2. Compound Addition is the same in principle as Simple Addition In the latter, it is true, we uniformly carry the tens, and in the former we carry for different numbers; yet in each we always carry for that number which it takes of the order or denomination we are adding to make one in the next higher order or denomination. 5. A farmer sold to one customer 3 tons, 5 cwt. 17 lbs. 13 oz. of hay; to another, 4 tons, 7 cwt. 35 lbs. 12 oz.; to another, 1 ton, 15 cwt. 63 lbs. 7 oz. : how much hay did he sell to all ? 6. What is the sum of 15 tons, 6 cwt. 45 lbs. 5 oz.; 3 tons, 17 cwt. 80 lbs. 6 oz.; 26 tons, 31 lbs. 7 oz. ? 7. What is the sum of 21 lbs. 7 oz. 12 pwts. 10 grs. ; 28 lbs. 5 oz. 8 pwts. 7 grs.; 7 lbs. 6 pwts. 15 grs.; 41 lbs. 6 oz. 20 grs. ; 9 lbs. 7 grs. ? 8. What is the sum of 16 lbs. 3 oz. 6 pwts. 19 grs.; 100 lbs. 8 oz. 16 pwts. ; 97 lbs. 5 oz. 10 grs.; 115 lbs. 9 oz. ? 9. Add together 19 rods, 12 ft. 8 in.; 64 rods, 13 ft. 3 in.; 28 rods, 10 ft. 5 in.; 60 rods, 9 ft. 11 in. 10. Add together 5 leagues, 2 m. 4 fur. 7 rods, 4 yds. ; 18 leagues, 2 m. 3 fur. 21 rods, 3 yds.; 85 leagues, 6 fur. 10 rods, 4 yds. 1 ft. 11. Add together 19 yds. 3 qrs. 3 na. ; 21 yds. 2 qrs. 1 na. ; 42 yds. 1 qr. 2 na.; 30 yds. 3 qrs. 2 na. 12. Add together 65 yds. 3 qrs. 1 na.; 81 yds. 2 qrs. 2 na ; 100 yds. 3 qrs. 1 na. ; 95 yds. 1 qr. 1 na. ; 15 yds. 3 na.; 28 yds. 2 qrs. 13. Add together 17 A. 25 r. 29 sq. ft. ; 49 A. 15 r. 4 sq. ft. : 62 A. 29 r. 31 sq. ft. ; 10 A. 45 r. 16 sq. ft. 14. Add together 100 A. 3 R. 12 r. ; 115 A. 2 R. 20 r.; 160 A. 1 R. 15 r. ; 91 A. 2 R. 26 r. QUEST.--Obs. Does Compound Addition differ from Simple Addition? 15. One room in a house contains 15 sq. yds. 5 ft. 7 in. of plastering; another 10 yds. 7 ft. 30 in.; another 9 yds. 6 ft. 25 in.; another 7 yds. 5 ft. 63 in. : how much plastering is there in all of them ? 16. A merchant bought one cask of oil containing 73 gals. 3 qts.; another 60 gals. 2 qts.; another 40 gals. 1 qt.; another 65 gals. 2 qts. : how much oil did he buy? 17. What is the sum of 20 hhds. 41 gals. 3 qts. 1 pt. 3 gi.; 31 hhds. 20 gals. 1 qt. 1 pt. 3 gi. ; 48 hhds. 19 gals. 2 qts. 1 pt. 2 gi.; 81 hhds. 40 gals. 1 gi. ? 18. What is the sum of 10 wks, 5 d. 12 hrs. 40 min.; 21 wks, 3 d. 9 hrs. 15 min. ; 40 wks. 4 d. 17 hrs. 30 min. ; 42 wks. 1 d.? 19. What is the sum of 403 bu. 13 pks. 4 qts. ; 63 bu. 27 pks. 5 qts.; 80 bu. 7 pks. 1 qt. ; 45 bu. 2 pks. 3 qts.; 90 bu. 1 pk. ? 20. What is the sum of 7 qrs. 6 bu. 1 pk. 3 qts. ; 27 qrs. 6 bu. 6 qts. ; 34 qrs. 1 bu. 6 qts.; 65 qrs. 6 bu. 3 qts. ? SUBTRACTION OF COMPOUND NUMBERS. d. far. 301. The process of finding the difference between numbers of different denominations, is called ComPOUND SUBTRACTION. 1. From £35, 175. 6d. 3 far., subtract £16, 9s. 8d. 2 far. Operation. Having placed the less number under £ the greater, with farthings under far35 " 17" 6 3 things, pence under pence, &c., we sub911 8" 2 tract 2 far. from 3 far., and set the 7" 10" 1 Ans. remainder 1 far. under the column of farthings. But 8d. cannot be taken from 6d. ; we therefore borrow 1 from the next higher denomination, which is shillings; and is. or 12d. added to the 6d. make 18d. Now 8d. from 180. leaves 10d. Since we borrowed, we must carry 1 to the next denomination in the lower number, as in simple subtraction. (Art. 72.) 1 added to 9 makes 10; and 10 from 17, leaves 7. Finally, 16 from 35, leaves 19. Ans. £19, 7s. 10d. 1 far. 16 11 19 11 QUEST.--301. What is Compound Snbtraction ? 302. 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. 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 1 to the next denomination in the lower line, as in subtraction of simple numbers. (Art. 72.) PROOF.—The proof is the same as in Simple Subtraction. Obs. 1. Fracttonal compound numbers should be reduced to whole numbers of lower denominations, then subtracted as above. (Art. 166.) Obs. 2. Compound Subtraction is the same in principle as Simple Subtraction. In both cases, when the number in the lower line is larger than that above it, 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 £48, 17s. 6d. 2 far., take £39, 14s. 9d. 3 far. 3. From £1601, 64s. 3 d., take £100, 8s. 4. From £1000, take £500, 6s. 7d. 2 far. 5. From 16 cwt. 3 qrs. 15 lbs., take 8 cwt. 2 qrs. 8 lbs. 6 oz. 6. From 85 tons 16 cwt. 39 lbs., take 61 tons 14 cwt. 68 lbs. 7. Subtract 69 m. 41 r. 12 ft. from 89 m. 10 r. 14 ft. 8. Subtract 17 1. 