Q. What part of a dollar is 50 cents? A.. Q. Why? Q. What part of a dollar is 25 cents? A. Because 2 times 50 c. are 100 c. = = $1. $1. A.. Q. Why? A. Because 4 times 25 c. are 100 c. = A. Aliquot Parts. Q. When, then, one number is contained in another exactly 2, 3, 4, &c. times, what is it called? A. An Aliquot Part. Q. What is the method of finding the cost of articles, by taking liquot parts, usually called? A. Practice. Repeat the Table of the aliquot parts of a dollar. Q. From the illustrations now given, what appears to be a concise rule for calculating the cost of articles, when the price is an aliquot part of a dollar? A. Divide the number of gallons, yards, &c. by the number of aliquot parts which it takes of the price to make a dollar. Q. What will the quotient be? A. The answer, in dollars. Q. For example, what would you divide by, when the price is 50 cents? 33 cents? 25 cents? 20 cents? 163 cents? 12 cents? 10 cents? 6 cents? 5 cents? Exercises for the Slate. 1. What will 360010 yards of cloth cost, at 12 cents a yard Q. How do you get the di OPERATION. 8) 360010,00 $ 45001,25, Ans. visor, 8? A. 12 cents: = of a dollar. Q. How do you obtain the 25 cents in the answer? A. I annex 2 ciphers for cents, and continue dividing. 2. What cost 2640 bushels of rye, at 50 cents a bushel? A. $1320. 3. At 25 cents a bushel, what will 4680 bushels of potatoes cost?-1170. Will 3600 bushels cost?-900. Will 4200 bushels cost?-1050. A. $3120. 4. At 64 cents, or of a dollar, what will 6400 yards of tape cost?-400. Will 32000 yards?-2000. Will 128000 yards?8000. A. $10400. 5. What will 2700 yards of ribbon cost, at 12 cents a yard?-33750. Will 5400 yards?-675. Will 1080 yards ?-135. A. $1147,50. 6. What will 42124 oranges cost, at 5 cents, or of a dollar, apiece? A. $2106,20. 7. What will be the cost of 1200 yards of cloth, at 50 cents a yard?-600. At 33 cents a yard?-400. At 25 cents a yard?300. At 20 cents a yard ?-240. At 12 cents a yard?-150 At 64 cents a yard ?-75. A. $1765. 8. At 163 cents a pint, what will 2700 pints of brandy cost?-450. At 10 cents a pint, what will 5400 pints cost?-540 A. $990. 9. What will 36002 bushels of salt cost, at $1,12), or 11 of a dollar, a bushel? At $2,25 a bushel ? OPERATIONS. 8)$36002-cost at $1 a bushel. 4) 36002 2 4500,25 cost at $,12, a bu. $40502,25 Ans. 72004 cost at $2. 9000,50 cost at 25c. Ans. $81004,50=cost at $24. 10. What will 3700 acres of land cost, at $12,25 ($12) an acre?-45325. What will 3700 acres, at $15,50 ($15) an acre?57350. A. $1026,75. 11. What will 27000 yards of broadcloth cost, at $3,50 ($34) a yard?-94500. At $2,33 ($21) a yard ?-63000. "At $1,12 ($1}) a yard?-30375. At $4,064 ($46) a yard ?-10968750 At $1,05 ($12%) a yard?-28350. A. 325912,50+. Questions, involving the Principles of the foregoing Rules. 1. A man bought a farm for thirty-six hundred dollars, and stock for the same to the amount of seven hundred and twenty dollars; what did both cost? and how much did one cost more than the other? A. Both, $4320; the farm, $2880 the most. 2. What is the amount of the following numbers, viz., ten, thirty, one million, twenty-six thousand, one hundred and one? A. 1026141. 3. If the minuend be 26002, and the subtrahend 101 what is the remainder ?-25901. If the subtrahend be 601 and the remainder 5025, what is the minuend?-5626. A. 31527. 4. If the multiplicand be 4200, and the multiplier 48, what is the product?-201600. If the product be 201600, and the multiplicand 4200, what is the multiplier ?-48. A. 201648. 5. If the divisor be 25, and the dividend 5025, what is the quotient?-201. If the quotient be 201, and the divisor 25, what is the dividend?-5025. If the quotient be 201, and the dividend 5025, what is the divisor?-25. A. 5251. 6. If the sum of two numbers be 1800, and the greater 1000, what is the less?-800. If the less be 120, and the sum 1320, what is the greater?-1200. A. 2000. 7. 270034272+3+1=Ans. 2700418. 8. 367895437 — 72591: = Ans. 367822846. 9. 25432 × 67345 Ans. 1712718040. 10. 360042 ÷ 8542 = • Ans. 42. 11. 270000001111. = = Ans. 9000000. 30000 12. Bought 18 barrels of potatoes, each containing 3 bushels, at 25 cents a bushel; what did the whole cost? A. $13,50. 13. A farmer sold 30 bushels of rye, at 87 cents a bushel; 30 bushels of corn, at 53 cents a bushel; 8 bushels of white beans, at $1,25 a bushel; two yoke of oxen, at $62 a yoke; 10 calves, at $4 apiece; and 15 barrels of cider, at $2,371⁄2 a barrel; what was the amount of the whole? A. $251,625. 14. A merchant, failing trade, has on hand goods to the amount of $4800, and his borrowed money is $2400; the remainder, after paying his borrowed money, is to be equally divided among 121 creditors; how much will each receive? A. $19121. 15. A grocer bought 4 loads of wood, at $2,25 a load-9; 8 bushels of rye, at $,50 a bushel-4; 30 pounds of butter, at 12 cents a pound-375; 340 pounds of cheese, at 64 cents a pound-2125; for which he paid 5 barrels of flour, at $6,25 a barrel-3125; 35 pounds of sugar, at 83 cents a pound-2975; 3 gallons of molasses, at 25 cents a gallon-75; 15 bushels of salt, at $1,12 a bushel-16875; what is the balance between the articles bought and sold? A. $13,85. 16. What will be the price of 4 bales of goods, each bale containing 60 pieces, and each piece 49 yards, at 37 cents a yard? A. $4410. 17. How many oranges, at 2 cents apiece, can be bought for 4 cents? For $2, or 200 cents? A. 102. For $8600? For $10000? A. 930000. 18. How many yards of cloth, at $2 a yard, may be bought for 4 barrels of cider, at $3 a barrel? For 8 barrels? A. 18. For 28 barrels? For 50 barrels? A. 117. 19. How many gallons of molasses, at 23 cents a gallon, ay be had for 60 bushels of oats, at 46 cents a bushel? At 69 cents a bushel? 9. 300 gallons. June 5. To 8 barrels Cider, at $2,12 a barrel, "8. To 6 bushels Corn, " ,58 a bushel, July 16, 1828. Received payment, Rufus Paywell. In the Key, such examples as the two following have the several prices carried out, which renders the inspection of any erroneous process ex ceedingly easy. 1. At 2 cents a gill, what will 1 pint of molasses cost? What will 2 pints? 4 pints? 5 pints? 6 pints? 8 pints? 10 pints? 12 pints? 20 pints? 50 pints? 100 pints? 2. At 24 cts. a gallon, what will 1 qt. of ale cost? What will 2 qts.? a gallon? How much will 48 cents buy? Will 60 cts.? Will 72 cts.? Will 120 cts.? Will 150 cts.? Will 180 cts.? 3. When rum is a dollar a gallon, what is a barrel worth? *Hogsheads containing liquors, molasses, &c. are of various capacities, generally exceeding 100 gallons |