4. Reduce 2qr. 13lb. 10oz. 21dr. to the fraction of a cwt. Ans. 11 5. What part of a pound avoirdupois are 7oz. 1]dr. ? 6. What part of a pound troy are 10oz. 13pwt. 8gr. ? Ans. S. 7. Express 1 gallon liquid measure as a fraction of a gallop Ans. 11 dry measure. Ans. 73 8. What part of a yard are 2qr. Ona. 11 in. ? 9. What part of an ell English are 2qr. 3na. Ofin.? Ans. . 10. What part of a mile are 6fur. 30rd. 12ft. 84 in. ? 11. Reduce 35rd. 9ft. 2in. to the fraction of a furlong. Ans. g. 12. What part of an acre are 2R. 6rd. 4yd. 5ft. 127 in. Ans. To 13. What part of a square rod are 144ft. 194in. ? Ans. 17. 14. What part of a cord are 9ft. 1462 4in. ? 15. What part of a hogshead of wine are 6gal. 2qt. lpt. Ans. 1g. 04gi..? 16. What part of a pound avoirdupois is 1 pound troy ? Ans. 14. 17. What part of a year (3651 days) are 174d. 16h. 26m. Ans. 13. 52 sec. ? ADDITION OF DENOMINATE FRACTIONS. 257. To add denominate fractions. Ex. 1. Add 13 of a £. to i of a £. Ans. 1£. 7s. 1d. 2,4 far. We find the value of each 15 of a £. = 103. 9d. 013 far. fraction separately, and add the two values together, of a £. = 163. 4d. 1 far. according to the rule for Ans. 1£. 7s. 1d. 23 far. adding compound numbers. (Art. 145.) FIRST OPERATION SECOND OPERATION, 73£. + 1£. = 1!4£. = 1£. 7s. 1d. 21 far. Ans. 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 11 of a ton and 13 of a cwt. Ans. 13cwt. 2qr. 3. Add together of a yard, 7 of an ell English, and of a qr. 4. Add together it of a mile, is of a furlong, and of a yard. Ans. 5fur. 16rd. Oft. 3.in. 5. A has three house-lots; the first contains $ of an acre, the second f of an acre, and the third it of an acre. How many acres do they all contain ? Ans. 2A. 1R. 9p. 142ft. 87 in. 6. A man travelled 187 miles the first day, 2314 miles the second day, and 1921 miles the third day. How far did he travel in the three days? Ans. 61m. 2fur. 3rd. 13ft. 42 in. 7. Add 13 of a gallon of wine to the of a hhd. 8. Add of a week to } of a day. Ans. 2d. 9h. 18m. 9. Add f of a square foot to £ a foot square. Ans. 1 foot. 10. Add 6 inches to 11rd. 16ft. 5in. Ans. 12rd. Oft. 5in. SUBTRACTION OF DENOMINATE FRACTIONS. FIRST OPERATION. It of a £. 258, To subtract one denominate fraction from another. Ex. 1. From 11 of a £. take of a £. Ans. 8s. 3d. 1j far. We find the value of each fraction 12s. 88d. separately, and subtract one from the of of a £. 4s. 54d. other, according to the rule for sub tracting compound numbers. (Art. Ans. 8s. 31d. 146.) By the second 11£. — §£. £. = 8s. 3d. 14ffar. Ans. operation, we first subtract the less fraction from the greater, and then find the value of their difference, (Art. 255.) SECOND OPERATION. EXAMPLES. 2. From of an ell English take of a yard. Ans. 3qr. Ona. 2 in. 3. Take It of a furlong from šof 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 ti of an acre take of a rod. Ans. 1R. 17p. 22yd. 2ft. 108in.** 6. From 1 of a cord take it of a cord. 7. From 13 of a hogshead of wine there leaked out of it; what remained ? Ans. 6gal. 3qt. Opt. 18gi. 8. From Boston to Concord, N. H., the distance is 72 miles ; 4 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. 17 sec. 10. From t of an acre take 1 of a foot. MISCELLANEOUS EXAMPLES IN FRACTIONS. acre ? 1. How far will a man walk in 1741 hours, provided he goes at the rate of 47 miles an hour ? Ans. 82m. 4fur. Srd. 1ft. 4in. 2. How much land is there in a field which is 2913 rods square ? Ans. 5 A. 1R. 32p. 141ft. 1091&fin. 3. How much wood in a pile which is 174 feet long, 711 feet high, and 43 feet wide? Ans. 4C. 66117ft. 4. What is the value of 197 barrels of flour, at $ 64 a barrel ? 