18. If of a cwt. of sugar cost $5.40, what is the value of ; of a cwt. ? ILLUSTRATION. If f of a cwt. cost $5.40, will cost of $ 5.40, or $ 1.80; and 4, or a cwt., will cost 4 times $1.80, or $ 7.20. Now, if lcwt. cost $ 7.20, h of a cwt. will cost j of $7.20, or $ 0.80; and ; will cost 7 times $ 0.80, or $ 5.00, Ans. 19. If It of a pound of ipecacuanha cost $ 2.52, what is the value of of a pound? Ans. $ 1.76. 20. When $ 80 are paid for of an acre of land, what cost s of an acre ? Ans. $ 93.331. 21. If ic of a carding-mill are worth $ 631.89, what are a of it worth? Ans. $ 401.20. 22. If of a ship and cargo are valued at $ 141.52, what are of them worth? Ans. $ 30.50. 23. If the value of g of a farm containing 178747 acres. is $ 1728, what is the price of of the remainder? Ans. $ 2304. 24. E. Carter's garden is 17 4 rods long, and 11193 rods wide. He disposes of # of it for $82.80 ; what is the value of of the remainder ? Ans. $ 41.40. 25. When 26£ 123. 6d. are paid for f of a bale of cloth, what sum should be paid for ţ of the remainder ? Ans. 18£ 12s. 9d. 26. If 7cwt. of sugar cost $28.14, what will 98cwt. cost ? ILLUSTRATION. - If 7cwt. cost $28.14, 1cwt will cost 1 of $ 28.14, or $ 4.02. In 95cwt. there are 52cwt.; and if lcwt. cost $ 4.02, cwt. will cost of $ 4.02, or $ 0.67, and be will cost 59 times $ 0.67, or $ 39.53, Ans. 27. If three tons of hay cost $ 49, what will 74 tons cost ? Ans. $120.27 Pt 28. Gave $ 78.80 for 11 tons of coal; what should I give for 3 tons ? Ans. $ 24.6785 29. Paid 37£ 18s. 10d. for 3 bales of velvet ; what was the cost of 53 bales ? Ans. 67£ 19s. 614d. 30. Gave $ 40 for 5 yards of broadcloth ; what was the price of 194 yards ? Ans. $ 156.574. 31. Paid $360 for 20 barrels of beer; what must be given for 43 barrels ? Ans. $ 789. 32. If 7 bushels of rye cost $ 8.75, what cost 181 bushels ? Ans. $ 23.296. 33. Paid $ 19.80 for 3 yards of broadcloth ; what sum must be given for 114 yards ? Ans. $76.37+. 34. If 9fcwt. of sugar cost $39.53, what must be paid for 7cwt. ? ILLUSTRATION. — In 9fcwt. there are lcwt. If 52cwt. cost $39.53, cwt. will cost of $ 30.53, or $0.67; and f, or icwt., will cost 6 times $ 0.67, or $4.02; and 7cwt. will cost 7 times $ 4.02, or $ 28.14, Ans. 35. When $ 187 are paid for 3cwt. of sugar, how much may be purchased for $1? How much for $78? Ans. 12,8cwt. 36. If 3 tons of potash cost $ 276.18, what will be the value of 1 ton? Of 75 tons ? Ans. $ 6041.43 37. If 74 acres of land cost $ 875, what will one acre cost? What will 75 acres cost? Ans. $8912.0314 38. If 43 tons of coal cost $ 70, what will 1 ton cost? What will 86 tons cost? Ans. $ 1376. 39. For 27 acres of land there were paid $375 ; what cost 1 acre ? What cost 69 acres ? Ans. $ 932.4339 40. If 4 tons of hay cost $ 80.50, what costs 1 ton ? What cost 15 tons ? Ans. $ 262.50. 41. If 74cwt. of sugar cost $ 62.37, what will lcwt. cost ? What cost 19cwt. ? Ans. $ 160.93. 42. If 7 yards of cloth cost $ 13.95, what will be the value of 114 yards ? ILLUSTRATION. — In 78 yards there are o of a yard. If $t of a yard cost $ 13.95, 4 will cost i of $13.95, or $ 0.45; and 4, or 1 yard, will cost 4 times $ 0.45, or $ 1.80. In 114 yards there are 108 of a yard. If 1 yard cost $ 1.80, $ of a yard will cost of $ 1.80, or $ 0.20; and 108 will cost 103 times $0.20, or $ 20.60, Ans. 43. When $ 668.50 are paid for 17 11 acres, what would be the value of 894 acres ? Ans. $ 3457.30. 44. If $ 1738 are given for 194 tons of iron, what will be the cost of 374 tons ? Ans. $ 3288. 45. Paid $ 114 for 1128 feet of boards ; how many could I have purchased for $ 119 12? Ans. 11480 feet. 46. For 35 tons of potash I received 116cwt. of sugar ; required the quantity of sugar that may be received for 114 tons Ans. 376cwt. 47. For 114 tons of potash I received 876cwt. of sugar ; of potash. required the quantity of sugar that should be received for 33 tons. Ans. 116cwt. 48. When $8 are paid for 18 yards of broadcloth, how much must be given for 8 yards ? Ans. $ 49. 49. Gave $ 414 for 2017 acres of land ; what shall be given for 11% acres ? Ans. $ 236. MISCELLANEOUS QUESTIONS BY ANALYSIS. 1. Sold a small farm for $ 896.50; what was received for it of it? For 1 of it? For 11 of it? Ans. $ 815. 2. Gave $ 17 ( for 3 barrels of flour ; what cost 1 barrel ? What 37 barrels ? Ans. $ 213.0335. 3. Sold a house for $ 3687 ; what sum was received for } of it ? Ans. $ 3226.121. 4. Bought 1773 tons of hay for $187%; what is the cost of of a ton ? Ans. $ 7.61222 5. Bought a hogshead of molasses for $13%; what cost of it? What cost ?? What cost ??? Ans. $ 30.521. 6. When $ 37 are paid for 100 gallons of molasses, what cost of a gallon? Ans. $ 0.2174 7. When 12 cents are paid for ii of a gallon of molasses, what will 4875 gallons cost? Ans. $ 16.0115. 