weighed 8 lbs. 2 oz. 12 pwts., the second 5 lbs. 4 oz. 5. pwts., the third 6 lbs. 10 oz. 11 pwts., and the fourth 6 lbs. 11 oz. 15 pwts.; what was the weight of the whole? A. 27 lbs. 5 oz. 3 pwts.

18. James is 10 yrs. 2 mo. 3 wks. 4 da. old, Thomas is 11 yrs. 11 mo. 5 da. old, Rufus is 9 yrs. 10 mo. old, Harry is 14 yrs. old; what is the sum of all their ages? A. 46 yrs. 2 da.

By multiplying the answers to the following sums by 2, the true answers may be obtained.

Note. It will be well for the learner, not only in this, but in all rules, to prove his results, when practicable.

2 d. 2 qrs., 2 qrs., 18 £

19. Add together 17 £ 13 s. 11 d. 1 qr., 13£ 10 s. 10€ 17 s. 3 d. 1 qr., 77 s. 6 d. 2 qrs., 2£ 2 s. 3 d. 17 s. 10 d. 2 qrs. A. 35 £ 4 s. 6 d. 3 qrs. X 2. 20. Add together 46 £ 16 s. 5 d. 1 9 d. 2 qrs, 58 £ 16 s. 10 d. 1 qr., 316 £ 15 s. 8 d. 2 qrs., 651 £ 18 s. 9 d. 2 qrs., 405 £16 s. 5 d. A. 741 £ 6 s. 6d. X 2.

qr.,

2 £8s.

21. Add together 30£ 10 s. 3 d. 2 qrs., 14 £ 9 s. 8 d. 0 qr., 1£ Os. 1 d. 2 qrs., 2 £ 8 s. 7 d. 2 qrs., 42 £ 9 s. 6 d. 2 qrs., 28£ 5 s. 4 d. 2 qrs. A. 59 £ 11 s. 9 d. 3 qrs. X 2.

22. Add together 15 lbs. 10 oz. 18 pwts. 22 grs., 3 lbs. 3 oz. 15 pwts. 20 grs., 7 lbs. 7 oz. 18 pwts. 13 grs., 5 lbs. 8 oz. 13 pwts. 16 grs., 3 lbs. 6 oz. 9 pwts. 6 grs., 6 oz. 10 pwts. 11 grs. A. 18 lbs. 4 oz. 3 pwts. 8 grs. X 2.

23. Add together 2 cwt. 3 qrs. 27 lbs., 1 cwt. 2 qrs. 16 lbs., 3 cwt. 1 qr. 25 lbs., 5 cwt. 2 qrs. 12 lbs., 2 cwt. 2 qrs. 14 lbs., 5 cwt. 1 qr. 15 lbs. A. 10 cwt. 3 qrs. 12 lbs. 8 oz. × 2.

24. Add together 70 yds. 2 qrs. 1 na., 12 yds. 1 qr. 1 na., 9 yds. qr. 1 na., 40 yds. 2 qrs. 1 na.. 56 yds. 1 qr. 1 na., 48 yds. I qr. 1 na. A. 118 yds. 2 qrs. 1 na. X 2.

25. Add together 1 pk. 6 qts. 1 pt., 2 pks. 5 qts., 1 pk. 4 qts., 1 pk. 3 qts. I pt., 2 pks. 5 qts., pks. qts. pt. A. pks. 6 qts. 0 pt. × 2.

26. Add together 38 gals. 2 qts. 1 pt. 2 gi., 16 gals. 1 qt. 3 gi., 20 gals. 2 qts. 1 pt. 1 gi., 18 gals. 1 qt. 1 pt., 7 gals. 1 qt. 2 gi., 30 gals. 2 qts. 1 pt. A. 66 gals. 2.

27. Add together 80 lea. I m. 5 fur. 30 po., 50 lea. 2 m 6 fur. 20 po., 40 lea. 1 m. 7 fur. 15 po., 30 lea. 2 m. 4 fur. 25 po., 70 lea. 1 m. 3 fur. 10 po., 60 lea. 2 m. 2 fur. 4 po. A. 167 lea. 0 m. 2 fur. 32 po. X 2.

28. Add together 367 acres, 2 roods, 30 rods; 815 acres, 1 rood, 16 rods; 40 acres, 2 roods, 20 rods; 60 acres, 2 roods, 30 rods. A. 642 acres, 0 roods, 28 rods, × 2.

29. Solid measure.-Add together 12 feet, 1335 inches; 15 feet, 1615 inches; 2 feet, 755 inches; 13 feet, 1283 inches. 1. 22 feet, 766 inches, X 2.

30. Add together 20 yrs. 363 da. 20 h. 50 m. 30 sec., 20 yrs.

40 da. 10 h. 30 m. 20 sec., 12 yrs. 110 da. 13 h. 16 sec., 13 y yrs. 8 da. 10 h. 20 m. 14 sec., 7 yrs. 20 da. 8 h. 10 m. 12 sec. A. 36 yrs. 271 da. 19 h. 25 m. 46 sec. X 2.

31. Add together 11 S. 29° 16′ 59′′, 20° 45' 11", 8S.3° 10/50", 3S. 10° 6' 10". A. 12S. 1° 39′ 35′′ × 2.

COMPOUND SUBTRACTION.

¶ XXXI. 1. William had 2 qts. of walnuts, and gave James 1 pt.; how many had he left?

2. James, owing Rufus 1 s. 6 d., paid him 6 d.; how much did he then owe?

3. Thomas bought a knife for 9 d., and sold it for 1 s. 6 d.; how much did he make by the trade?

4. Harry and Rufus purchased 3 qts. of walnuts; Harry paid so much towards them, that he is entitled to 2 qts. 1 pt.; now, what is Rufus's part.