5. What is the value of 37613 acres of land, at $ 75% per Ans. $ 28387.064. 6. What cost 17.1. quintals of fish, at $ 4.75 per quintal ? Ans. $81.55612. 7. What cost 167013 pounds of coffee, at 124 cents per Ans. $ 212.9912 8. What cost 2841 tons of Lackawana coal, at $11} a ton ? Ans. $ 333.27 3. 9. Bought 37 hogsheads of molasses, at $17.624 a hogshead; what was the whole cost? Ans. $ 655.2011 10. What cost of a cord of wood, at $ 5.75 a cord ? 11. What are the contents of a field which is 1394 rods long, and 38% rods wide ? Ans. 33A. 3R. 154 p. 12. Bought 15 loads of wood, each containing 11f feet, cord pound ? measure. I divide it equally between 9 persons; what does each receive ? Ans. 193ft. 13. If the transportation of 183 tons of iron costs $ 48.153, what is it per Ans. $ 2.624. 14. If a hogshead of wine costs $983, what is the price of one gallon ? 15. If 5 bushels of wheat cost $87, what will a bushel be worth? Ans. $ 1.649. 16. What will 11 hogsheads and 17} gallons of wine cost, at 19 cents a gallon ? Ans. $140.323. 17. How many bottles, each containing 11 pints, are sufficient for bottling a hogshead of cider ? Ans. 288. 18. I have a shed which is 1873 feet long, 10 feet wide, and 711 feet high ; how many cords of wood will it contain ? Ans. 11C. 124 829ft. 19. What will 67 pounds of tea cost, at 654 cents per pound? Ans. $ 4.5232 20. How many cubic feet does a box contain, that is 8 feet long, 512 feet wide, and 3 feet high ? Ans. 146°cft. 21. How many feet of boards will it take to cover a side of a house which is 46 feet long and 174 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 31 feet wide; required also the number of cubic feet they would occupy ? Ans. 52759ft. ; 28633% cubic feet. 23. A certain room is 12 feet long, 114 feet wide, and 74 feet high ; how much will it cost to plaster it, at 2 cents per Ans. $13.487. 24. A man has a garden that is 14} rods long, and 104 rods wide; he wishes to have a ditch dug around it, that shall be 3 feet wide and 41 feet deep; what will be the expense, if he give 2 cents per cubic foot ? Ans. $ 223.761 25. How many bushels of grain will a box contain which is 1417 feet long, 511 feet deep, and 41 feet wide, there being 2150; cubic inches in a bushel ? Ans. 294313 bu. 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. square foot ? 27. Which will contain the most gallons, a cistern that is 74 feet long, 6 feet wide, and 51 feet deep, or one that is 94 feet long, 47 feet wide, and 54 feet deep ? Ans. The first cistern contains 924 gallons most. 28. My field has four sides. The first side is 31 rods 1313 feet in length; the second, 41 rods 1% feet; the third, 38 rods 04 feet; and the fourth, 45 rods 12 jo 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 lo of a foot; also the number of rails it will take to fence it. Ans. Length, 13 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 $, i, or 4 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 31 A. 3R. 6p., and J. Ford's farm contains 39A. 2R. 373p. 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. $5381. 33. What cost 8 acres of land, at $ 42; 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 8.1 feet high. This room contains 4 windows, each of which is 51 feet in height and 31 feet in width. There are two doors 7 feet high and 3 feet wide. The mop-boards are şof 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, $ 5.1138 ; for papering, $ 4.37; for paper, $ 2.8035 |