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57. Give the difference between of a guinea and 3 of a £; and between 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 of half a cwt. to make it up to of 3 quarters avoirdupois?

60. What is the value of 3 qrs. of oats, if 17 qrs. cost £3384?

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61. Find the difference of of 191, and of 11 of 34; and the sum of 2 and 5.

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62. Express the sum and difference of £ 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 ft. 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.?

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65. Multiply together 2+3, 91-74, and 66. A pound Troy of standard gold is coined into 462% sovereigns; what is the weight of a sovereign in grains?

67. What is the quotient of the sum divided by the difference of 20 and?

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68. Define a simple, compound, and complex fraction; give an example of each; and find what fraction bears the same proportion to 1 as bears to

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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; (b) 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?

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72. (a) If A be 23 of B, and B be 1 of C, and D be 73 of C. what fraction is A of D?

(b) If 2 of B= 1 of (A+ of A), then find two whole numbers which shall bear to each other the ratio of A and B.

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73. What is the value of (7+ of 4%)+(83-1 of 15) of a guinea?

74. Find the sum of money that shall be the same fraction of £69, 9s. 6d. that 2 qrs. 10 lbs. is of 36 cwt. I qr.

75. Add together 1, 2, and 3; multiply their sum by the product of these fractions: subtract from the result the difference of 2 and 12, and divide the remainder by the sum of 5 and 1 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.

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Reduction of Decimal to Vulgar Fractions, and vice versa.

1. Give the vulgar fraction equal to each of the following decimals-05, 0075, 13, 10937, 500'005.

2. Express as vulgar fractions in their lowest terms, 365, 125, 0035, 012, 11'94, and 8:06.

3. Reduce to decimals

of 2, 1, and; and reduce to vulgar fractions 875, 0703125, '016, and 809523.

4. Reduce to a decimal:-
:-

=

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× (1 of 1) +33 of 11 of 10000•

5. Reduce the three following quantities to their equivalent decimals:

2} 5 4 4%

(a) of 7 of 1}; (b) + ; (c) (1% −4) × (§ − 2).

6. Reduce to decimals, and add together:

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7. Reduce to vulgar fractions :

·2, ̈05, ·18, ·156, 19°305.

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10. Find the vulgar fraction equal to the sum of 483 and 2756, less by 0094.

11. Express as decimals, 17 31; and as vulgar fractions, 14715, 9:36, 10956, 7.285714.

Reduction to the Decimal of (Money).

1. (a) Reduce five-sevenths of 175. 34d. to the decimal of £2, 6s. 3d.

(b) Express £3, 17s. 10d., the value of 1 oz. of sterling gold, as the decimal of £5.

2. What decimal of £1, 175. 6d. is of 3s. 9d., and what decimal of half-a-guinea is of 4s. 8d. ?

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3. Add together, and reduce to the decimal of £1, 1673125 of 2s. 6d. and 3.785025 of 4d.

4. (a) Reduce

of a crown, of half-a-crown, and 117 of

3s. 4d., each to the decimal of £i.

(b) Reduce £6, 12s. 6d. 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.

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6. Reduce of 10s. + of 5s. 3d. + of half-a-crown to the decimal of £1, 5s. 9d.

7. What decimal of a £5 note is 3 of 7s. 6d. +625 of 10s. —*545 of 9s. 2d. ?

8. Reduce

9. Express the

of £1, 125., and

to the decimal of a guinea.

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sum total of 428571 of £15, † of of of 3d., as the decimal of £10.

10. Express each of the silver coins now in use in England by a decimal of 2 d.

11. What decimal of £100 is the quotient of £61, 4s. 71d. by 267?

12. Reduce of a shilling to the decimal of a guinea.

13. What decimal of £2 is each of the gold, silver, and copper coins in circulation in England?

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Reduction to the Decimal of (Weights and Measures).

1. Reduce 3 ac. 2 rds. 22 pls. to the decimal of 4 acres ; and of 4 ac. 3 rds. 16 pls.

2. What decimal is (a) 3 bush. 3 pks. of 1 qr.? (6) 19 qrs. I nl. of 11 yds.? (c) 59 yds. 1 ft. of 1 mile?

3. Reduce 9 of 1 pks. to the decimal of 33 qrs.; and of a year to the decimal of a day.

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4. Add together 5.5 of a cwt. and 3.125 qrs., and reduce this sum to the decimal of 10,000 tons.

5. What decimal of 1 lb. Troy is 64 grains?

6. Reduce 33 dwts. to the decimal and to the vulgar fraction of 24 lbs. Troy.

7. Express as the decimal of 1 lb. Troy each of the lower denominations of Troy weight.

8. What part of 10 ac. 2 rds. 3710 pls. is 1 ac. 3 rds. 3712 pls.? Give answer in vulgar fraction, and in decimals to

four places.

9. Reduce 2 wks. 61 dys. to the decimal of 4 dys. 3 hrs. 10. Reduce 3 fur. 10 pls. to the decimal of a mile; and 2 ft. 3 in. to the decimal of 3 yds. 2 ft.

11. Three Russian versts = 10,500 ft.; reduce a verst to the decimal of a mile.

21. If £187, 10s. pay for the education of 20 boys for 6 months, how long will £150 pay for 8 boys?

22. If 6 masons, each receiving 31s. 6d. a week (6 days), earn as much as 7 bricklayers in the same time, in how many days at this rate will the wages of 35 bricklayers amount to £141, 15s.?

23. If 12 be charged for conveying 21 tons 10 cwts. of iron for 63 miles, how far should 430 tons 5 cwts. be carried for £4?

24. 115 men undertake to make a road 2 miles long in 46 days, but when it is half done at that rate, 69 men go off to another job; how many days altogether were spent in making the road?

25. A 20 horse-power engine pumps 40 gallons of water from a pit 100 yards deep in 3 hours; what quantity of water would an engine of 35 horse-power pump from a depth of 235 feet in 141 days, working night and day?

26. If the carriage of 1 cwt. 3 qrs. 21 lbs. for 104 miles come to £1, 14s. 10d., what sum would be charged for conveying 2 tons for 23 miles?

27. I get 8 oz. of bread for 6d. when wheat is 15s. a bushel; what ought a bushel of wheat to cost when I get 12 oz. of bread for 4d.?

28. If 10 men or 15 boys can reap 20 acres of corn in 6 days, working 14 hours a day, how many boys must be employed to assist 3 men to reap 11 acres in 1 days of 8 hours a day?

29. If the carriage of 5 tons 5 cwt. 2 qrs. 1 lb. for 50 miles cost £27, 10s., what will be charged for conveying 254 cwt. 117 miles?

30. If 24 cakes can be made out of 3s. worth of oatmeal when its price is 18d. per peck, how many cakes can be made out of 10s. 31d. worth when oatmeal is at 13d. per peck?

31. If 7 men earn £9, 10s. 6d. in 10 days will 28 men earn £114, 6s. ?

days, in how many

32. If a family of 9 persons spend £120 in 8 months, how much will serve a family of 24 persons 16 months?

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