7. What part of 30 days are 8 days 17h. 20m. ? Ans. 1. 8. From a piece of cloth containing 13yd. 0qr. 2na. there were taken 5yd. 2qr. 2na. What part of the whole piece was taken? Ans.. 9. What part of 3 yards square are 3 square yards? Ans.. ADDITION OF FRACTIONS OF COMPOUND NUMBERS. 9 X 20 = Ans. 17s. 11d. 04far. We find the value of each fraction separately, and add the two values together, according to the rule for adding compound numbers. (Art. 101.) 9£. +180£.=188£. 17s. 11d. 0 far. = We first reduce the fraction of a shilling to the of a fraction pound, then add the two fractions together and find the value of their sum. (Art. 171.) EXAMPLES FOR PRACTICE. 2. Add of a pound to of a shilling. Ans. 7s. 11d. 329far. 3. Add together 10 of a ton, 7 of a ton, and 4 of a cwt. 4. Add together 5. Add together and of a yard. 6. Add together rod. Ans. 1T. 14cwt. 1qr. 5. of a yard, § of a yard, of a quarter. of an acre, of a rood, and of a square 7. Sold 4 house-lots; the first of an acre, the second of an acre, the third of an acre, and the fourth of an acre; what was the quantity of land in the four lots? QUESTIONS. Art. 173. What is the first method of adding fractions of compound numbers? What is the second? SUBTRACTION OF FRACTIONS OF COMPOUND NUMBERS. ART. 174. To subtract fractional parts of compound numbers. Ex. 1. From of a pound take of a pound. SECOND OPERATION. G£.—47£.=3&£.= 9s. 10d. 19far. Ans. 9s. 10d. 159far. We find the value of each fraction separately, and subtract one from the other, according to the rule for subtracting compound numbers. (Art 102.) We first subtract the less fraction from the greater, and then find the value of their difference. (Art. 171.) EXAMPLES FOR PRACTICE. 5. From a hogshead of molasses of it leaked out; quantity remained for sale? Ans. 3R. 16p. 154ft. of the remainder I kept for my family; what 6. The distance from Boston to Worcester is about 41 miles. A sets out from Worcester, and travels of this distance towards Boston; B then starts from Boston to meet A, and, hav-` ing travelled of the remaining distance, it is required to find the distance between A and B. Ans. 12m. 6fur. 9rd. 5ft. 9ĝin. 7. A agrees to labor for B 365 days; but he was absent on account of sickness part of the time; he was also obliged to be employed in his own business of the remaining time; required the time lost. Ans. 137da. 11h. 13m. 149 sec. 8. From 11 acres, 33 poles, 101 feet of land, I sold to A, of the remainder to B, and four house-lots, each 144 feet square, to C; what is the value of the remainder, at 83 cents per square foot? Ans. $3937.89. QUESTIONS. -Art. 174. What is the first method of subtracting fractions of compound numbers? The second? QUESTIONS TO BE PERFORMED BY ANALYSIS. 1. If one yard of cloth cost $4.40, what will of a yard cost? ILLUSTRATION. If 1 yard cost $4.40, of a yard will cost of $4.40, equal to $0.88; and will cost 4 times $0.88, equal to $3.52, Ans. 2. If a barrel of flour cost $7.80, what will of a barrel cost? 3. If a load of hay cost $17.84, what will Ans. $2.34. of a load cost? Ans. $15.61. 4. If $786.63 are paid for a cargo of wheat, what is the cost of 11 of the cargo ? 5. What is of $87.50? 6. What is 2 of 17£. 18s. 9d.? 7. What is 4 of 3T. 16cwt. 3qr. 23lb.? Ans. $665.61. Ans. $80.203. Ans. 13£. 9s. 03d. Ans. 2T. 3cwt. 3qr. 23 lb. 8. What is of 27A. 3R. 33p.? 9. If $3.52 are paid for of a yard of cloth, what is the price of 1 yard? ILLUSTRATION. Ans. $4.40. If of a yard cost $3.52, will cost of $3.52, equal to $0.88; and ğ, or a whole yard, will cost 5 times $0.88, equal to $4.40, Ans. 10. If of a barrel of flour cost $2.34, what will be the cost of a whole barrel? Ans. $7.80. 11. When $15.57 are paid for of a ton of hay, what will 1 ton cost? 12. When Ans. $17.80. of a cargo of flour cost $665.50, what sum will Ans. $786.50. pay for the whole cargo? 13. If $73.60g are paid for 11 of a ton of potash, what sum must be paid for a ton? Ans. $80.30. 