II. Beginning with the lowest denomination, find the sum of each column separately, and divide it by that number which it requires of the column added to make ONE of the next higher denomination. Set the remainder under the column, and carry the quotient to the next column.

III. Proceed in this manner with all the other denominations except the highest, whose entire sum is set down as in simple addition. (Art. 29.)

PROOF-The proof is the same as in Simple Addition. (Art. 28.)

OBS. The process of adding numbers of different denominations is called Compound Addition. It is the same as Simple Addition, except the method of carrying from one denomination to another.

2. What is the sum of £10, 6s. 7d.; £18, 12s. 10d., £5, 3s. 4d.? Ans. £34, 2s. 9d.

9. Add 7 lbs. 9 oz. 16 pwts. 10 grs.; 3 lbs. 10 oz. 8 pwts. 9 grs. ; 8 lbs. 3 oz. 1 pwt. 4 grs.

10. An Englishman bought a carriage for £35, 12s.; a horse for £27, 8s. 10d.; a harness for £7, 16s. 11d.: how much did he give for the whole?

QUEST.-What is done with the last column? How is the operation proved? Obs. What is the process of adding coinpound numbers called? How does it differ from simple addition?

11. A merchant bought of one dairyman 5 cwt. 11 lbs. 6 oz. of butter; of another, 3 cwt. 15 lbs. 9 oz.; of another, 7 cwt. 6 lbs. 10 oz.; how much did he buy of all?

12. A manufacturer bought of one man 73 lbs of wool; of another, 96 lbs. 6 oz.; of another, 135 lbs. 11 oz.; of another, 320 lbs. 9 oz.; of another, 642 lbs. 3 oz.: how much wool did he buy?

13. A man sold to one customer 2 tons, 62 lbs. 10 oz. of hay; to another, 5 tons, 40 lbs. 12 oz.; to another, 3 tons, 75 lbs. 6 oz.: how much did he sell to all!

14. A man wove 7 yds. 3 qrs. 2 na. of cloth in one day; the next day, 6 yds. 1 qr. 3 na.; the next, 8 yds. 3 qrs. 1 na.; the next, 5 yds. 2 qrs. 3 na.: how much did he weave in all?

15. Bought several pieces of cotton; one contained 26 yds. 1 qr. 2 na.; another, 30 yds. 2 qrs.; another, 29 yds. 3 na.; another, 324 yds. 1 na.: how many did they all contain?

16. A hotel keeper bought at one time, 15 bu. 2 pks. 3 qts. of oats; at another, 10 bu. 1 pk. 2 qts. ; at another, 20 bu. 6 qts.; at another, 18 bu. 5 qts.: what was the amount of all his purchases?

17. Bought 4 loads of wheat; the first containing 23 bu. 3 pks. 5 qts. ; the second, 20 bu 6 qts.; the third, 26 bu.; the fourth, 214 bu. 7 qts.: how many bushels did they all contain?

18. What is the sum of 16 m. 3 fur. 16 r.; 26 m. 1 fur. 33 r.; 10 m. 8 fur. 22 r.; 45 m. 7 fur. 20 r?

19. A merchant bought 3 casks of oil; one held 2 hhds. 30 gals. 2 qts.; another, 3 hhds. 10 gals.; another, 1 hhd. 13 gals. 1 qt: how much did they all hold?

20. Sold several lots of wine, in the following quantities: 1 pipe, 1 hhd. 21 gals. 2 qts. 1 pt. ; 2 pipes, 11 gals. 3 qts. 1 pt. 3 hhds. 15 gals. 2 qts.; 3 pipes, 10 gals. 2 qts. 1 pt. how much was sold in all?

21. A mason plastered one room containing 45 square yards, 7 ft. 6 in.; another, 25 yds. 6 ft. 95 in.; another, 38 yds. 4 ft. 41 in.: what was the amount of plastering in all the rooms?

22. Sold 10 A. 35 r. 10 sq. ft. of land at one time; at another, 3 A. 10 r. 15 ft.; at another, 18 A. 16 r. 23 ft.: what was the amount of land sold?

23. A merchant received several boxes of goods; one contained 16 cu. ft. 61 in.; another, 25 ft. 81 in.; another, 20 ft. 13 in.; another, 38 ft. 72 in.: how many cubic feet and inches did they all contain?

24. One pile of wood contains 10 C. 38 ft. 39 in. ; another, 15 C. 56 ft. 73 in.; another, 30 C. 19 ft. 44 in.; another, 17 C. 84 ft. 21 in.: how much do they all contain?

SUBTRACTION OF COMPOUND NUMBERS.

Ex. J. From £15, 7s. 6d. 3 far., subtract £6, 4s. 8d. 2 far.

Operation.

