 8 yards of broadcloth cost £10 4s. 6d., what will 1 yard cost? What will 5 yards cost?

2. A merchant bought 5 cwt. 3 qr. 7 lb. of cheese, at one time; 8 cwt. 3 qr. 25 lb., at another; and 15 cwt. 2 qr. 17 lb., at another. How much did he buy?

3. How many pounds were there, reckoning the qr. at 28 pounds, and how much did it cost at 6 cts. per lb. ?

4. If the merchant sells 18 cwt. 3 qr. 24 lb., how much has he left?

5. A farmer raised 185 bu. 3 pk. of oats, 237 bu. 2 pk. of corn, 115 bu. 1 pk. of wheat, and 145 bu. of rye. How many bushels were there in all? How many pecks?

6. A grocer bought 5 firkins of butter, weighing as follows: No. 1, 47 lb. 14 oz.; No. 2, 58 lb. 13 oz. ; No. 3, 38 lb. 10 oz. ; No. 4, 73 lb. 8 oz.; No. 5, 46 lb. 3 oz. How much was there

in all? What did he pay for it at $0.175 a lb. ?

7. If the grocer should divide the butter into 10 equal portions, how much would there be in each?

8. If he should sell it at 20 cents a lb., how much would he gain?

9. A merchant bought in England 15 yds. of broadcloth, at £1 17s. 9d. per yd. How much did it come to? If he should sell it for £1 19s. Sd. more than he gave for it, what would be the price per yard?

10. A locomotive has gone 78 m. 3 fur. 15 rd. 4 yd. 2 st. in 5 hours. How far has it run per hour?

11. How much further would another locomotive go in 7 hours, if its rate of travelling was 2 m. 2 fur. 25 rd. more per hour?

12. A merchant bought 560 bu. 3 pk. of corn, which he wishes to put in equal parcels in 6 different bins. How much must be put in each?

13. A farmer raised 35 T. 17 cwt. 3 qr. of hay; 5 loads, each weighing 2 T. 13 cwt. 1 qr. 14 lb. has he left?

he has sold How much

14. He wishes to make 15 loads of the remainder, how much must he take at each load?

15. How much butter in 12 firkins, if each contains 47 lb. 7 oz.?

16. There are 848 gallons of molasses in 6 casks. How much in each cask?

17. A farmer would divide 87 A. 3 R. 15 rd. of land into 5 fields of equal size. How much shall each field contain? 18. A silversmith having 48 lb. 5 oz. 2 dwt. of silver, has used 25 lb. 8 oz. 17 dwt. How much remains on hand?

19. He wishes to make of the remainder 15 tea-pots of equal weight. How much shall each weigh, and what is its value at 64 cents a dwt.?

20. A man bought 2 A. 3 R. 28 sq. rd. of land. How many

sq. rods does it contain? How many sq. ft.? What is its value at 1 ct. per sq. ft.?

21. If he sells 1 A. 35 sq. rd. 6 sq. yd. 8 sq. ft., how much land has he left?

22. A farmer had 85 C. 102 cu. ft. of wood, which he carried to market in 67 loads. How much did he carry at a load?

23. A tailor bought 85 yds. of cloth, from which he has cut 21 coats, each containing 2 yd. 3 qr. 2 na. How much cloth

remains?

24. If he makes the remainder into 15 coats, how much cloth will each coat contain?

25. 8 horses have eaten 47 bushels of oats in 20 days. How much has each horse eaten? How much per day?

26. A farmer carried 47 cords of wood to market in 21 loads. How much did each load contain?

69. To find the time between two different dates.

1. What is the time from April 14th to June 23d? From April 14th to June 14th is 2 months; and from June 14th to June 23d is 9 days. Ans. 2 mo. 9 da.

2. What is the time from Nov. 15th, 1848, to Feb. 7th, 1849? From Nov. 15th to Jan. 15th is 2 months; there are 16 days in Jan. after the 15th; adding to this the 7 days in Feb., gives 23 days. Ans. 2 mo. 23 da.

3. What is the time from Jan. 19th, 1845, to March 17th, 1846? From Jan. 19th, 1845, to Jan. 19th, 1846, is 1 year; from Jan. 19th to Feb. 19th is 1 month, and from Feb. 19th to March 17th is 26 da. • Ans. 1 yr. 1 m. 26 da.

4. What is the time from June 15th, 1847, to Nov. 12th, 1849? From Dec. 15th, 1840, to July 10, 1848? From June 10, 1835, to Nov. 8, 1850? From April 6, 1832, to Oct. 15, 1845? From Aug. 4, 1847, to March 3, 1848?

