8. A merchant bought a piece of broadcloth, containing 40 yds., from which he sold 36 yds. 1 qr. 2 na.; how much did he have left? A. 3 yds. 2 qrs. 2 na.

9. A grocer bought a hhd. of rum, containing 65 gals., and by accident 2 gals. 2 qts. 1 pt. leaked out; how many gallons did he have left? A. 62 gals. 1 qt. 1 pt.

10 A merchant bought a quantity of corn, weighing 20 cwt. 2 qrs. 15 lbs., of which he sold 10 ewt. 3 qrs. 12 lbs.; how much had he left? A. 9 cwt. 3 qrs. 3 lbs.

11. A grocer retailed 10 gals. 3 qts. 1 pt. 1 gi. of rum from a hhd. containing 54 gals. 2 qts. 1 pt. 2 gi., how much had he left? A. 43 gals. 3 qts. Opt. 1 gi.

12. If, from a box of butter, containing 20 lbs., there be sold 10 lbs. 8 oz., how much will there be left? 4.9 lbs. 8 oz.

13. If, from a field, containing 40 acres, 2 roods, 20 poles, there be taken 19 acres, 3 roods, 30 poles, how much will there be left? A. 20 acres, 2 roods, 30 poles.

14. William engaged himself in a store for 3 yrs.; after having stayed 2 yrs. 2mo. 2w. 2 da., how much longer had he to stay? A. 9 mo. 1 w. 5 da.

15. A farmer, having raised 40 bu. of corn, kept 23 bu. 2 pks. for his own use, and sold the rest; how much did he sell? A. 16 bu. 2 pks.

16. A farmer made in one year, from his orchard, 200 bbls. 14 gals. of cider, of which he sold precisely 118 bbls. 3 qts. 1 pt. ; how much had he left for his own use? A. 82 bbls. 13 gals. I pt.

17. If, from a parcel of wood, containing 40 cords and 64 feet, there be sold 39 cords and 32 feet, how much will there be left? A. 1 cord 32 feet.

18. The distance from Providence to Norwich is 45 miles; now, when a man has travelled 30 m. 7 fur 20 rods of the distance, how much farther has he to travel? A. 14 m. 20 rods. 19. From 14£ 15 s. 6d. 2 qrs. take 12£ 15 s. 6d. 3 qrs. A 1£ 19 s. 11 d. 3 qrs.

20. From 1£

21. From 1£

22. From 1£
23. From 1 lb.
24. From 1 ton
25. From 1 lb.
26. From 1 yd.
27. From 1 bu.
28. From 1 yd."

take 2 s.

take 2 d.

take 2 qrs. take 19 grs. take 10 oz. take 15 grs. take 2 qrs. take 1 pt

29. From 1 yd. take 1 in.

A. 18 s.

A. 19 s. 10 d.

A. 19 s. 11 d. 2 qrs.
A. 11 oz. 19 pwts. 5 grs.
A. 19 cwt. 3 qrs. 27 lbs. 6 oz.
A. 11 oz. 19 pwts. 9 grs.
A. 2 qrs.

A. 3 pks. 7 qts. 1 pt.
A. 2 ft. 11 in. 2 b. c.

take 1 b.c.

30. From 1 sq. yd. take 3 sq ft. 21 From 1 ton)

r. timber

COMPOUND MULTIPLICATION.

↑ XXXII. 1. If one knife cost 9 d., how many shillings will buy 2 knives? Will buy 4? Will buy 6? Will buy 8? Will buy 12?

2. William, having a basket that would hold 1 qt. 1 pt., filled it with nuts; how many qts. can be put in a basket that will hold twice as much? 3 times as much? 4 times as much?

3. At 1s. 6 d. a bushel, how many shillings will 2 bushels of apples cost? Will 4 bu.? Will 6 bu.? Will 8 bu.?

4. Multiply 2 s. 6 d. by 2.

5. Multiply 2 pwts. 12 grs. by 2.
6. Multiply 2 bu. 4 qts. by 3.
7. Multiply 3 gals. 2 qts. by 2.
8. Multiply 20 m. 20 sec. by 3.

