17. Bought 4 loads of wheat; the first containing 23 bu. 3 pks. 5 qts.; the second, 201⁄2 bu. 6 qts.; the third, 261 bu.; the fourth, 213 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 his plastering?

23 ft.

what

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 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?

25. Find the sum of 16 lbs. 6 oz. 5 drs. 2 sc. 9 grs.; 25 lbs. 8 oz. 7 drs. 1 sc.; and 45 lbs. 3 oz. 2 drs. 2 sc. Apothecaries' weight.

26. Find the sum of 45 m. 21 fur. 17 r. 5 yds. 2 ft. 9 in.; 43 m. 5 fur. 4 yds. 1 ft. 8 in.; 89 m. 16 r. 3 yds. 2 ft. 5 in.

27. Add together 17 leagues, 2 m. 32 fur. 35 r. 11 ft.; 19 1. 1 m. 71⁄2 fur. 28 r. 15 ft.; 26 1. 2 m. 3 fur. 2 r. 14 ft.

28. Add together 23 years, 2 mos. 3 wks. 5 d.; 68 yrs. 3 mos. 2 wks. 3 d.; 60 yrs. 4 mos. 1 wk. 6 d.; 49 yrs. and 4 d.

29. Add together 145 acres, 35 sq. r. 25 sq. yds. 71⁄2 sq. ft.; 123 A. 65 sq. r. 28 sq. yds. 8 sq. ft.; 84 A. 110 sq. r. 16 sq. yds. 61 sq. ft.

30. Add together 7 circles, 8 s. 17°, 18', 43"; 4 cir. 3 s. 21°, 82', 54"; 18 cir. 9 s. 11°, 17', 39".

ADDITION OF FRACTIONAL COMPOUND NUMBERS.

1. What is the sum of £, s. and }d? Suggestion.-We first reduce the fractions to whole numbers of lower denominations, (Art. 165,) then adding them as in the preceding rule, the result is 3s. 3 far. which is the answer required.

First Method. £}=3s. 4d. 0 far. s.=0s. 1d. 2 far. 5d.d.=0s. Od. 1} far, Ans. 3s. 5d. 3 far.

Or, we may reduce the given fractions to the same denomination, viz: fractions of a penny; £24°d.; js.=12d. jd.=}d. (Art. 166.) Then, reducing these fractions to a common denominator as in the margin, and adding them, the sum is 6024d., which being reduced to whole numbers, gives the same result as before. Hence,

168.a. To add fractional compound numbers.

Reduce the given fractions to whole numbers of lower denominations, then proceed as in compound addition.

Or, reduce the given fractions to the same denomination, then proceed as in adding common fractions. (Art. 127.)

OBS. The result will be the same, whether the given fractions are reduced to fractions of lower denominations, or to higher.

Ans. £1, 4s. 4d. 31⁄2 f. 4. Add 1 oz. 3 pwt. 3 gr. 6. Add cwt. lb. oz. 8. Add 72 in. 23 ft. 6,5 r. 10. Add in. § na. § yd.

12. Add

14. Add

sq. r. 3 yd. § ft. cu. yd. to 211 cu.

ft.

2. Add £1, s. Jd. £}, Js. 3. Add lb. to oz. pwt. 5. Add ton, cwt. lb. 7. Add m. to 1⁄2 of 51 fur. 9. Add yard na. 7 in. 11. Add acre rood r. 13. Add 43 cord to 7 cu. ft. 15. Add hhd. wine, 33 gals. 11⁄2 16. Add bu. 1 pk. 3 qt. bu.pk.qt. pt. 17. Add of day, of hr. of 18 min. and 3 of 23 sec. 18. Bought two remnants of silk, one containing § yd. qr. na., and the other yd. § qr. na.: how much did both contain? 19. How many pounds in a load of hay which weighs ton 21 qrs. and 173 lbs.?

pt.;

qt., and ¦ hhd. 1⁄2 of 63 gals.

QUEST.-168.a. How add fractional compound numbers?

