2 lbs. 7 oz. 3 prots. into pennyweights, multiply by 15 for a dividend, divide, and the quotient will be the answer. Ꭿ. 7.

116. In 26880 lbs. of sugar, how many hhds., each 12 cwt › A. 20.

117. How many barley corns will reach round the globe, it being 360 degrees? A. 4755801600.

118. In running 300 miles, how many times will a wheel 9 feet 2 inches in circumference, turn round? A. 172800.

119. In 172800 turns of a wheel measuring 9 feet 2 inches, how many miles? A. 300.

120. How many times will a wheel, which is 15 feet 9 inches in circumference, turn round in going from Providence to Norwich, it being 45 miles? A. 15085+

121. A farmer rents a plantation of 400 acres, of which no more than 200 are to be tilled; how many poles are there in the remainder? A, 32000.

122. In a lunar month, of 27 days, 7 hours, 43 minutes, 5 seconds, how many seconds A. 2360585.

123. How many seconds is it from the birth of our Saviour to Christmas, 1828, allowing the year to contain 3651 days, or 365 days, 6 hours? A. 57637292800.

124. When a person is 21 years old, how many seconds old is he? A. 662709600.

125. It is supposed the wars of Bonaparte, in 20 years, caused the death of 2000000 of persons; how many was this per hour, allowing the year to contain 365 days 6 hours? A. 117488.

COMPOUND ADDITION.

↑ XXX. 1. William bought an arithmetic for 2 s. 6 d., and rn inkstand for 6 d.; how many shillings did both cost?

2. Harry purchased a vest; the cloth and making cost 5 s., the buttons 9 d., and the thread 3 d.; how much did the vest cost?

3. William, Harry, and Thomas gathered some nuts; and when they measured them, it was found that William had 2 qts. and 1 pt., Harry 3 qts. 1 pt., and Thomas 2 qts.; how many pecks did they gather in all?'

4. How many pecks are 3 qts. + 1 qt. + 4 qts.?
5. How many yards are 2 qrs. + qrs. + 3 qrs.?
6. How many gallons are 1 qt. + 2 qts. + 1 qt. ?
7. How many pence are 1 qr. + 3 grs. + 1
8. How many shillings are 3 d. + 8 d. +1 d

9. How many pounds are 10 s. + 18 s. + 12 s.?
10. How many hours are 50 m. + 20 m. + 10 m. ?
11. How many feet are 4 in. + 10 in. + 11 in.?
12. How many minutes in 45 sec. + 15 sec. + 10 sec.?
13. How many pounds in 8 oz. + 12 oz. + 12 oz.?
14. How many bushels in 1 pk. +3 pks. + 2 pks.?

15. Sold a Virgil, that cost me 12 s. 6 d., so as to gain 1 s. 6d. how much did I get for it?

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

Q. Why do you call it Compound? why not Simple Addition ? A. Because there are more denominations than one.

Q. What do you mean by more denominations than one ? A. Shillings, pence, &c. in one sum; pecks, quarts, pints, &c. in another sum.

Q. What, then, is the collecting numbers of different denominations into one sum called? A. Compound Addition.

Operation by Slate illustrated.

1. A man bought a cart for 6£ 12 s. 3 d., a load of hay for 3£ 9 s. 7 d., and a cow for 4£ 4 s. 1d.; what did he pay for the whole ?

OPERATION.

20 12

£ s. d.

6 12 3
9 17

3

4 4 1

Ans. 14 5 11

How do you write the numbers down? A. Pounds under pounds, shillings under shillings, &c.

How do you get the 11 d. in the answer? A. I find, by adding up the column of pence, that it makes 11 d., which I write under the column of pence.

How do you get the 5 shillings? A. Adding up the column of shillings, I find it makes 25 s. = 1£5 s. (for 20 s. in 25, 1 time, and 5 over), writing the 5 s. under the column of shillings.

What is to be done with the 1£? A. I must, of course, add pounds to pounds, and, to do this, I join, or carry it to the next column, which is pounds.

How do you get the 14£? A. Adding up the column of pounds makes 13 pounds, and 1£ (to carry) makes 14£.

From these illustrations we derive the following

RULE.

I. How do you place the numbers to be added? A. Pounds under pounds, shillings under shillings, drams under drams, &c.

II. At which hand do you begir ‘o add? A. At the right. III. How do you add up the first column? A. As in Simple Addition.

IV. What do you divide the amount by? A. By as many of this denomination as make one of the next higher, as in Reduction.

V. What do you do with the remainder? A. Write it ur derneath.

VI. What do you carry to the next column? A. The quo tient.

VII How long do you proceed in this way? A. Till I come to the last column.

VIII. How do you proceed with this? A. Add it up, and set the whole amount down, as in Simple Addition.

PROOF.-Q. What is the proof? A. The same as in Simple Addition.

More Exercises for the Slate.

2. Bought a cart for 2£ 15 s., a plough for 18 s.; how much did both cost? A. 3 £ 13 s.

3. Bought a coat for 5£ 6 s., a watch for 1£ 19 s.; how much did they come to? A. 7£ 5 s.

4. A man bought one load of hay for 6£ 3 s. and another for 7£ 15 s. 6 d.; how much did he give for both? A 13£ 18 s. 6 d.

5. Sold an ox for 10£ 15 s. 6 d., a cow for 6€ 19 s. 11 d., a horse for 12£ 6 s. 4 d.; how much money did I receive? A. 30£ 1 s. 9 d.

