4. Reduce 2qr. 13lb. 10oz. 21fdr. to the fraction of a cwt. Ans. 5. What part of a pound avoirdupois are 7oz. 1zdr.? Ans. 8. 7. Express 1 gallon liquid measure as a fraction of a gallon dry measure. 8. What part of a yard are 2qr. Ona. 15in.? Ans. 1 Ans. 73 Ans. . 10. What part Ans. . 12. What part of an acre are 2R. 6rd. 4yd. 5ft. 127in. Ans. 73. 13. What part of a square rod are 144ft. 194in.? Ans. 17. 14. What part of a cord are 9ft. 1462in.? 15. What part of a hogshead of wine are 6gal. 2qt. 1pt. 04gi.? Ans. 16. What part of a pound avoirdupois is 1 pound troy? Ans. 14. 17. What part of a year (365 days) are 174d. 16h. 26m. By the second operation, we first add the two fractions together, and then find the value of their sum. (Art. 255.) EXAMPLES. 2. Add together of a ton and 13 of a cwt. Ans. 13cwt. 2qr. 3. Add together of a yard, of an ell English, and of a qr. 4. Add together of a mile, of a furlong, and of a yard. Ans. 5fur. 16rd. Oft. 393in. 5. A has three house-lots; the first contains of an acre, the second of an acre, and the third 1 of an acre. How many acres do they all contain? Ans. 2A. 1R. 9p. 142ft. 873in. 6. A man travelled 183 miles the first day, 2311 miles the second day, and 19 miles the third day. How far did he travel in the three days? Ans. 61m. 2fur. 3rd. 13ft. 4 in. of a gallon of wine to of a hhd. of a week to of a day. 7. Add Ans. 2d. 9h. 18m. Ans. 12rd. Oft. 5in. 8. Add 9. Add of a square foot to a foot square. 10. Add 6 inches to 11rd. 16ft. 5in. Ans. 1 foot. SUBTRACTION, OF DENOMINATE FRACTIONS. 258. To subtract one denominate fraction from another. Ex. 1. From 71 of a £. take of a £. Ans. 8s. 3d. 11 far. We find the value of each fraction separately, and subtract one from the other, according to the rule for subtracting compound numbers. (Art. 146.) 8s. 3d. 148far. Ans. fraction from the greater, and then find the value By the second operation, we first subtract the less of their difference. (Art. 255.) EXAMPLES. 2. From of an ell English take of a yard. Ans. 3qr. Ona. 2in. 3. Take of a furlong from & of a mile. Ans. 1fur. 5rd. 10ft. 10in. 4. Take of a mile from of a degree. Ans. 48m. 6fur. 17rd. 8ft. 7 in. 5. From of an acre take of a rod. 6. From 7. From what remained? Ans. 1R. 17p. 22yd. 2ft. 108in. of a cord take of a cord. of a hogshead of wine there leaked out of it; Ans. 6gal. 3qt. Opt. 17gi. 8. From Boston to Concord, N. H., the distance is 72 miles; of this distance having been travelled, how much remains? Ans. 30m. 6fur. 34rd. 4ft. 84in. 9. From of a year take of a week. Ans. 101da. 5h. 54m. 174sec. 10. From of an acre take of a foot. MISCELLANEOUS EXAMPLES IN FRACTIONS. 1. How far will a man walk in 17 hours, provided he goes at the rate of 43 miles an hour? Ans. 82m. 4fur. 8rd. 1ft. 4in. 2. How much land is there in a field which is 29 rods square? Ans. 5A. 1R. 32p. 141ft. 10915ğin. 3. How much wood in a pile which is 172 feet long, 7 feet high, and 4 feet wide? Ans. 4C. 66107ft. 4. What is the value of 197 barrels of flour, at $ 62 a barrel? 5. What is the value of 3761 acres of land, at $753 per acre? Ans. $28387.06. 6. What cost 1712 quintals of fish, at $4.75 per quintal? Ans. $81.556. 19 7. What cost 1670 pounds of coffee, at 12 cents per pound? Ans. $212.9919. 8. What cost 28 tons of Lackawana coal, at $112 a ton? Ans. $333.27. 9. Bought 37 hogsheads of molasses, head; what was the whole cost? at $17.62 a hogsAns. $655.201• 10. What cost of a cord of wood, at $5.75 a cord? 11. What are the contents of a field which is 139 rods Ans. 33A. 3R. 1513p. long, and 38 rods wide? 12. Bought 15 loads of wood, each containing 11g feet, cord measure. I divide it equally between 9 persons; what does each receive? Ans. 19 ft. 13. If the transportation of 183 tons of iron costs $48.152, what is it per ton? Ans. $2.62. 