23. The gold coin of Great Britain of the value of a pound is called a sovereign. How many shillings are there in 1 guinea, 2 crowns, 3 sovereigns, 1 half-sovereign, and 3 half-crowns? REDUCTION. 283. To change denominate numbers to numbers of lower denominations. Illustrative Example. Change 3 yd. 2 ft. 6 in. to inches. WRITTEN WORK. 3 yd. 2 ft. 6 in. 3 11 ft. 12 138 in Since there are 3 ft. in 1 yd., in 3 yd there are 3 times 3 ft. or 9 ft. ; 9 ft. and 2 ft. = 11 ft. Since there are 12 in. in 1 ft., in 11 ft. there are 11 times 12 in. or 132 in.; 132 in. and 6 in. = 138 in. Ans. 138 in. 284. From the foregoing illustration may be derived the following Rule. To change a compound denominate number to units of a lower denomination: Multiply the number of the highest denomination by the number of units it takes of the next lower denomination to make one of that higher, and to the product add the given number of the next lower denomination. Multiply this sum in like manner, and so proceed till the given number is changed to units of the required denomination. Examples for Written Work. 285. How many 24. Inches are 3 yd. 1 ft. 4 in.? 25. Minutes are 5 h. 40 min. ? 26. Pounds are 2 T. 180 lb. ? 27. Ounces are 6 lb. 9 oz. Av.? 28. Pence are £5 6s.? 29. Feet are 3 rd. 4 yd.? 34. What is the value of 2 lb. 8 oz. of gold at $20 an ounce? 35. At 114 a quart for nuts and 45¢ a peck for apples, find the value of 4 bushels of nuts and 12 bushels of apples. 36. At 74 per quart for milk, and 30¢ per pint for cream, how much will a dealer receive for 24 gal. 2 qt. of milk and 3 qt. 1 pt. of cream? 37. What will it cost to fence both sides of a road 36 rd. 6 ft. long, at 284 a foot? 38. The tropic of Cancer is 23° 30′ north of the equator. What is the distance in geographical miles? What is the distance in common miles? (See Art. 276.) 286. Illustrative Examples. (1) Change of a rod to yards and feet. (2) Change 0.66 of a rod to yards and feet. 287. From the foregoing illustration may be derived the following Rule. To change a fraction of one denomination to integers of lower denominations: Change the fraction, as far as possible, to an integer of the next lower denomination. If a fraction occurs in the result, proceed with it as with the first fraction, and so continue as far as required. 47. At 20¢ a foot, what is the cost of of an acre of land? 288. To change a simple denominate number to a compound number of higher denominations. Illustrative Example. Change 424 feet to rods, yards, etc. 289. From the foregoing illustration may be derived the following Rule. To change a simple denominate number to a compound number of higher denominations: Divide the given number by the number of units it takes of its denomination to make one of the next higher. Set aside the remainder, and divide, as before, the quotient thus obtained. Proceed in the same manner till the required denomination is reached. The last quotient with the several remainders is the compound number sought. Examples for Written Work. 290. Change to units of higher denominations: 63. 321 pints of berries. 64. 562 pints of water. 65. 428 ounces of salt. 66. 1418 grains of gold. 67. 3286 sheets of paper. 68. 18,642 minutes. 69. 38,741 seconds. 70. 2320 feet. 71 5841 square feet. 72. 31,728 cubic inches. 73. What will 20 old silver dollars weigh in ounces, pennyweights, and grains, each dollar weighing 412 grains? 74. How many miles is it through the earth from pole to pole, the distance being 41,707,308 feet? 75. Change 58,642 farthings English money to pounds, shillings, etc. 76. Change 9862 pence to pounds, shillings, etc. 291. To change a compound denominate number to a fraction of a higher denomination. Illustrative Examples. (1) Change 3 qt. 1 pt. 3 gi. to the fraction of a gallon. (2) Change 4 yd. 2 ft. 3 in. to the decimal of a rod. SOLUTIONS.-(1) 3 qt. 1 pt. gi. changed to gills equals 31 gills; 1 gallon equals 32 gills. 31 gills is of a gallon. Ans. gal. (2) 4 yd. 2 ft. 3 in. changed to inches equals 171 inches; 1 rod equals 198 inches. 171 in. is 17 rd. ; 171 equals 0.8636. Ans. 0.8636 rd. 292. From the preceding illustration may be derived the following Rule. 1. To change a compound number to a fraction of a higher denomination: Change the given compound number to its lowest denomination, and make it the numerator of a fraction; also change to the same denomination a unit of the required denomination and make it the denominator of the fraction. 2. To change a compound number to a decimal of a higher denomination: Proceed as above and then change the common fraction to a decimal. 77. 1 pk. 2 qt. is what part of a bushel? 78. 4 yd. 0 ft. 9 in. is what part of a rod? 79. 75 sq. rd. 903 sq. ft. is what part of an acre? 80. Change 6 oz. 5 pwt. to the decimal of a pound. 81. Change 87 rd. 10 ft. to the decimal of a mile. 82. Change 4s. 6d. to the decimal of a £. 83. Change 11s. 10d. to the decimal of a £. 84. Find the cost of 3 pk. 2 qt. of meal at $0.60 a bushel. 85. What will be the cost of 2 qt. 1 pt. of kerosene at $0.12 a gallon? 86. How much will a man earn in 5 days 7 hours at the rate of $15 per week of 6 days of 10 hours each? 87. At $60 an acre, what must be paid for 2 A. 113} sq. rd. of land? 88. At $200 a lb., what is the value of 10 oz. 10 pwt. 10 gr. of gold? 89. At $4.8665 per £, what is the value of £9 12s. 6d. English money? 90. Change 5 francs 50 centimes French money to U. S. money. (Art. 281.) 91. Change 10 marks 20 pfennigs German money to U. S. money. (Art. 281.) |