ADDITION OF COMPOUND NUMBERS. 299. The process of adding numbers of different denominations, is called COMPOUND ADDITION. 1. What is the sum of £6, 11s. 5d. 1 far.; £4, 9s. 6d. 2 far.; £3, 12s. 8d. 3 far.; and £8, 6s. 9d. 1 far. ? £ Operation. 6 // 11 / 5 1 4 " 3 // 9 6 12 11 "3 811 6" 11 9 1 Having placed the farthings under farthings, the pence under pence, &c., we add the column of farthings together, as in simple addition, and find the sum is 7, which is equal to 1d. and 3 far. over. Set the 3 far. under the column of far5 "3 Ans. things, and carry the 1d. to the column The sum of the pence is 29, which is equal to 2s. and id. over. Place the 5d. under the column of pence, and carry he 2s. to the column of shillings. The sum of the shillings is 40, which is equal to £2, and nothing over. Write a cipher under the column of shillings, and carry the £2 to the column of pounds. The sum of the pounds is 23. Ans. £23, 0s. 5d. 3 far. 23/1 0 of pence. 300. Hence, we derive the following general RULE FOR ADDING COMPOUND NUMBERS. 1. Write the numbers so that the same denominations shall stand under each other. 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 added, and carry the quotics t to the next column. III. Proceed in this manner with all the other denominations xcept the highest, whose entire sum is set down. PROOF.-The proof is the same as in Simple Addition. (Art. 55. OBS. 1. Fractional compound numbers should be reduced to whole nun bers of lower denominations, then added as above. (Art. 166.) QUEST.-299. What is Compound Addition? 300. How do you write compound numbers or addition? Which denomination do you add first? When the sum of any column is found, what is to be done with it? What is done with the last column ? 2. Compound Addi ion is the same in principle as Simple Addition In the latter, it is true, we uniformly carry the tens, and in the former we car for different numbers; yet in each we always carry for that number which takes of the order or denomination we are adding to make one in the nez 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 tor 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 Ib 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 8 oz. 16 pwts.; 97 lbs. 5 oz. lbs. 3 oz. 6 pwts. 19 grs.; 100 lbs. 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, 2 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.; 62 A. 29 r. 31 sq. ft.; 10 A. 45 r. 16 sq. ft. 49 A. 15 r 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. 2 pts. 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. d. 9 hrs. 15 min.; 40 wks. 4 d. 17 hrs. 30 min.; 42 wks. 1 d.? 19. What is the sum of 40 bu. 31 pks. 4 qts. ; 63 bu. 24 pks. qts.; 80 bu. 74 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. 301. The process of finding the difference between numbers of different denominations, is called COMPOUND SUBTRACTION. 1. From £35, 17s. 6d. 3 far., subtract £16, 9s. 8d. 2 far. Operation. d. far. 6 3 £ 35" 17" 16" 9 11 S. 19 // 7 10 8" 2 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 column of farthings. But 8d. cannot be taken from Sd.; we therefore borrow 1 from the next higher denomination, which is shillings; and 1s. or 12d. added to the 6d. make 18d. Now 8d. from 18d. 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. QUEST.-301. What is Compound Subtraction? 302. Hence, we derive the following general RULE FOR SUBTRACTING COMPOUND NUMBERS. I. Write the less number under the greater, so that the same de nominations 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? t, 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 de nomination and add it to the number in the upper line. Subtract as before, and carry 1 to the next denomination in the lower line, cis in subtraction of simple numbers. (Art. 72.) PROOF.-The proof is the same as in Simple Subtraction. OBS. 1. Fractional compound numbers should be reduced to whole numbers of lower denominations, then subtracted as above. (Art. 166.) 2. Compound Subtraction is the same in principle as Simple Subtra ction. 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 £160, 61s. 33d., 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 1. 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 144 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 *at of the North Cape, 71° 10' required their difference. 21. The longitude of New York is 74° 1', and that of Cincin nati 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? May is the 5th month, and Feb. the 2d. Since 22 days cannot be taken from 21 d., we borrow I mo, or 30 d.; then say 22 from 51 leaves 29. 1 to carry to 2 makes 3, and 3 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 2 QUEST.-303. How do you find the time between two dates? Obs In finding time be tween two dates, and in casting interest, how many days are considered a month How many months a year? |