43. How many days in 391256 seconds? Ans. 4 days 12 hr. 40 min. 56 sec. 44. How many yards in 3912 English ells? Ans. 4890 yd. Ans. 49395 sixp. Ans. £1309, 1s. Ans. 148 lb. 10 oz. 6 dwt. 48. How many pounds in 26 tons 3 cwt. 1 qr. of soap? 49. How many yards in 78325 nails of cloth? Ans. 58604 lb. Ans. 4895 yd. 1 qr. 1 nl. 50. How many poles in 76 ac. 1 ro. 39 po. of land? Ans. 12239 po. 51. How many years, of 365 days each, would it take a body, moving at the rate of 60 miles an hour, to pass from the earth to the sun, the mean distance being 95 millions of miles? Ans. 180 yr. 272 d. 5 hr. 20 min. 52. The total revenue of the French government in 1858 was 1773919114 francs, estimating the franc at 93d.; find the revenue in pounds sterling, Ans. £72065464, Os. 1 d. 53. The velocity of the earth in its orbit is 101173 feet per second; find its velocity in miles per second, Ans. 19 miles 1 fur. 64 yd. 1 ft. 54. A cubic foot of gold weighs 19259 ounces avoirdupois ; find its weight in hundredweights, &c., Ans. 10 cwt. 2 qr. 27 lb. 11 oz. 55. The length of a sidereal year is 365 days 6 hours 9 minutes and 12 seconds; find its length in seconds, Ans. 31558152 seconds. 56. The total quantity of coffee imported into the United Kingdom in the year 1857 was 58912619 lb.; find its weight in tons, Ans. 26300 tons 5 cwt. 2 qr. 3 Ib. 57. In the year 1857 there was paid to the king of Denmark £1125206 for abolition of the Sound dues. The value of gold imported from New South Wales the same year was £3, 15s. 10d. per ounce troy; how many pounds troy of gold would be required to pay the king of Denmark? Ans. 24729 lb. 987 oz. 58. A pound avoirdupois is 7000 troy grains; find the weight in tons of the gold in the answer to the last question, Ans. 9 tons 1 cwt. 2 qr. 21 lb. 1 oz. nearly. APPLICATION OF REDUCTION TO THE CALCULATION OF PRICES, WHEN THE VALUE OF ONE ARTICLE IS GIVEN. Rule.-Reduce the price to the lowest denomination it contains, then multiply the price by the number of articles, or the number of articles by the price; the product will be the answer in the same denomination to which the price of one was reduced, which may be changed to a higher denomination, by Rule II. Example 1.-What is the value of 345 feet of mahogany, at 1s. 7 d. per foot? Example 2.-What is the value of 28 yards of broad cloth, at £1, 38. 4d. per yard? 59. What is the value of 327 tons of guano at £7, 3s. 4d., £6, 7s. 112d., and £5, 19s. 7 d. per ton? Ans. £2343, 10s., £2092, 9s. 24d., £1955, 17s. 41d. 60. What cost 739 gallons of ale at 3s. 4 d., 2s. 11d., and 2s. 1 d. per gallon? Ans. £124, 14s. 11d., £107, 15s. 5d., £79, 5s. 94d. 61. What is the price of 29 oxen at £10, 17s., £8, 19s. 3d., and £9, 6s. 8d. each? . Ans. £314, 13s., £259, 18s. 3d., £270, 13s. 4d. 62. What is the price of 536 yards of linen at 2s. 7 d., 3s. 6d., and 4s. 94d. per yard? Ans. £70, 7s., £93, 16s., £128, 19s. 6d. 63. What will a man's wages amount to in 313 days at 1s. 10d., 2s. 3 d., and 4s. 9åd. per day? Ans. £28, 13s. 10d., £35, 17s. 3 d., £75, 6s. 32d. 64. What is the price of 3456 lb. of tea at 4s. 6d., 5s. 74d., and Ans. £777, 12s., £968, 8s., £1087, 4s. 65. What cost 659 cwt. of raisins at £4, £4, 11s. 5d., and £3, 19s. per cwt.? Ans. £2636, £3012, 3s. 7d., £2603, 1s. 6s. 3 d. per lb. ? COMPOUND ADDITION. RULE.-1. Write the numbers under one another, so that those of the same denomination may stand in the same column, and draw a line under them. 2. Add together the numbers in the lowest denomination, and find (by REDUCTION) how many of the next higher denomination are contained in the sum; mark any remainder below the column added, and carry the quotient to the next denomination. 3. Repeat this process until all the columns are added. The highest denomination is added as in Simple Addition. The last sum, with the several remainders, will be the answer required. THE METHODS OF PROOF are the same as in Simple Addition. The REASONS for the Rules of Compound Addition, Subtraction, Multiplication, and Division, are obviously the same as for the Rules of Simple Addition, &c. Example.-Add together £31, 17s. 2 d., £307, 6s. 91d., £29, 19s. 4 d., £78, 1s. 111⁄2d., £691, 13s. 11ąd, and £12, 18s. 9åd. £ s. d. 31 17 23 307 6 9 29 19 4 78 1 11 691 13 11 12 18 93 £1151 18 1 In this example, the numbers are arranged as in the margin. The lowest being farthings, the pupil begins at this column, and adds-Pupil. 3, 6, 8, 9, 11, 14; fours in 14? 3 times and 2; I put down 2 farthings, or a halfpenny, and carry the 3. Teacher. Why do you divide the sum by 4? Pupil. Because 4 farthings make a penny. I carry 3. 3, 12, 13, 14, 18, 27, 29, 39, 49; twelves in 49? 4 times and 1; I put down 1, and carry 4. 4, 12, 15, 16, 25, 31, 38; I put down 8, and carry 3. 3, 4, 5, 6, 7; twos in 7? 3 times and 1. Teacher. This is the short method of dividing by what number? Pupil. 20. Teacher. Why? &c. Pupil. 3, 5, 6, 14, 23, 30, 31; 1 and carry 3. 3, 4, 13, 20, 22, 25; 5 and carry 2. 2, 8, 11. Therefore the whole sum is £1151, 18s. 13d. Note. In adding the shillings, first add the column of units; put down the right-hand figure, and carry the remaining figure or figures to the tens; divide their sum by 2; if 1 remain, put it down, and carry the quotient to the pounds. 29. A collector of taxes drew in January, £757, 14s. 32d.; in February, £839, 14s. 112d.; in March, £269, 17s. 5d.; in April, £392, 12s. 11d.; in May, £6732, 7s. 54d.; in June, £735, 13s. 104d.; in July, £76, 19s. 32d.; in August, £325, 6s. 14d.; in September, £37, 18s. 74d.; in October, £269, 5s. 11d.; in November, £3752, 16s. 113d.; in December, £67, 13s. 101d. How much did he collect throughout the year? Ans. £14258, 1s. 9ąd. 17. £4760, 1s. 6d. Answers. 23. 437 tons 0 cwt. 1 qr. 24. 126 lb. 2 oz. 14 dr. 25. 201 lb. 3 oz. 14 dwt. 13 gr. 26. 470 ac. 2 ro. 38 po. 27. 3586 ac. 1 ro. 12 po. 28. 275 m. 6 fur. 18 yd. 1 ft. 1 in. |