£ S. d. far.

15 7

6 // 4

9

6

3

8 2

2 10 1 Ans.

umn of farthings.

Having placed the less number under the greater, with farthings under farthings, pence under pence, &c., we subtract 2 far. from 3 far., and set the remainder 1 far. under the colNow 8d. cannot be taken from 6d.; we therefore borrow 1 from the next higher denomination, which is shillings; and 1s. or 12d. added to the 6d. make 18d. And 8d. from 18d. leaves 10d. Since we borrowed 1, we must carry 1 to the next column, as in simple subtraction. 1 added to 4 makes 5; and 5 from 7, leaves 2. 6 from 15 leaves 9. Ans. £9, 2s. 10d. 1 far 169. Hence, we derive the following general

RULE FOR SUBTRACTING COMPOUND NUMBERS. I. Write the less number under the greater, so that the same denominations may stand under each other.

II. Beginning with the lowest denomination, subtract the number in each denomination of the lower line from the number above it, and set the remainder below.

QUEST. 169. How do you write compound numbers for subtraction? Where begin to subtract? When the number in the lower line is larger than that above it, what is to be done? How is the operation proved?

III. When a number in any denomination of the lower line is larger than the number above it, borrow one of the next higher denomination and add it to the number in the upper line. Subtract as before, and carry one to the next denomination in the lower line, as in subtraction of simple numbers. (Art. 40.)

PROOF. The proof is the same as in Simple Subtraction. (Art. 39.)

OBS. The process of finding the difference between numbers of different denominations, is called Compound Subtraction. It differs from Simple Subtraction only in the mode of borrowing from one denomination to another.

2. Subtract £2, 6s. 9d. from £10, 7s. 4d.

Ans. £8, 0s. 7d. 3. From £15, 16s. 10d. 3 far., take £7, 8s. lld. 1 far. 4. From £56, 7s. 6d. 1 far., take £20, 3s. 10d. 3 far.

9. Bought 2 silver pitchers, one weighing 2 lbs. 10 oz. 10 pwts. 7 grs. ; the other, 1 lb. 15 oz. 12 pwts. 5 grs.: what is the difference in their weight?

10. A merchant had a piece of cloth measuring 28 yds. 3 qrs. 2 na., and sold 15 yds. 1 qr. 3 na.: how much had he left?

11. A lady bought 2 pieces of silk, one of which contained 19 yds. 2 qrs. 1 na., the other, 15 yds. 3 qrs. 3 na.: what is the difference in the length ?

12. From 25 m. 7 fur. 8 r. 12 ft. 6 in, take 16 m. 6 fur. 30 r. 4 ft 8 in.

QUEST. Obs. What is the process of subtracting compound numbers called? Wherein does it differ from simple subtraction?

13. A man owning 95 A. 75 r. 67 sq. ft. of l 40 A. 86 r. 29 ft. how much had he left?

14. A farmer having bought 120 A. 3 R. 28 r. divided it into two pastures, one of which co 50 A. 2 R. 35 r.: how much did the other contai

15. A tanner built two cubical vats, one containing 116 ft. 149 in., the other 245 ft. 73 in.: what is the difference between them?

16. A man having 65 C. 95 ft. 123 in. of wood in his shed, sold 16 C. 117 ft. 65 in.: how much had he left?

17. From 27 yrs. 8 mos. 3 wks. 4 ds. 13 hrs. 35 min. Take 19 yrs. 5 mos. 6 wks. 5 ds. 21 hrs. 20 min. 18. What is the time from July 4th, 1840, to March 1st, 1845?

Operation. Yr. mo. d. 1845 3

1840 7

1

4

March is the 3d month, and July the 7th. Since 4 d. cannot be taken from 1 d., we borrow 1 mo. or 30 d.; then say, 4 from 31 leaves 27. 1 to carry to 7 makes 8, but 8 from 3 is impossible; we therefore borrow 1 yr. or 12 mos., and say, 8 from 15 leaves 1 to carry to 0 is 1, and 1 from 5 leaves 4.

7.

4

7 27 Ans.

170. To find the time between two dates.

Write the earlier date under the later, placing the years on the left, the number of the month next, and the day of the month on the right, and subtract as before. (Art. 169.)

OBS. 1. The number of the month is easily determined by reckoning from January, the 1st mo., Feb. the 2d, &c. (Art. 158. Obs. 3.) 2. In finding the time between two dates, and in casting interest, 30 days are considered a month, and 12 months a year.

19. What is the time from Oct. 15th, 1835, to March 10th, 1842 ?

20 The Independence of the United States was de

QUEST.-170. How is the time found between two dates? Obs. In finding time between two dates, and in casting interest, how many days are considered a month? How many months, a year?