2 m. 3 fur. 4 r. 4 ft. from 19 l. 1 m. 2 fur. 15 r. 9. Subtract 49 bu. 3 pks. 6 qts. from 85 bu. 2 pks. 4 qts. 10. Subtract 95 qrs. 4 bu. 3 pks. from 115 qrs. 3 bu. 1 pk. 11. Subtract 29 yds. 2 qrs. 3 na. from 85 yds. 1 qr. 2 na. 12. Subtract 55 yds. 2 qrs. 1 na. from 100 yds. 13. Subtract 75 gals. 3 qts. 1 pt. from 82 gals. 2 qts. QUEST.--302. 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 ? Obs. Does Compound Subtraction differ from Simple Subtraction ? 15. A man having 140 A. 17 r. of land, sold 54 A. 58 r.: how much had he left ? 16. Two men having bought 465 A. 48 r. of land, one of them wished to take 230 A.: how much would the other have ? 17. A farmer having 140 cords, 55 ft. of wood, sold 87 c. 93 ft. : how much had he left ? 18. In a certain village there are two public cisterns; one contains 446 cu. ft. 69 in., the other 785 cu. ft. 95 in.: what is the difference in their capacity ? 19. The latitude of the Cape of Good Hope is 30° 55' 15", and that of Cape Horn, 55° 58' 30": what is their difference? 20. The latitude of the Straits of Gibraltar is 36° 6' 30", and that of the North Cape, 71° 10': required their difference. 21. The longitude of New York is 74° 1', and that of Cincinnati 84° 27' : required their difference. 22. From 160 yrs. 11 mo. 2 wks. 5 ds. 16 hrs. 30 min. 40 sec., take 106 yrs. 8 mo. 3 wks. 6 ds. 13 hrs. 45 min. 34 sec. 23. What is the time from Feb. 22d, 1845, to May 21st, 1847 ? Operation. May is the 5th month, and Feb. the 2d. yr. mo. d. Since 22 days cannot be taken from 21 d., we 1847 11 5 21 borrow 1 mo. or 30 d.; then say 22 from 51 1845 2 22 leaves 29. 1 to carry to 2 makes 3, and 3 Ans. 211 2 29 from 5 leaves 2. 5 from 7 leaves 2. Hence, 303. 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. 302.) OBs. 1. The number of the month is easily determined by reckoning from January, the 1st month, February the 2d, &c. (Art. 264.) 2. In finding the time between two dates, and in casting interest, 30 days are considered a month, and 12 months a year. 3. Instead of setting down the ordinal number of the month, as in the solution above, some prefer to write the number of whole months that have QUEST.-303. 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 ? Huw many months a year ? elapsed in the given year. E. g., if the date is Feb. 220, 1845, they would write 1 in the place of months; because, it is said, 2 whole months have not elapsed in the year 1845. But it may be doubted whether this method would not lead to frequent mistakes. Besides, it may be urged with equal reason, that 1 ought to be deducted from the day of the month, and 1 from the year; for neither 22 whole days, nor 1845 whole years had elapsed at the time of the date, but the 221 day and the 1845th year were then passing. In this way, the subject, which in itself is simple, becomes intricate and perplexing. 24. General Washington was born Feb. 22d, 1732, and died Dec. 14th, 1799: how old was he? 25. The Independence of the United States was declared, July 4th, 1776: how long is it since ? 26. A note was given Aug. 25th, 1840, and paid Feb. 6th, 1842: how long did it run ? 27. The United States Exploring Expedition sailed from Norfolk on the 18th of Aug., 1838, and returned to New York on the 10th of June, 1842: how long was the voyage ? COMPOUND MULTIPLICATION. S. 304. The process of multiplying numbers of different denominations, is called COMPOUND MULTIPLICATION. Ex. 1. What will 6 cows cost, at £5, 2s. 7d. apiece ? Analysis.-Since 1 cow costs £5, Operation. 2s. 7 d., 6 cows will cost 6 times as £ d. far. much. Beginning with the lowest 5 li 2 11 7 1 3 denomination, 6 times 3 far. are 18 far., 6 equal to 4d. and 2 far. over. Set the 30 " 15" 10" 2 Ans. 2 far. under the denomination multiplied and carry the 4d. to the next product. 6 times 7d. are 42d. and 4d. make 46d., equal to 3s. and 10d. Set the 10d. under the pence, and carry the 3s. to the next product. 6 times 2s. are 12s. and 3s. make 15s. As the product 15s. does not make one in the next denomination, we set it under the column multiplied. Finally, 6 times £5 are £30. The answer is £30, 15s. 10d. QUEST.--304. What is Compound Multiplication ? |