5. A servant, returning with a two gallon jug of molasses, perceived that it had leaked out some considerable, and, wishing to know how much, by emptying it into a 6 quart and 1 pint measure, found it exactly filled the measure; how much had leaked out?

6. From 1 gallon take 3 qts.

7. From 8 gills take 2 pints. 8. From 1 ounce take 12 drams. 9. From 2 quarters take 3 nails. 10. From 1 pound take 11 shillings. 11. From 2 shillings take 10 pence. 12. From 2 quarters take 20 pounds. 13. From 3 weeks take 7 days.

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

Q. What, then, is the taking one number from another, of different denominations, called?

A. Compound Subtraction.

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

Operation by Slate illustrated.

1. A merchant bought a piece of cloth containing 10 yo 2 qrs. 3 na., and sold 7 yds. 3 qrs. 2 na.; how much had he left

A. I begin with nails, the least denomination, and say, 2 na. from 3 na. leaves 1 na.

Q. How do you proceed to get the 3 qrs.?

A. I cannot take 3 qrs. from 2 qrs., but I can borrow, as in Simple Subtraction, 1 yd. 4 qrs., from the yards; then say, 4 qrs. joined or added to the 2 qrs. (the top figure) makes 6 qrs., from which taking 3 qrs. leaves 3 qrs.

Q. But suppose that, instead of adding first, we subtract first, how would you proceed?

A. Taking 3 qrs. from 4 qrs. (borrowed) leaves 1 qr., and 2 qrs. makes 3 qrs.

Q. How do you get the 2 yds. ?

A. I must carry 1 yd. (for the yard which I borrowed) to 7 yds., making 8 yds., which, subtracted from 10 yds., leaves 2yds. From this example we derive the following

RULE.

Q. How do you write the numbers down?

A. The less under the greater, placing each denomination as in Compound Addition.

Q. With which denomination do you begin to subtract?
A. The least denomination.

Q. How do you subtract each denomination?

A. From the denomination above it, as in Simple Subtraction.

Q. If the lower number in any denomination be greater than the upper, how do you proceed?

A. Borrow as many units as make one in the next higher denomination, from which subtract the lower number.

Q. What must the remainder be added to ?

A. The upper number.

Q. How many do you carry in such cases?

A. One.

Q. How do you subtract the last denomination?
A. As in Simple Subtraction.

PROOF. Q. How do you prove the operation?

A. By adding the Remainder and Subtrahend together, as in Simple Subtraction, the amount of which must be equal to the Minuend.

More Exercises for the Slate.

B

2. If, from a piece of cloth containing 10 yds. 2 qrs., you cut off 2 yds. 2 qrs., how much will there be left? A. 8 yds. 3. A bought of B a bushel of barley for 8 s. 6 d.; he gave 1 bu. of rye, worth 4 s. 3 d., and paid the rest in money; how much did he pay? A. 4s. 3 d.

4. A bought of B a bale of cotton for 20£ 4 s., and B. bought of A 4 tierces of rice for 15€ 18 s.; A paid B the rest in money; how much did he pay? A. 4£ 6 s.

5. A man bought a wagon for 6£ 10 s., and sold it for 12€ 18 s.; how much did he make by the trade? A. 6£ 8s..

6. A man bought one load of hay for 4£ 10 s., and another for 5£ 15 s.; how much more did he give for one than the other? A. 1£ 5 s.

7. A man bought two loads of hay, one weighing 18 cwt. 3 qrs. 25 lbs., and the other 17 cwt. 0 qr. 26 lbs.; how much did one weigh more than the other? A. 1 cwt. 2 qrs. 27 lbs.

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.

2

10. A merchant bought a quantity of corn, weighing 20 cwt. qrs. 15 lbs., of which he sold 10 cwt. 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? 9. 43 gals. 3 qts. O pt. 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? A. 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 staid 2 yrs. 2 mo. 2 w. 2 d., how much longer had he to stay? A. 9 mo. 1 w. 5 d.

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. 1 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 dis tance, how much farther has he to travel? A. 14. m. 20 rods 19. From 14 15 s. 6 d. 2 qrs. take 12£ 15 s, 6 d. 3 qrs. 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.

A. 1£

take 2 s.

A. 18 s.

take 2 d.

A. 19 s. 10 d.

take 2 qrs.

A. 19 s 11 d. 2 qrs.

A.

11 oz. 19 pwts. 5 grs. A. 19 cwt. 3 qr. 27 lb. 6oz

A.

11 oz. 19 pwts. 9 grs.

A. 3 pks. 7 qts. 1 pt.

take 1 b. c.

A. 2 ft. 11 in, 2 b. e.

29. From 1 vd,

take 1 in.

4. 2 ft. 11 in.

30. From 1 sq. yd.

take 3 sq. ft.

31. From 1 ton

take 2 qrs.
take 1 pt.

r. timber

32. From 1 yr.
take 12 h.
33. From 12£ 2 qrs. take 6 d.
34. From 10 cwt. 10 oz. take 5 drs.
35. From 1 E. E. 2 qrs. take 3 na.
36. From 8 gals. 3 gills take 1 pt.
37. From 12 m. 15 rods take 3 fur.
38. From 1 mo. 2 h.
take 45 m.

11 mo. 3 w. 6 da. 12 h.
A. 11£ 19 s. 6 d. 2 qrs.
A. 10 cwt. 9 oz. 11 drs.
A. 1 E. E. 1 qr. 1 na.
A. 7 gals. 3 qts. 1 pt. 3 g.
A. 11 m. 5 fur. 15 rods,
A. 1 mo. 1 h. 15 m.

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?