oats at 25. 4d. His landlord gives him a receipt in full for £4, 1os. ; how much does the landlord forego? 29. I spent of my money yesterday, and of the remainder to-day, thereby leaving half-a-guinea in hand; how much money had I at first, and what fraction of it is left ? 30. I bought a watch and chain for 20 guineas; the watch cost me 31 guineas more than the chain. Find the price of each in £ s. d. 31. If the wages of 13 men for 74 days amount to £13, 75. old., how many men ought to work 4 weeks for £173, 8s.? 32. Multiply 155 shillings by 109!; and divide £61, 45. 7.d. by 267 1 33. Find the difference between 419 and 3:11, and multiply it by the quotient of 3 + 25. 34. Divide 11 acres by 28%, and find the value of the quotient at the rate of 7s. 6d. per pole. 35. In a map drawn on the scale of you of that of nature, how many inches represent a mile? 36. A dollar weighs 54 of an oz. Troy, and an English crown piece is of a lb. Troy; express the weight of the former as the fraction of the latter. 37. If of a yard of silk cost 45. 11¢d., what is the cost of 3 of of 4 yards of it? 38. Divide 7s. 1 £d. by liz, and subtract from the quotient 88 of 7 half-crowns. 39. What fraction should be multiplied by 3 of 3} to produce 3, and what number should be divided by the same fraction to produce $? 40. A farmer went to market with £2% in his pocket. He received for wheat sold £173, for poultry 183s., for eggs 3 s. ; how much did he bring home? 41. A merchant owns of a ship worth £3poo, and its cargo worth £27,000. He purchases another person's share, which is of of it; what part of it has he now, and what is its value? 42. A yard measure worn io of an inch short is used to find the length of a ropewalk, and gives it as 175 yards; what is the real length of the ropewalk ? 43. If, of is of a ship and her cargo is worth £7800, what loss will be experienced by the owner of } share of the ship and cargo if she goes to the bottom? 44. A bricklayer has just built 19 of a wall in 4 days of 11 hours; how much longer will he take to finish it? 45. Find the value of 4 of 4s. 8d. + 3} of £2, 6s. + } of a guinea - i of £51. 46. Multiply 7-3} and divide the product by 6+13 21-9 12! +21 47. A man and a boy working together for 9 hours a day can do a job in 1 days; the man by himself would be 17 days about it: how long would it take the boy alone to do it? 48. If 2ui oz. of tea cost 111s., what part of a pound of tea may be had for 2js.? 49. If, of a yard of silk cost 41 s., how much of it should there be in a gown which, with 233s. for making, costs £10, 195. 2 d.? 50. Find the value of (910 +76 +1333) £, divided by 27. 51. If, after selling of an estate, I sell of of the remainder for off of £2005, what is the value of the estate? 52. A clock, 4 min. 8, sec. too fast at 9.30 A.M. on Tuesday, loses 2 min. 45 sec. daily; what time will it show at a quarter past 5 P... on the following Friday? 53. If the value of of an estate be £541, 135. od., how much should I get for of į of what was left of the whole estate, after disposing of of it to another purchaser? 54. If I earn £7, os. 1}d. per week, and put by } of my gains, in how many weeks shall I have saved £5, 16s. 91d. ? 55. Find the price of 11198 tons of sugar, at the rate of 7 d. for 1 lb. 8 oz. 56. What must be added to 14.7 to make up 333, and what must be subtracted from 288103 to reduce it to 132191? 57. Give the difference between of a guinea and l of a £; and between g of a mile and of a furlong. 58. If 81 cwts. cost £1383, find the cost of 7% lbs. 59. What weight must be added to of iof half a civt. to make it up to so of 38 quarters avoirdupois ? 60. What is the value of 3 qrs. of oats, if 175 grs. cost £337,? 