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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
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?
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 :
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.