14. Bought of a bale of broadcloth for 13£. 9s. 0ąd.; what -would have been the cost of the whole bale? Ans. 17£. 18s. 9d. 15. If of an acre produce 18cwt. Oqr. 12lb. of hay, what quantity will a whole acre produce? Ans. 77cwt. 0qr. 1lb. 16. Bought of a lot of land containing 12A. 1R. 30p.; what were the contents of the whole lot? Ans. 27A. 3R. 394p. 17. If of a ton of potash cost $80.20g, what is the value of a ton? Ans. $87.50. SECT. XVIII.] QUESTIONS TO BE PERFORMED BY ANALYSIS. 177 18. If of a cwt. of sugar cost $5.40, what is the value of of a cwt.? ILLUSTRATION. If of a cwt. cost $5.40, will cost of $5.40, equal to $1.80; and, or a cwt., will cost 4 times $1.80, equal to $7.20. Now, if lewt. cost $7.20, of $7.20, equal to $0.80; and will cost 7 to $5.60, Ans. of a cwt. will cost times $0.80, equal $2.52, what is the Ans. $1.76. 19. If of a pound of ipecacuanha cost value of of a pound? 20. When $80 are paid for 2 of an acre of land, what cost of an acre? Ans. $93.331. 21. If of a carding-mill are worth $631.89, what are of it worth? 6 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 of a farm containing 178 acres is $1728, what is the price of of the remainder? Ans. $2304. 24. E. Carter's garden is 174 rods long, and 11 rods wide. He disposes of of it for $82.80; what is the value of of the remainder? Ans. $41.40. 25. When 26£. 12s. 6d. are paid for § of a bale of cloth, what sum should be paid for 3 of the remainder? Ans. 18£. 12s. 9d. 26. If 7ewt. of sugar cost $28.14, what will 9gcwt. cost? ILLUSTRATION. If 7cwt. cost $28.14, lcwt. will cost of $28.14, equal to $4.02. In 9gcwt. there are 52cwt.; and if lcwt. cost $4.02, cwt. will cost of $4.02, equal to $0.67, and 52 will cost 59 times $0.67, equal to $39.53, Ans. 27. If three tons of hay cost $49, what will 74 tons cost? Ans. $120.27. 28. Gave $78.80 for 11 tons of coal; what should I give for 3 tons? Ans. $24.677. 29. Paid 37£. 18s. 10d. for 3 bales of velvet; what was the cost of 5 bales? Ans. 67£. 19s. 611d. 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 187 bushels? Ans. $23.29. 33. Paid $19.80 for 3 yards of broadcloth; what sum must be given for 11 yards? Ans. $76.37. 34. If 9gcwt. of sugar cost $39.53, what must be paid for 7cwt.? ILLUSTRATION. — In 9gcwt. there are 52cwt. If 52cwt. cost $39.53, cwt. will cost of $39.53, equal to $0.67; and g, or lewt., will cost 6 times $0.67, equal to $4.02; and 7cwt. will cost 7 times $4.02, equal to $28.14, Ans. 35. When $187 are paid for 3cwt. of sugar, how much may be purchased for $1? How much for $78? Ans. 1260 cwt. 36. If 33 tons of potash cost $276.18, what will be the value of 1 ton? Of 75 tons? Ans. $6041.433. Ans. $1376. 37. If 74 acres of land cost $875, what will one acre cost? What will 75 acres cost? Ans. $8912.0319. 38. If 4 tons of coal cost $70, what will 1 ton cost? What will 86 tons cost? 39. For 27 acres of land there were paid $375; what cost 1 acre? What cost 69 acres? Ans $932.432. 40. If 4 tons of hay cost $80.50, what costs 1 ton? What cost 15 tons? Ans. $262.50. 41. If 7cwt. of sugar cost $62.37, what will lewt. 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 73 yards there are 31 of a yard. If 31 of a yard cost $13.95, will cost of $13.95, equal to $0.45; and, or 1 yard, will cost 4 times $0.45, equal to $1.80. In 11 yards there are 103 of a yard. If 1 yard cost $1.80, of ₫ a yard will cost of $1.80, equal to $0.20, and 183 will cost 103 times $0.20, equal to $20.60, Ans. 43. When $668.50 are paid for 17 the value of 89 acres? acres, what would be Ans. $3457.30. iron, what will be the 44. If $1738 are given for 193 tons of cost of 37 tons? 45. Paid $112 for 1128 feet of boards; have purchased for $119,7? 46. For 3 tons of potash I received quired the quantity of sugar that may be of potash. Ans. $3288. how many could I Ans. 11480 feet. 116cwt. of sugar; rereceived for 11 tons Ans. 376cwt. 47. For 11 tons of potash I received 376cwt. of sugar' |