61. Find the difference of 18 of 19), and no of 1 of 3}; and the sum of 21 and 523. 62. Express the sum and difference of his and of a crown as fractions of half-a-sovereign ; and find how many times the second is contained in the first. 63. Multiply 2 fur, 8 pls. 2 st. 1 in. by 27, and prove the product by division. 64. A bankrupt is able to pay only of of his debts. How much will be lost by each of two creditors, one of whom is owed £1190, and the other £3867, 103. ? 65. Multiply together 2} +38, 94-71, and -'-*. 66. A pound Troy of standard gold is coined into 4670 sovereigns; what is the weight of a sovereign in grains ? 67. What is the quotient of the sum divided by the difference of 30% and ? 68. Define a simple, compound, and complex fraction; give an example of each; and find what fraction bears the same proportion to it as 10 bears to g. 69. Find the sum and difference of of £5, and of 5 guineas. 70. In a boy's copy-book there are 16 pages, and 12 lines in a page. What fraction of the book has he written, (a) half through the second page; (6) within 4 lines of the last page but one? 71. One-fourth of an estate belongs to A, ; of it to B, and the remainder to C, which is worth £2500 more than A's share; what is the value of the whole ? 72. (a) If A be 23 of B, and B be ig of C, and D be 73 of C, what fraction is A of D? (1) If as of Bri} of (A + # of A), then find two whole numbers which shall bear to each other the ratio of A and B. 73. What is the value of (7}+of 4) =(81-1 of 154) of a guinea? 74. Find the sum of money that shall be the same fraction of £69, gs. 6d. that 2 qrs. 10 lbs. is of 36 cwt. I qr. 75. Add together 11, 23, and 31; multiply their sum by the product of these fractions : subtract from the result the cirference of 2} and 1.), and divide the remainder by the sum of 5) and it of 31. 76. There were 154 fewer wrecks on the British coasts in 1855 than in 1854; and this difference was 22, of the number in 1854: what was the number of wrecks in 1855? DECIMAL FRACTIONS. Reduction of Decimal to Vulgar Fractions, and vice versa. 1. Give the vulgar fraction equal to each of the following decimals ;-'05, '0075, 1'3, 10'937, 500'005. 2. Express as vulgar fractions in their lowest terms, 365, *125, 0035, 012, 11-94, and 8.06. 3. Reduce to decimals i of 2), 12., and 3333; and reduce to vulgar fractions •875, 0703125, 016, and 809523. 4. Reduce to a decimal: x )1 . 5. Reduce the three following quantities to their equivalent decimals : 41, 21 53.43 + 3 2 55 849 256 3 4 7 2 8. Reduce the following to vulgar fractions : 3'07, 1-283, 01236. And the following to decimals : , ex 9. Reduce to a decimal. 39 191 16 10. Find the vulgar fraction equal to the sum of .483 and -2756, less by '0094. 11. Express as decimals :3, 1711, 317; and as vulgar fractions, '147i5, 9-36, '10956, 7.285714. Reduction to the Decimal of (Money). 1. (a) Reduce five-sevenths of 175. 3 d. to the decimal of £2, 6s. 3d. (6) Express £3, 175. 10$d., the value of 1 oz. of sterling gold, as the decimal of £5. 2. What decimal of £1, 175. 6d. is & of 35. od., and what decimal of half-a-guinea is 1 of 45. 8d. ? 3. Add together, and reduce to the decimal of £1, 16.73125 of 2s. 6d. and 3785025 of 4d. 4. (a) Reduce of a crown, of half-a-crown, and of 35. 4d., each to the decimal of £i. (6) Reduce £6, 125. 6 d. to the decimal of one and a half guineas. 5. Reduce the sum of £125, £ 26, £ 3625, and £83, to the decimal of £6'35. 6. Reduce it of 1os. +of 55. 3d. +1of half-a-crown to the decimal of £1, 5s. 9d. 7. What decimal of a £5 note is of 75. 6d. +°625 of 1os. -'545 of gs. 2d. ? 8. Reduce £s to the decimal of a guinea. 9. Express the sum total of 428571 of £15, of of 3 of £1, 12s., and 1 of 3d., as the decimal of £10. |