8. If f of a barrel of flour cost $34, what will 6 barrels cost ? Ans. $ 48111. 9. When $ 236 are paid for 114 acres, what will be paid for 2070 acres ? Ans. $ 414. 10. Paid in Liverpool 974£ for 3 bales of cloth; how many bales should be received for 10737£ ? Ans. 33 bales. 11. If 6} barrels of flour cost $4814d, what will of a barrel Ans. $ 3.284. 12. If 3 pounds of coffee cost 34 cents, what sum must be paid for 741 pounds ? Ans. $6.90 41 13. If 24 tons of hay cost $ 63, what will be the cost of 167 tons ? Ans. $ 38113. 14. If a piece of land 3 rods square cost $ 1711, what will be the cost of 4 square rods? Ans. $775. 15. Paid $314 for 2fcwt. of iron; required the sum to be paid for 689 ycwt. Ans. $ 76809. 16. For 6 cords of wood J. Holț paid $63; what sum must be paid for 18 cords? Ans. $ 170.10. 17. Gave $ 24314 for 96 barrels of tar; what quantity could, be purchased for $ 1000 ? Ans. 3941334 þarrels, cost? 18. Paid $7888.30 for 837& acres of wild land; what sum did I pay for each acre, and what would be the cost of 7 acres ? Ans. $ 660.80. 19. Gave 132£ 12s. for 72 tons of starch ; what cost 12} tons ? Ans. 224£ 53. 20. For 17 days' work I paid $ 25.44; what should be paid for 89 days' labor ? Ans. $ 128.64. 21. Sold 715 bushels of apples for $ 7.28; what should I receive for 1911 bushels ? Ans. $ 19.12. 22. Paid $ 4355.52 for 49% pieces of carpeting; what did 374 pieces cost ? Ans. $ 3294.72. 23. If of of the cost of the Capitol at Washington was $ 300,000, what was the whole cost ? Ans. $ 2,000,000. 24. Purchased 75 thousand of boards for $135.80; what must be paid for 191 thousand ? Ans. $ 359.45. 25. My wood-pile contains 6 cords and 76 cubic feet. If I dispose of of it, what is the value of the remainder at 45 cents per cubic foot ? Ans. $23.145 26. I have a field 30 rods square, and having sold 18 square rods to S. Brown, and 82 square rods to J. Smith, what part of the field remained unsold ? Ans. g. 27. Bought 7T. 12cwt. 3qr. 18lb. of iron, and having sold 3T. 18cwt. lqr. 20lb., what is the value of of the remainder at 53 cents per Ans. $ 242.591 28. Bought 37 tons of iron at $ 68.50 per ton, for of which I paid in coffee at $ 8.50 per cwt., and for the remainder I paid cash. Required the amount of cash paid, and also the value of the coffee. Ans. Cash, $ 633.621; Value of the coffee, $ 1900.874. 29. A man, having received a legacy of $ 7896, spent of it in speculations, and the remainder he put in the savings bank, where it continued 15 years. It was then found that the sum deposited had doubled. Required the sum in the bank. Ans. $ 3948. 30. Bought a piece of broadcloth for $88, and sold of it to J. Smith, and is of the remainder to 0. Lake; what is the value of the part unsold ? Ans. $ 37.491009 31. A gentleman gave of his estate to his wife, of the remainder to his oldest son, and of what then remained to his daughter, who received $ 750; required the whole estate. Ans. $ 12,000. 32. From an acre of land I sold two-house-lots, each 100 feet square ; what is the value of the remainder, at 8 cents per square foot ? Ans. $ 1884.80. DECIMAL FRACTIONS, 175. A Decimal Fraction is a fraction whose denominator is 10, or the product of several 10's. Decimal fractions are commonly expressed by writing the numerator only, with a point (.), called the decimal point, before it, care being taken to put a cipher in any decimal place not requiring a significant figure; thus, of a proper 99 100 By examining the foregoing fractions, it will be seen that, — .9 can occupy only one place while it remains in the form fraction ; .99, only two places ; and 99% .999, only three places; for, if their numerators are increased respectively by to =.1, tdo=.01, tooo =.001, each fraction becomes a unit or whole number. Hence, The first figure or place of any decimal on the right of the point is tenths, the second hundredths, the third thousandths, fc. 1000 176. The denominator of % .9 is 1 with one cipher annexed; the denominator of 99 .99 is 1 with two ciphers annexed; the denominator of 99.9 .999 is 1 with three ciphers annexed. Hence, The denominator of a decimal fraction is 1 with as many ciphers annexed as the numerator has places. 177. Decimal fractions originate from dividing the unit, first, into 10 equal parts, and then each of these parts into 10 other equal parts, and so on indefinitely. Thus, 1 10 = t' = .1; Ib • 10 = IDO .01 ; Tdo • 10 To'OU –.001. Hence, The unit in decimal fractions is divided into 10, 100, 1000, &c., equal parts. 175. What is a decimal fraction? How are decimal fractions commonly expressed? What is the first figure or place of any decimal ? The second? The third ? &c. Why? What must be done when a decimal place has no significant figure to åll it? — 176. What is the denominator of a decimal fraction ?- 177. How do decimal fractions originato ? |