9. How many pence in 2 times 2 farthings? 4x2 farthings, or 2 qrs.? 4x3 qrs.? How many shillings in 2 times 6 d. ? 2 x 12d.? 4 x 6 d.? 5 x 12 d.? 8 x 3 d.? 4X7d.? 3x5 d. · 8 x 12 d. ?

10. How many pounds in 4 times 10 s.? 3 x 10 s.? 4 × 6s.?

Operation by Slate illustrated.

1. A merchant bought 5 yards of cloth for 2£ 6 s. 1 d. 3 qrs per yard; what did the whole cost?

OPERATION.

20 12 4

£

2

s. d. qrs. 613

5

Ans. £11 10 8 3

How do you get the 3 qrs. in the

answer?

3 d

A. 5 times 3 qrs. qrs. are 15 3 qrs., writing down the 3 qrs. and carrying 3 d. as in Compound Addi tion.

How do you get the 8d ? A. 5 times 1 d. are 5 d., and 3 d. (to carry) makes 8 d.

How do you get the 10s.? A. 5 times 6 s. are 30 s. 10 s., writing down the 10 s. and carrying the 1£

=

1£

How do you get the11£? A. 5 times 2£ are 10£, and 1£ (to carry) makes 11£.

From these illustrations we derive the following

RULE.

I. With which denomination do you begin to multiply? A. With the lowest.

II. How do you multiply that, and each denomination? A. Separately, as in Simple Multiplication.

III. How do you divide each product and carry? A. As in Compound Addition.

PROOF. What is the proof? A. As in Simple Multiplication

More Exercises for the Slate.

2. At 5 s. 6 d. a gallon, what will 2 gals. of rum cost? A. 11 s.

3. At 2s. 6d. 1 qr. a quart, what will 2 qts. of brandy cost? (5-0-2) What will 3 qts.? (7-6-3) What will 4 qts.? (10-1) What will 5 qts.? (12-7-1) What will 6 qts. (15-1-2). A. 2£. 10 s. 5 d

4. How much wine in 7 bottles, each containing 2 qts. 1 pt. 2 gills? (4-3-0-2) How much in 8 bottles? (5-2) In 9? (6-0-1-2) In 10? (6-3-1) In 11? (7-2-0-2). A. 30 gals. 3 qts. 1 pt. 2 gills.

5. What is the weight of 3 doz. silver spoons, each doz. weigh ing 2 lbs. 6 oz. 12 pwts. 3 grs.? (7-7-16-9) What will 4 doz. weigh? (10-2-8-12) What will 5 doz.? (12-9-0-15) What will 6 doz.? (15-3-12-18). A. 45 lbs. 10 oz. 18 pwts. 6 grs.

6. Bought 4 loads of hay, each load weighing 1T. 10 cwt. 2 qrs. 20 lbs. 5 oz. 15 drs.; what was the weight of the whole? (6-2-2-25-7-12) What would be the weight of 5 loads? (7-13-1-17-13-11) Of 11 loads? (16-17-2-0-1-5) Of 12 loads? (18-8-0-20-7-4). A. 49 T. 1 cwt. 3 qrs. 7 lbs. 14 oz.

7. At the rate of 36 lea. 2 m. 3 fur. a day, how far will a vessel sail in 6 days? (220-2-2) In 15 days? (551-2-5) In 10 days? (367-2-6) In 9 days? (331-0-3.) A. 1471 lea. 2 m.

8. In 8 bales of cloth, each bale containing 12 pieces, each piece 27 yds. 1 qr. 2 na., how many yards? A. 2628 yds.

COMPOUND DIVISION.

¶ XXXIII. 1. William had 2 qts. 1 pt. of walnuts, which ne wished to divide equally among his two little brothers. now many must he give each?

2. James bought 2 books for 2 s. 6 d.; how much did he pay apiece?

3. If you pay 1 s. 6 d. for 2 inkstands, how many shillings would that be apiece?

4. A man bought 4 lambs for 6 shillings; how many did he pay apiece?

pence

5. William has 3 pks. 4 qts. of walnuts, which he wishes to put into 4 little baskets, each of which will hold 7 qts; will his baskets hold all his walnuts, or not? and inform me how you do it.