6. Bought of a grocer 3 gals. 2 qts. of rum, 5 gals. 3 qts. of gin, and 4 gals. 1 qt. of molasses; how many gallons did I buy in all? A. 13 gals. 2 qts.

7. Sold 4 hhds. of molasses, the first of which contained 42 gals. 2 qts. 1 pt., the second 65 gals. O qt. 1 pt., the third 50 gals. 3 qts., and the fourth 55 gais. 1 qt. 1 pt.; how much was sold in all? A. 213 gals. 3 qts. 1 pt.

8. A grocer sold 4 hhds. of sugar, weighing as follows; the first 7 cwt. 1 qr. 14 lbs., the second 5 cwt. 2 qrs. 10 lbs., the

third 9 cwt. 1 qr. 15 lbs., the fourth 7 cwt. 1 qr. 10 lbs.; what did the whole weigh? A. 29 cwt. 2 qrs. 21 lbs.

na., the third

9. A merchant bought 4 pieces of cloth, the first containing 20 yds. 3 qrs. 1 na, the second 15 yds. 3 qrs. 26 yds., and the fourth 10 yds. 1 qr. did he buy in all? A. 73 yds. 0 qr. I na.

3 na.; how many yards

10. A man bought 3 bu. 3 pks. of wheat at one time, 6 bu. at another time, 7 bu. 2 pks. 7 qts. at a third, and 4 bu. 1 pk. 6 qts. at a fourth; how many bushels did he buy in all' A. 21 bu. 3 pks. 5 qts.

11. A man bought two loads of hay, one weighing 19 cwt. qr., and the other 18 cwt. qrs.; how much did both weigh

A. 37 cwt. 3 qrs.

12. A man travelled in one day 27 miles, 3 fur., in another day 30 m. 2 fur. 25 rods; how far did he travel in all? A. 57 m. 5 fur. 25 rods.

13. A merchant bought 3 bales of cotton; the first contained 4 cwt. 3 qrs. 18 lbs., the second 3 cwt. 1 qr. 5 lbs., and the third 5 cwt. 0 qr. 24 lbs.; what was the weight of the whole : A. 13 cwt. 1 qr. 19 lbs.

14. A man has 3 farms; the first containing 150 acres, 2 roods, 25 rods; the second, 200 acres, 1 rood, 15 rods; and the third, 100 acres, 1 rood, 10 rods: how many acres has he in all? A. 451 acres, 1 rood, 10 rods.

15. William resided in Providence, his native place, till he was 15 yrs. 6 m. 4 days old; he then went to Boston, where he resided 7 yrs. 2 m. 2 da.; from Boston he emigrated to Salem, where he remained 4 yrs. 3 da.; from Salem he went to Portsmouth, and resided there two years precisely: now how much time did he spend in these places in all? A. 28 yrs. 8 m. 1 w. 2 d.

16. A man brings to market 3 loads of wood; the first containing 1 cord, 64 feet, 864 in.; the second, 2 cords, 63 ft. 64 in.; and the third, 1 cord. 60 ft. 931 in.: how much did he bring in all? A. 5 cords, 60 ft. 131 inches.

17. A goldsmith bought 4 ingots of silver, the first of which 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.

19. Add together 17£ 13 s. 11 d. 1 qr., 13£ 10 s. 2 d. 2 qrs.

10t 17s. 3 d. 1 qr., 7£ 7 s. 6d. 2 qrs., 2£ 2 s. 3d. 2 qrs. 18£ 17 s. 10 d. 2 qrs. A. 35£ 4 s. 6 d. 3 qrs. X 2.

20. Add together 46£ 16 s. 5 1 qr., 2£ 8 s. 9 d. 2 qrs., 58£ 16 s. 10 d. 1 qr., 316€ 15 s. 8 d. 2 qrs., 651£ 18 s. 9 d. 2 grs., 405£ 16 s. 5 d. A. 741£ 6 s. 6 d. x 2.

21. Add together 30£ 10 s. 3 d. 2 qrs., 14£ 9 s. 8 d. 0 qr. 10 s. 1 d. 2qrs., 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 lb. 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.

i

oz. X 2.

9

24. Add together 70 yds. 2 qrs. 1 na., 12 yds. 1 qr. 1 na., yds. 0 qr. 1 na., 40 yds. 2 qrs. I na., 56 yds. I qr. 1 na., 48 yds gr. 1 na. A. 118 yds. 2 qrs. 1 na. X 2. 25. Add together 1 pk. 6 qts. pt., 2 pks. 5 qts., 1 pk. 4 qts., 1 pk. 3 qts. 1 pt., 2 pks. 5 qts., 3 pks. 4 qts. 0 pt. A. 6 pks qts. 0 pt. X 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. 1 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. X 2.

29. Solid measure.-Add together 12 feet, 1335 inches; 15 feet, 1615 inches; 2 feet, 755 inches; 13 feet, 1283 inches. A. 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 yrs. 8 da. 10 h. 20 m. 14. sec., 7 yrs. 20 da. 8 h. 10 m. 12 sec. 1. 36 yrs. 271 da. 19 h. 25 m. 46 sec. X 2.

31. Add together 11S. 290. 16'. 59., 20° 45'. 11., 8S. 3°. 10. 50., 3 S. 10°. 6. 10. A. 128. 1°. 39. 35. X 2.

COMPOUND SUBTRACTION.

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