24

If we call the farthings in 6d. 24, there will be a loss of 24000-1000; if we add 1 to the 1000ths place, we have, in this instance, precisely the decimal required.

3. Reduce 7s. 8d. to the decimal of a pound.

4. Find by inspection the decimal expression of 18s. 31d., and 178. 84d. Ans. £.914 and £.885. 5. Reduce to a decimal by inspection the following sums, and add them together, viz:-15s. 3d.; 8s. 11d.; 10s. 6d. 18. 8d.; 23d. Ans. 1.832.

Decimals may be reduced back to shillings, pence, and farthings, by reversing the above process. Double the left-hand figure, or tenths, for the shillings; if the second figure be 5, or greater than 5, deduct 5 from it, and add 1 to the shillings. Then consider the second and third figures so many farthings; if they exceed 12, deduct 1; if they exceed 36, deduct 2. 6. Find by inspection the value of £.385. 7. Find by inspection the value of £.927.

Ans. 18s. 6d. 2qrs. 8. Find by inspection the value of £.491, and £.984.

Ans. 9s. 9d. 3qrs.; 19s. 8d. 1qr.

COMPOUND ADDITION.

Art. 135.—1. A boy bought a slate for 4d. and a book for

8d. What did both cost?

I

2. If I buy a book for 2s. 4d., another for 4s.

pay for both?

Ans. 1s. 8d., what do

Ans. 7s. wagon, what Ans. 9s. 8d.

3. If a boy pay 4s. 8d. for a sled, and 5s. for a does he pay for both?

4. How many shillings in 4d. 8d. 9d. 3d. 6d.?

Ans. 2s. 6d.

5. How many pounds are 8s. 7s. 4ɛ. 3s. 9s. 5s. ?

Ans. £1 168.

6. How many yards are 3 feet, 4 feet, 5 feet, 6 feet?

Ans. 6 yards. 7. Bought two pieces of cloth; one 10 yards, 1 foot; the other 12 yards, 2 feet. What was the length of both pieces? Ans. 23 yards.

8. What is the amount of £1 4s. 2d. 3qrs., and £10 8s. 3d. and 2qrs.? Ans. £11 12s. 6d. 1gr. 9. Add £4 5s. 6d. 3qrs., and £5 17s. 7d. 2grs.

In adding the first column, or column of farthings, we find the amount to be 5 farthings. Now as 4 farthings are equal to 1 penny, we write the 1 of farthings, and carry the 1 penny One to 7 is 8, and 6 are 14d.

In

farthing over, in the line to the column of pence. 14d. there is 1 shilling and 2d. over, which we write in the column of pence, carrying the 1s. to the column of shillings. One added to 17 is 18, and 5 are 23. In 23s. there is £1 and 3s. over, which we write in the column of shillings, and carry 1 to the column of pounds.

Had the numbers to be added in the question been simple numbers, we should have had none to carry, because 5, in the column of units, is not equal to 1 in the column of tens. Again, had 14 been in the column of tens, we should have written 4 and carried 1. Lastly, had 23 been in the column of hundreds, we should have written 3, and carried 2, because 23 in the right-hand column, is equal to 2 in the left, and 3 remain; or, 23 hundred is equal to 2 thousand, and 3 hundreds remain.

Art. 136. From the foregoing questions and illustration we derive the following definition and rules,

COMPOUND ADDITION is the adding of numbers of different denominations. By different denominations is meant a different name-as shillings, pence, farthings, etc. Were the numbers given to be added, all pence, or all farthings, there would be but one denomination.

RULE.

I. Write numbers of the same denomination directly under each other, pounds under pounds, shillings under shillings, etc.

II. Begin to add at the right-hand column, observing to carry one for as many in that column as make one in the next left-hand column.

Proof-The same as in addition of simple numbers.

EXAMPLES.

1. Bought 4 books at the following prices, viz., £1 4s. 6d.; £2 3s. 8d.; £2 19s. 11d.; 28. 3d. 2qrs. To what did they Ans. £6 10s. 4d. 2qrs.

amount?

2. Add the following numbers: 18s. 5d. 1qr.; £57 17s. 9d. 2qrs.;

£46 26s. 7d. 3qrs.; £49 £102 19s. 10d. 1qr.