5. A note was given July 17, 1845, and paid Jan. 15, 1848. How long was it on interest? (5.)

NOTE. The above mode of computing time, although different from the mode given in most works on arithmetic, is the mode adopted by merchants and accountants in computing the time between two different dates. It may be thus expressed :

Find the number of months from the first date to the corresponding day next preceding the last date; then count the days that intervene between that day and the last date.

QUESTIONS. What are simple numbers? Compound numbers? What is compound addition? What is the rule for compound addition?

What is the rule for compound subtraction? What is the rule

for compound multiplication? What may be done if the multiplier is a composite number? What is the rule for compound division? When is the work to be done by long division? When by short division? What is the rule for computing the time between two different dates?

SQUARE AND CUBIC MEASURE.

70. EXERCISES IN SQUARE AND CUBIC MEASURE.

1. A surface 1 inch long and 1 inch wide contains 1 square inch. How many square inches in a surface 2 in. long and 1 in. wide? 3 in. long and 1 in. wide? 5 in. long and 1 in. wide?

1 2 3 4

The diagram in the margin may represent a surface 5 inches or feet, &c., long, and 4 inches, &c., wide; each square representing 1 square inch or 1 square foot, &c.

2. How many square inches in a surface 5 in. long and 2 in. wide? 5 in. long and 3 in. wide? (56.)

3. How many square feet in a board 5 ft. long and 4 ft. wide? 8 ft. long and 5 ft. wide?

4. How many square inches in a board 216 in. long and 18 in. wide? How many sq. ft.?

5. How many square feet in a floor 18 ft. long and 13.5 ft. wide? How many of the above boards will cover it?

6. How many square inches in a board 1 ft. 4 in. wide, and 15 ft. 8 in. long? How many sq. ft.?

7. A room is 30 ft. long and 12 ft. high; how many sq. ft. on one of its sides? How many on its 2 opposite sides?

8. The room is 20 ft. wide; how many square feet in one of its ends? In both ends? How many in the ceiling? In the floor?

9. How many square feet in the four sides and the ceiling? How many square yards? What will the plastering come to, at 6 cents a sq. yd.?

10. How much will the flooring cost, at 6 cents per sq. ft.? 11. There are 12 windows in the room, and in each window 12 panes of glass, each pane being 16 in. by 10 in. How many square inches of glass in each window? In all the windows? How many square feet? How much did the glazing cost, at 8 cts. per sq. ft.?

12. How many square yards in the 4 sides and ceiling of a room 15 ft. long, 12 ft. wide, and 9 ft. high?

13. How many square rods in a rectangular field 48 rods long and 40 rods wide? How many acres?

14. How much land in a road 4 rods wide and 1 mile long? 15. What is the value of a rectangular field 12 rods long and 8 rods wide, at $1.125 per square foot?

[graphic]

The diagram in the margin represents a solid, 5 inches or feet long, 4 inches, &c., wide, and 3 inches, &c., deep.

16. How many pieces, each containing 1 sq. inch, can be cut from a board 8 in. long and 4 in. wide, allowing nothing for waste? How many cubic inches are there in the board, if the board is 1 in. thick? (57.)

17. How many if it were 2 in. thick? 3 in. thick?

18. How many cubic feet in a block 3 ft. long, 2 ft. wide, and 1 ft. thick?

19. A load of wood is 8 ft. long, 4 ft. wide, and 4 ft. high. How many cords does it contain?

20. How many cubic feet in 5 loads, each measuring 10 ft. long, 4 ft. wide, and 6 ft. high? How many cord feet? How many cords?

21. A pile of wood is 32 ft. long, 15 ft. wide, and 10 ft. high. How many cords does it contain? How much will it come to, at $4.50 per cord? Answer in cords and decimals.

22. How many cubic inches in a block of marble 8 ft. 3 in. long, 4 ft. 5 in. wide, and 3 ft. 7 in. thick? How many cubic

feet?

23. How many tons of 2000 lb. will the above block weigh, allowing 12 cubic feet to weigh a ton?

24. How many gallons of water will a rectangular cistern hold, that is 5 ft. long, 8 ft. high, and 4 ft. wide, allowing a cubic foot to hold 7.5 gallons?

SECTION VII.-ARITHMETICAL TERMS DEFINED AND ILLUSTRATED.

71. A Unit is a single thing of a kind; as one hat, one school, one nation.

An Integer is any whole number; as 1, 8, 15.

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