COMPOUND SUBTRACTION.

168.6. Compound Subtraction is the process of finding the difference between two compound numbers.

Ans.

Operation. £ 8. d. far. 15" 7"

6" 3

6" 4

8 2

9 2 10 1

Ex. 1. From £15, 7s. 6d. 3 far., subtract £6, 4s. 8d. 2 far. Suggestion.-We write the less number under the greater, pounds under pounds, shillings under shillings, &c., and beginning with the lowest denomination proceed thus: 2 far. from 3 far. leave 1 far.; set the 1 far. under the column of farthings. Next, Sd. cannot be taken from 6d.; we therefore borrow as many pence, as it takes to make one of the next higher denomination which is shillings; and 12d. added to 6d., make 18d. Now 8d. from 18d. leave 10d. But since we borrowed we must carry 1 to the 4s. which makes 5s., and 53. from 7s. leave 2s. Finally, £6 from £15 leave £9. The answer therefore is £9, 2s. 10d. 1 far.

169. Hence, we derive the following general

RULE FOR COMPOUND SUBTRACTION.

I. Write the less number under the greater, so that the same denominations may stand under each other.

II. Beginning at the right hand, subtract each lower number from the number above it, and set the remainder under the number subtracted.

III. When a number in the lower line is larger than that above it, add as many units to the upper number as it takes to make ONE of the next higher denomination; then subtract as before, and adding 1 to the next number in the lower line, proceed as in Simple Subtraction.

PROOF.—The proof is the same as in Simple Subtraction.

OBS. Compound Subtraction is the same in principle as Simple Subtraction, and the reasons of the rule are the same. In both cases we begin to subtract at the right hand, and when the number in the lower line is larger than that above it,

QUEST.-168.b. What is Compound Subtraction? 169. How do you write compound numbers for subtraction? Where begin to subtract, and how proceed? When a number in the lower line is larger than that above it, what is to be done? How is Compound Subtraction proved?

we borrow as many units as it takes of the order or denomination we are subtracting to make one of the next higher order or denomination; and in both, we carry 1 to the next figure in the lower number.

2. From £10, 7s. 4d. 3 far. take £2, 6s. 9d. 2 fai.

Ans. £8, 0s. 7d. 1 far.

3. From £15, 16s. 10d. 3 far., take £7, 8s. 11d. 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 2 lbs. 3 oz. 12 pwts. 5 grs.: what is the difference in their weight?

10. A merchant had 28 yds. 3 qrs. 2 na. of cloth, 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.

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

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

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.

QUEST.-Obs. Does Compound Subtraction differ in principle from Simple Subtraction?

18. What is the time from July 4th, 1840, to March 1st, 1845 ?

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

170. To find the time between two dates.

Operation.
Yr. mo. d.

1845 3 1

1840 7 4

Ans. 4

"

Hence,

7

27

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, then subtract as in the preceding rule. (Art. 169.)

OBS. 1. The number of the month is easily determined by reckoning from January, the 1st month, Feb. the 2d, &c. (Art. 158. Obs.)

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 declared July 4th, 1776. How much time had elapsed on the 25th of Aug. 1845?

21. A note dated Oct. 2d, 1840, was paid Dec. 25th 1843: how long was it from its date to its payment?

22. A ship sailed on a whaling voyage, Aug. 25th, 1840, and returned April 15th, 1844: how long was she gone?

23. From 268 m. 3 fur. 2 r. 10 ft. 3 in., take 149 m. 6 fur. tr. 12 ft. 5 in.

24. From 160 deg. 18 statute m. 210 r. 3 yds. 1 ft., take 63 deg. 25 m. 305 r. 4 yds. 2 ft.

25. From 275 A. 21 r. 18 yds. 4 ft. 81 in., take 112 A. 65 r. 28 yds. 5 ft. 130 in.

26. From 367 A. 2 roods, 8 r. 25 ft., take 175 A. 3 roods, 25 r. 210 ft.

QUEST.-170. How do you find the time 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?