6. 3 men have 4 gals. 2 qts. of cider allowed them every day; how much is that apiece?

7. How many pence is of 1 s.? 6 d.? of 1 s. 3 d. ? † of 1 s. 6 d. ? of 1 d. 2 qrs.

of 2 s.? of 3 s.?

of1s.

of 2 s. 6d.? of 1d.?

Q. What is this, which you have now been doing, called? A. Compound Division.

Q. Wherein does it differ from Simple? A. Simple consists of only one denomination; Compound, of more than one.

Q. What, then, is the process called, by which we find how many times one number is contained in another of different denominations? A. Compound Division.

Operation by Slate illustrated.

1. A man bought 2 loads of hay for 15£ 3 s. 8 d.; how much was that a load?

OPERATION.

20 12

£ 8. d.

2) 15

3 8

Ans. £7 11 10

How do you get the 7£ in the answer? A. I begin as in Short Division of whole numbers, and say, 2 is contained in 15£, 7(£) times, and 1£ over, writing down

the 7 times.

What do you do with the i£ over? A. 1£20 s., which I join or carry to the 3s., making 23 s.

How do you proceed, then, to get the 11 s.? A. I say, 2 in 23, 11 times, and I s. over, writing down the 11 s. underneath.

How do you get the 10 d.? A. The 1 s. over being equal to 12 d., I join or carry it to 8 d., making 20 d.; then, 2 in 20, 10 times.

From these illustrations we derive the following

RULE.

I. At which hand do you begin to divide, and how do you proceed? A. With the highest enomination, and divide us in Simple Division.

II. If you have a remainder, how do you proceed? A. Find how many of the next lower denomination this remainder is equal to, which add to the next denomination; after which divide as in whole numbers.

PROOF. What is the proof? A. The same as in Simple Di vision.

More Exercises for the Slate.

2. If 8 tons of hay cost 40£ 14 s. 8 d., what will 1 ton cost? A. 5£ 1 s. 10 d.

3. If 11 gals. of brandy cost 5£ 16 s. 5 d., what will 1 gallon cost A. 10 s. 7 d.

4. If a man spend 60£ 13 s. 4 d. a week, how much is that a day? A. 8£ 13 s. 4 d.

5. If 1 cwt. of rice cost 2£ 6 s. 8 d., what will 1 lb. cost? A. 0£ 0 s. 5 d.

.. 6. You have 31£ 9s. 6 d. to be divided equally among 2 men; how much would it be apiece? (15-14-9) How much would it be apiece to be divided among 3? (10-9-10) Among 6? (5-4-11) A. 31£ 9 s. 6d.

7. Divide 2 gals. 2 qts. by 4; (0-2-1) by 5; (0-2) by 10; (0-1) by 2; (1-1). A. 2 gals. 2 qts. 1 pt.

8. Divide 96 acres 2 roods, 16 rods, by 7; (13-3-8) by 8; (12-0-12) by 12; (8-0-8). A. 33 acres, 3 roods, 28 rods.

Questions to exercise the foregoing Rules.

1. What is the sum of the following numbers, viz. one, two thousand, thirty thousand, four millions, twenty thousand, nine. teen, four hundred millions? A. 404052020.

2. Bought a coat for 15 dollars, a vest for 1 dollar 37 cents, a pair of boots for 6 dollars 12; what did the whole cost me ? A. $22,50.

3. Bought a horse for $75, and sold him for 37 cents less than he cost me; what did I get for him? A. $74,62,5.

4. What will 3200 yards of tape come to at 6 cents, or T of a dollar, a yard' (200) At 12 cents, or of a dollar? (400) At 25 cents, or of a dollar? (800). A. $1400.

5. How many yards in 31557600 rods? A. 173566800.

6. How many years in 31557600 seconds, allowing the year to contain 365 days? A. 1 year.

7. At 4 cents a gill, what will 1 tun of wine cost? A. $322,56.

8. How much wine can be bought for $322,56, at 4 cents a .gill? A. 1 tun.

9. How many rods in 1100 yds.? In 3300 yds.? A. 800 rods