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. Subtruct 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, Os. 7d. 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. 5. 6. From 16T. 10cwt. 3qrs. 7lbs. 125T. 7cwt. 2qrs. 20lbs. Take 8T. 5cwt. lqr. 2lbs. 96T. 9cwt. 3qrs. 12lbs. 7. 8. From 16 gals. 3 qts. 1 pt. 2 gi. 121 hhds. 28 gals. 1 qt. Take 7 gals. 2 qts. Opt. 3 gi. 63 hhds. 21 gals. 3 qts. 9. Bought 2 silver pitchers, one weighing 2 lbs. 10 oz. 10 pwis. 7 grs.; the other, 1 lb. 15 oz. 12 pwts. 5 grs. : 7 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. I na., the other, 15 yds. 3 qrs. 3 na.: 1 what is the difference in the length ? 12. From 25 m. 7 sur. 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 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 st. 123 in. of wood in his shed, sold 16 C. 117 ii. 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. March is the 3d month, and July the 7th. Since 4 d. cannot be taYr. d. ken from 1 d., we borrow 1 mo. or 1845 3 1 1840 7 30 d. ; then say, 4 from 31 leaves 4 27. 1 to carry to 7 makes 8, but 4 7 27 Ans. 8 from 3 is impossible'; we therefore borrow 1 yr. or 12 mos., and say, 8 from 15 leaves 7. 1 to carry to 0 is 1, and 1 froin 5 leaves 4. mo. 1/ 11 1/ 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? clared 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 her voyage ? MULTIPLICATION OF COMPOUND NUMBERS. S. Ex. 1. What will 5 yards of broadcloth cost, at £2, 3s. 6d. 3 far. per yard ? Suggestion. If 1 yard costs £2, 3s. 63. 3 far., 5 yards will cost 5 times as much. Operation. Beginning with the lowest £ d. far. denomination, we say, 5 times 2 11. 3 6 3 3 far. are 15 far. ; now 15 far. 5 are equal to 3d. and 3 far. over. Set the 3 far, under the denomi. 10 17 9 3 Ans. nation multiplied, and carry the 3d. to the next product. 5 times 6d. are 30d. and 3d. make 33d., equal to 2s. and 9d. Set the 9d. under the pence, and carry the 2s. to the next product. 5 times 3s. are 15s. and 2s. make 17s. As the product 175. does not make one in the next denomination, we set it under the column multiplied. Finally, 5 times £2 are £10. The answer is £10, 17s. 9d. 3 far. 171. Hence, we deduce the following general RULE FOR MULTIPLYING COMPOUND NUMBERS. Multiply each denomination separutely, beginning with the lowest, and divide each product by that number which it takes of the denomination multiplied, to make one of the QUEST.–171. Where do you begin to multiply a compound number? What is done with each product ? Obs. When the multiplier is a composite number, how proceed? What is the process of multiplying different denominations, called? next higher; set down the remainler, and carry the quotient to the next product, as in addition of compound numbers. (Art. 168.) Obs. 1. When the multiplier is a composite number, it is advisable to multiply first by one factor and that product by the other. (Art. 57.) 2. The process of multiplying different denominations is called Compound Multiplication. 2. Multiply £5, 7s. 8d. 2 far. by 18. Operation. £ d. far. 5 7 8 2 Multiply by the factors of 18, 6 which are 6 and 3. 3211 6 3 0 3 96 18 O Ans. 3. What will 5 horses cost, at £25, 10s. 6d. apiece? 4. A colony of 6 persons agreed to pay £31, 5s. 8d. apiece for their passage from Hamburg to New York : what was the expense of their passage ? 5. What cost 9 yards of cloth, at 18s. 9 d. per yard ? 6. What cost 6 pipes of wine, at £9, 78. 83d. apiece ? 7. What cost 8 cows, at £5, 10s. 6d. apiece ? 8. In a solar year there are 365 days, 5 hrs. 48 min. 48 sec. : how many days, hours, &c., has a person lived, who is 21 years old ? 9. Bought 10 silver cups, each weighing 3 oz. 15 pwts. 3 10 grs.: what is the weight of the whole ? 10. What is the weight of 72 silver dollars, each weighing 17 pwts. 8 grs. ? 11. Bought 7 loads of hay, each weighing 1 T. 3 cwt. 3 qrs. 12 lbs.: what is the weight of the whole ? 12. What is the weight of 20 hogsheads of inolasses, each weighing 5 cwt. 3 qrs. 17 lbs. 10 oz. ? 13. A man bought 9 oxen, weighing 1123 lbs. 15 oz. apiece: what was the weight of the whole ? 14. A grocer bought 11 casks of ndy, each containing 54 gals. 3 qts. 1 pt. 2 gills : how much did they all contain ? a 15. If a stage-coach goes at the rate of 5 m. 2 sur. 30 r. per hour, how far will it go in 10 hours ? 16. If a Railroad car goes 21 m. 2 fur. 10 r. per hour, how far will it go in 10 hours ? 17. Bought 12 pieces of broadcloth, each containing 27 yds. 1 qr. 2 na. : how many yards did all contain ? 18 If a man mows 3 A. 35 sq. r. per day, how many acres can he mow in 30 days ? 19. How many square yards of plastering will a house which has 9 rooms require, allowing 75 yds. 18 ft. to a room? 20. A man bought 15 loads of wood, each containing 1 C. 33 ft.: how many cords did he buy ? 21. A miller constructed 7 cubical bins for grain, each containing 216 feet 152 in.: what was the contents of the whole ? 22. If a ship sails 2° 25' 10" per day, how far will she sail in 20 days? 23. Multiply 56°, 42' 11" by 32. 24. If a brewer sells 33 gals. 2 qts. 1 pt. of beer a day, how much will he sell in 24 days ? 25. If a milk-man sells 40 gals. 3 qts. 1 pt. of milk per 3 day, how much will he sell in 60 days? 26. What cost 82 tons of iron, at £4, 15s. 6 d. per pound? 27. If 1 acre produce 33 bu. 2 pks. 5 qts. of wheat, 5 how much will 100 acres produce ? 28. If 1 suit of clothes requires 9 yds. 3 qrs. 2 na., how much will 500 suits require ? 29. If 1 mile of Railroad require 60 T. 5 cwt. 9 lbs. of iron, how much will 50 miles require ? 30. How much wheat will it require to make 1000 barrels of flour, allowing 4 bu. 2 pks. 6 qts. to a barrel ? |