4 of a minute? of a day? of 3 of a gill? 4. What part of 4 days is 2 Ans. 2560. Ans. g. Ans £0.0097. 9. Reduce 34.374 sec. to the decimal of a day. Ans. 0.000397 days. 10. Reduce 517.44 ft. to the decimal of a mile. Ans. 0.098 mi 239. To reduce a denominate fraction to integers of lowes denomination. 1. What is the value of of a £? OPERATION. £ 8. d. far. 0 0 ANALYSIS. of £1 is the same as of 7)30 £3=8s. 6d. 33 far. Rule. Consider the numerator of the fraction as so many units of the given denomination, and divide them by the denominator. Ans. 4 mo. 2 wk. 3 da. 5hr. 32 min. 18, sec. 8. What is the value of 3 of a circle? 37 9. What is the value of & of a ton? Ans. Ans. 17 cwt. 3 qr. 2 lb. 12 oz. 71⁄2 dr. 10. What is the value of 660 of a mile? Ans. Rule. Find the values of the given fractions by (239) and the sum of these values by (226). Ans. 3 R. 10 sq. rd. 8 sq. yd. 5 sq. ft. 1134 sq. in. 7. Add of a hogshead to of a gallon. Ans. 8. Add together of a bushel, of a peck, and 3 of a quart. Ans. Rule. Find the values of the given fractions by (239) and their difference by (227). EXAMPLES. 1 From of a day take of an hour. Ans. 9 hr. 30 min. 284 sec. 15 2. From of a bushel take 1 of a peck. 6 Ans. 2 T. 17 cwt. 1 qr. 25 lb. 6. A company agree to construct 14 mi. 5 fur. 18 rd. of road, but after constructing 3 mi. 1 fur. 20 rd. 2 ft. more than of it, they relinquished the job. How much remains to be constructed? Ans. 1 mi. 5 fur. 25 rd. 4 yd. 1 ft. 7. A merchant having of 14 hogsheads of molasses, sold of 21 gallons of it; how much remained unsold? Ans. MISCELLANEOUS QUESTIONS. Required the cost of 1. 15.75 lb. of butter, at 183 cts. a pound? Ans. $2.95+. 2. 137.95 T. of hay, at $12.125 a T.? Ans. $1672.643+. 3. of 15 yd. of cloth, at $4.25 a yd.? 3 4. of 2 bu. of berries, at 6 cls. a quart? 8 Ans. $27.32+. Ans. $43.16+. Ans. $43.855. 5. of 12 cords of wood, at $4.625 a cd.? 6. If 5 pounds of tea cost $6.913, how much will 1. pound cost? Ans. $1.22. 7. What will 4 cwt. 3 qr. 15 lb. of sugar cost, at $8.95 a cwt.? 8. What will 9 bu. 3 pk. 7 qt. 1 pt. of grass seed cost, at $5.375 a bushel? Ans. $53.66+. 9. What cost 4 hhd. 50 gal. 1.6 qt. of molasses, at $32.25 a hogshead? Ans. $154.80. 10. What cost 96 bu. 3 pk. 5 qt. of wheat at $1.75 a bu.? Ars. $169.59 nearly. 11. If it require 3 hr. 20 min. for a man to cut 1 cord of wood, how many days of 8 hours each will be required to cut 746 cords, 96 feet? Ans. 311 da. 1 hr. 10 min. 12. Four persons divide 125 pounds of sugar as follows: the first takes of of the whole; the second takes 4 of of the remainder; the third takes of 3 of what now remains; and the fourth takes what is left. How much did each receive? Ans. The 1st 12.5 lb., 2d 14.0625 lb., 3d 78.75 lb., and tl 4th 19.6875 lb. 13. A received of a certain quantity of flour, B, of it, and C the remainder. Now it is found that A has 76 lb. and 8 oz. more than B. How much did each receive? Ans. A received 2103 lb., B 1333 lb. and C 11283 lb. 14. A farmer owning 195 A. 3 R. 38 sq. rd. of land, divided of it equally among his four sons. How much did each son receive, and how much had the father remaining? Ans. 36 A. 2 R. 393 sq. rd. each, and 48 A. 3 R. 391⁄2 sq. rd. remaining. 15. If I buy 147 gal. 3 qt. of molasses, at 25 cents a gallon, and use 33 gal. of it, how must I sell the remainder per gallon, so as to receive as much as the whole cost? Ans. $0.3219, nearly. 16. A person gave of all his money for a horse, of the remainder for a colt, and of what then remained for a sheep. He then had $12.12 remaining. What was the cost of each article, and how much money had he at first? Ans. H. $48, C. $321, S. $4, and he had at first $97. 17. A certain sum of money is to be divided among 5 persons: the first is to have of it; the second, the third, the fourth, and the fifth the remainder. It now appears that the third has $19 more than the fourth. What was the sum to be divided, and how much did each receive? Ans. The 1st rec'd $190, 2d $1421⁄2, 3d $114, 4th $95, and the 5th $281. 18. How much butter, at 183 cents a pound, must be given for 12 gal. 3 qt. of molasses, at 37 cents a gallon? Ans. 19. From a piece of cloth containing 97 yards, 9 coats, each containing 3 yd. were taken; required the value of the remainder at $4.37 a yard? Ans. 20. A grocer lost from of a hogshead of molasses, of a gallon and of a quart. How much of the hogshead, expressed decimally, leaked out, and how much remained? Ans. 1.008 gal. leaked out, and 54.11 gal. remained. 21. What is the value of of a year of 365 days, and § of a week? Ans. 5 22. Bought 12 T. 12 cwt. 2 gr. 20 lb. of iron, and sold 8 T. 4 cut. 1 gr. 23 lb. of it; what is the value of of the remainder at 63 cents a pound. Ans. 13 25 9 23. Bought a quantity of grain for $258.40, and sold of it to one man, of it to another man, and used of it myself; what is the value of the remainder? 24. A gentleman gave remainder to his son, and Ans. 323 of his estate to his wife, & of the of what then remained to his daughter, and had remaining $630; required the value of the estate, and the amount each received? Ans. $30240 the estate, $10080 W. received, $15120 S., and $4410 D. 25. Bought 42 tons of hay for $12.50 per ton; for of which I paid sheep, at $1.25 each; and for the remainder I paid butter, at 23 cents a pound. Required the number of sheep, and the number of pounds of butter it took to pay the debt? |