14. If a hogshead of wine costs $987, what is the price of one gallon? 15. If 5 bushels of wheat cost $83, what will a bushel be worth? Ans. $1.644. 16. What will 11 hogsheads and 17 gallons of wine cost, at 19 cents a gallon? Ans. $140.323. 1 pints, are suffi 17. How many bottles, each containing cient for bottling a hogshead of cider? Ans. 288. long, 10 feet cords of wood will it conAns. 11C. 124,829 ft. 18. I have a shed which is 18 feet wide, and 711 feet high; how many tain? 19. What will 67 pounds of tea cost, at 652 cents per pound? Ans. $4.52'. 20. How many cubic feet does a box contain, that is 8 feet long, 5 feet wide, and 3 feet high? Ans. 146ft. 21. How many feet of boards will it take to cover a side of a house which is 465 feet long and 171⁄2 feet high? 22. Required the number of square feet on the surface of 7 boxes, each of which is 5 feet long, 2 feet high, and 3 feet wide; required also the number of cubic feet they would occupy? Ans. 527 ft. 2863 cubic feet. 23. A certain room is feet high; how much will square foot? 12 feet long, 11 feet wide, and 71 it cost to plaster it, at 22 cents per Ans. $13.487. 24. A man has a garden that is 144 rods long, and 104 rods wide; he wishes to have a ditch dug around it, that shall be 3 feet wide and 4 feet deep; what will be the expense, if he give 2 cents per cubic foot? Ans. $223.764. 25. How many bushels of grain will a box contain which is 14 feet long, 511 feet deep, and 4 feet wide, there being 2150 cubic inches in a bushel? Ans. 294242bu. 26. Which will contain the most, and by how much, a box that is 10 feet long, 8 feet wide, and 6 feet deep, or a cubical one, each of whose sides measures 8 feet? Ans. The last contains 32 cubic feet the most. 27. Which will contain the most gallons, a cistern that is 7+ feet long, 6 feet wide, and 5 feet deep, or one that is 9 feet long, 4 feet wide, and 5 feet deep? Ans. The first cistern contains 924 gallons most. 28. My field has four sides. The first side is 31 rods 13 feet in length; the second, 41 rods 15 feet; the third, 38 rods 0 feet; and the fourth, 45 rods 12 feet. I wish to enclose this field with a rail-fence four rails high, using rails of equal length. Required the length of the longest rails that can be used, allowing that the rails lap by each other of a foot; also the number of rails it will take to fence it. Ans. Length, 131⁄2 feet; number, 808. 29. Required the least number of yards of velvet, expressed by a whole number, that can be cut up without waste, into vest patterns of,, or yards each? Ans. 30 yards. 30. If a company whose capital stock is divided into 100 equal shares should conclude to divide the same stock into only 30 shares, how much larger would a share of the latter be than one of the former size? 31. D. Ripley's farm contains 31A. 3R. 6p., and J. Ford's farm contains 39A. 2R. 37p. What is the fraction, in its simplest form, that will express their comparative size? Ans. . 32. Bought 68 barrels of flour, at $711 per barrel; what was the amount of the whole? Ans. $538. 33. What cost 8 acres of land, at $ 423 per acre? Ans. $369.20. 34. How shall four 3's be arranged, that their value shall be nothing? 35. I have a room 20 feet long, 15 feet wide, and 8 feet high. This room contains 4 windows, each of which is 5 feet in height and 3 feet in width. There are two doors 7 feet high and 3 feet wide. The mop-boards are of a foot wide. A mason has agreed to plaster this room at 64 cents per square yard; a painter is to lay on the paper at 9 cents per square yard; the paper which I wish to have laid on is 23 feet wide, for which I pay 5 cents per yard. What is the amount of my bill for plastering, for papering, and for paper? Ans. For plastering, $5.11; for papering, $4.37; for paper, $2.805. |