Ans. £258 28. 8d. 3qrs.

3. Add $286 12 cts. 6 m.; $347 20 cts. 4 m.; $119 18 cts. 7 m.; $542 93 cts. 9 m.; $314 89 cts. 1`m.

Ans. $1610 34 cts. 7 m.

4. Add 45 lbs. 9 oz. 15 pwt. 18 grs.; 90 lbs. 6 oz. 16 pwt. 23 grs.; 30 lbs. 10 oz. 11 pwt. 6 grs.; 85 lbs. 11 oz. 13 pwt. 4 grs.; 91 lbs. 7 oz. 7 pwt. 23 grs.

16. Add 49 bushels, 3 pecks, 4 quarts, 1 pint; 39 bu 1 pk. 5 qt. 1 pt.; 59 bu. 2 pk. 3 qt. O pt.; 40 bu. 7 pk. 2 qt. 1 pt.; 150 bu. 0 pk. 6 qt. 1 pt.; 69 bu. 1 pk. 2 qt. 0 pt.

17. Add 360 degrees, 15 miles, 6 furlongs, 16 poles, 13 feet, 6 inches; 240 deg. 19 m. 5 fur. 29 p. 11 ft. 5 in. 2 b.; 159 deg. 51 m. 7 fur. 32 p. 14 ft. 7 in. 2 b.; 201 deg. 63 m. 3 fur. 15 p. 12 ft. 9 in. 2 b.

18. Add 971 miles, 6 furlongs, 11 poles, 3 yards, 1 foot; 239 m. 5 fur. 9 p. 2 yd. 2 ft.; 269 m. 7 fur. 31 p. 1 yd. 2 ft.; 67 m. 6 fur. 9 p. 2 yd. 2 ft.; 691 m. 5 fur. 8 p. 2 yd. 2 ft.

19. Add 69 acres, 2 roods, 1 rod; 76 acr. 3 ro. 39 rd.; 88 acr. 1 ro. 32 rd.; 150 acr. 3 ro. 29 rd.

20. Add 150 years, 221 days, 13 hours, 31 minutes, 29 seconds; 230 yr. 300 d. 23 h. 49 m. 59 s.; 191 yr. 149 d. 21 h. 39 m. 23 s.; 359 yr. 75 d. 23 h. 59 m. 19 s.

COMPOUND SUBTRACTION.

Art. 137.-1. If a picture-book cost 4d. and a spellingbook 11d., how much more does one cost than the other?

2. James bought a book for 9d. and sold it for 1s. How much did he gain by the bargain?

3. From 2s. 6d., take 1s. 8d.

4. From 8s. 9d. 3qrs., take 6s. 8d. 2qrs.

5. From 4 qts., take 3 pts.

6. If a bushel of rye be worth 7s. 6d., and a bushel of corn 68. 4d., how much more is the rye worth than the corn?

7. How much more is wheat worth at 9s. 8d. per bushel, than corn at 7s. 6d. per bushel ?

8. How much more is 2 bushels 2 pccks, than 1 bushel 3 pecks?

9. From £29 9s. 6d. 3qrs., take £23 10s. 7d. 2qrs.

Operation.

8.

£ d. qrs. 29 9 6 3 23 10 7

In this example, we write the difference between 2 and 3 farthings in the line of farthings, and 2 proceed to the column of pence; 5 18 11 1 we carry none, because we borrowed none-but 7d. from 6d. cannot be obtained; we therefore borrow as many pence as make a shilling, and say, 7 from 12-the remainder 5, we add to 6, in the upper line, and write 11 in the column of pence. We now carry 1 to the column of shillings, which is equal to the 12 pence we borrowed, and say, 11 from 9, which cannot be obtained; again we must borrow as many of the denomination we have to subtract as make one of the next higher, which is 20s., and say, 11 from 20, and 9 remain, which added to 9 in the upper

QUESTIONS.-1. What does Compound Subtraction teach? 2. Rule? 3. If the number in the upper line be less than the one standing under it, how may you proceed? 4. Why do you carry 1 to the next left-hand column?