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.? 4×3 qrs.? How many shillings in 2 times 6 d.? 2 X 12 d.? 4 × 6 d.? 5 × 12 d.? 8×3d.? 4x7d.? 3X 5 d.? 8 × 12 d. ?

10. How many pounds in 4 times 10 s.?

4 X 6 s.?

Operation by Slate illustrated.

3X 10 s. ?

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

£ S. d. qrs.
6 1 3

5

Ans. 11 10 8 3

Q. How do you get the 10 s.?

Q. How do you get the 3 qrs. in the answer?

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

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

A. 5 times 6 s. are 30 s.=1£ 10 s., writing down the 10 s. and carrying the 1£.

Q. How do you get the 11£?

A. 5 times 2£ are 10£, and 1£ (to carry) makes 11£.

From these illustrations, we derive the following

RULE.

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

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

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

PROOF. Q. 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 gr. 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 1 T. 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 ?-7-13-117-13-11. Of11 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 A. 2628 yds. piece 27 yds. 1 qr. 2 na., how many yards

COMPOUND DIVISION.

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

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

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?

な

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. 8d.; how much was that a load?

OPERATION.

20 12

£

S. d.

3 2) 15

8

Ans. £7 11 10

Q. 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.

Q. What do you do with the 1£ over?

A. 1£= 20 s. which I join or carry to the 3 s., making 23 s. Q. How do you proceed then, to get the 11 s.?

A. I say, 2 in 23, 11 times, and 1 s. over, writing down the 11 s. underneath.

Q. 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.

Q. At which hand do you begin to divide, and how do you proceed? A. With the highest denomination, and divide as in Simple Division.

Q. 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. Q. What is the proof?

A. The same as in Simple Division.

More Exercises for the Slate.

2. If 8 tons of hay cost 40£ 14 s. 8 d., what will 1 ton cost? A. 5£ 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£ 9 s. 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. 6 d.

7. Will you 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. Will you 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, nineteen, 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 64 cents, or 16 of a dollar, a yard ?-200. At 12 cents, or of a dollar 2-400. 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. 10. How many dollars in 300£? In 900£? A. $4000. 11. Reduce 5£ 17 s. 6 d. to farthings. A. 5640 farthings.

12. How many pounds in 5640 farthings? A. 5£ 17 s. 6 d. 13. Multiply 3600 by 25. A. 90600.

14. What will 1 ton of clover-seed cost, at 5 mills an ounce ? A. $179,20.

15. At 2 cents an inch, what will 1 yard of cloth cost? A 72 cents.

16. Reduce 1 tun to gills. A. 8064 gills.

17. Reduce 20 bushels to pints. A. 1280 pints.

18. Reduce 4 tons to drams. A. 2293760.

19. How many barley corns will reach across the Atlantic Ocean, allowing it to be 3000 miles. A. 570240000.

20. How many times will a watch click in 20 years, if it click at the usual rate of 60 times in a minute? A. 631152000.

21. A father left legacies to his children as follows: to Thomas 75£ 14 s. 6 d., to William 3 times as much as Thomas, to his daughter Mary as much as Thomas, and to Susan, his youngest child, as much as all the rest, lacking 20£ 13 s. 8 d.: how much did each receive? A. William 227£ 3 s. 6 d., Mary 12£ 12 s. 5 d., Susan 294£ 16 s. 9 d.

Mr. Charles Testy

1827. Jan. 1.

To Lewis P. Child,

To 3 yds. Linen Cloth, at 1 s. 6 d. a yard, 66 15. "1 ton of Hay, at 4 s. 6 d. a hundred, Feb. 28. "25 bushels of Rye, at 3 s. 9 d. a bushel, Mar. 9. "3 cows, at 5£ 10 s. a head,

£25 18 s. 3 d.

Halifax, April 1, 1827.

Received payment,

Lewis P. Child.

¶ XXXIV.

FRACTIONS.

1. If one third (3) of an apple cost 2 cents, what will a whole apple cost?

2. If one third cost 3 cents, what will a whole one cost? If one third cost 4 cents, what will one whole apple cost? If one third cost 6 cents? 8 cents? 9 cents? 20 cents? 50 cents? 100 cents?