1 Bale. NOTE. A sheet folded in 2 leaves forms a folio; in 4 leaves, a quarto; in 8 leaves, an octavo; in 12 leaves, a 12mo; in 18 leaves, an 18mo; and in 24 leaves, a 24mo. MISCELLANEOUS EXERCISES. 1. In $345.18 how many mills? 8. In 7852 scruples how many pounds? 9. In 83T. 11cwt. 3qr. 18lb. how many ounces? 10. How many tons in 2675088 ounces? 11. How many nails in 97yd. 3qr. 3na.? 12. In 1567 nails how many yards? 13. In 57 ells English how many yards? 14. How many ells English in 71yd. 1qr.? 15. How many inches in 15m. 7fur. 18rd. 10ft. 6in.? 17. In 95,000,000 of miles how many inches? 100. What gives name to the size or form of books? 24. In 100362240000 square inches how many square miles? 25. How many cubic inches in 15 tons of timber? 26. In 1036800 cubic inches how many tons? 27. How many gills of wine in 5hhd. 17gal. 3qt.? 28. In 10648 gills how many hogsheads of wine? 29. How many quarts of beer in 29hhd. 30gal. 3qt.? 30. In 6387 quarts of beer how many hogsheads? 31. How many pints in 15ch. 16bu. 3pk. of wheat? 32. In 35632 pints of wheat how many chaldrons ? 33. How many seconds of time in 365 days 6 hours? 34. In 31557600 seconds how many days? 35. How many hours in 1842 years (of 365da. 6h. each)? 36. In 16146972 hours how many years? 37. How many seconds in 8S. 14° 18′ 17′′? 38. In 915497" how many signs? 39. What will be the cost of 13 gross of steel pens, at 2 cents per pen? Ans. $48. Ans. $46.80. 40. Bought 12 reams of paper at 20 cents per quire; how much did it cost? 41. I wish to put 2 hogsheads of wine into bottles that will contain 3 quarts each; how many bottles are required? Ans. 168 bottles. 42. When $1480 are paid for 25 acres of land, what costs 1 acre? What costs 1 rood? What cost 37A. 2R. 18p.? Ans. $2226.66. 43. John Webster bought 5cwt. 3qr. 18lb. of sugar at 9 cents per lb., for which he paid 25 barrels of apples at $1.75 per barrel; how much remains due? Ans. $9.62. 44. Bought a silver tankard weighing 2lb. 7oz. for $ 46.50; what did it cost per oz. ? How much per lb.? Ans. $18. 18lb. of leather at 12 cents per lb., and what did I lose? Ans. $183.54. 45. Bought 3T. 1cwt. sold it at 9 cents per lb.; 46. Phineas Bailey has agreed to grade a certain railroad at $5.75 per rod; what will he receive for grading the road, its length being 37m. 7fur. 29rd.? Ans. $69856.75. 47. If it cost $17.29 a rod to grade a certain piece of railroad, what will be the expense of grading 15m. 6fur. 37rd.? Ans. $87,781.33. 48. What is the value of a house-lot, containing 40 square rods and 200 square feet, at $ 1.50 per square foot? Ans. $16635. 49. How many yards of carpeting, one yard in width, will be required to carpet a room 18ft. long and 15ft. wide? Ans. 30 yards. 50. A certain machine will cut 120 shingle-nails in a minute, how many will it cut in 47 days 7 hours, admitting the machine to be in operation 10 hours per day? Ans. 3434400 nails. 51. In a field 80 rods long and 50 rods wide, how many square rods? How many acres? Ans. 25 acres. 52. How long will it take to count 18 millions, counting at the rate of 90 a minute? Ans. 138da. 21h. 20m. 53. A merchant purchased 9 bales of cloth, each containing 15 pieces, each piece 23 yards, at 8 cents per yard; what was the amount paid? Ans. $248.40. 54. Suppose a certain township is 6 miles long and 4 miles wide, how many lots of land of 90 acres each does it contain? Ans. 192 lots. 55. The pendulum of a certain clock vibrates 47 times in 1 minute; how many times will it vibrate in 196 days 49m.? Ans. 13267583 times. 56. How many shingles will it take to cover a roof, each of whose equal sides is 36 feet long, with rafters 16 feet in length, supposing 1 shingle to cover 27 square inches? Ans. 6144 shingles. 57. How many times will the large wheels of an engine turn round in going from Boston to Portland, a distance of 110 miles, supposing the wheels to be 12 feet and 6 inches in circumference? Ans. 46464 times. 58. In a certain house there are 25 rooms, in each room 7 bureaus, in each bureau 5 drawers, in each drawer 12 boxes, in each box 15 purses, in each purse 178 sovereigns, each sovereign valued at $4.84; what is the amount of the money? 59. In 18rd. 5yd. 2ft. 11in. how many 60. In 3779 inches how many rods? Ans. $135689400. inches? Ans. 3779 inches. Ans. 18rd. 5yd. 2ft. 11in. 61. Sold 5T. 17cwt. 3qr. 18lb. of potash for 3 cents per pound; what was the amount? Ans. $353.79. 62. A gentleman purchased a house-lot that was 25 rods long and 16 rods wide for $100,000, and sold the same for $1.25 per square foot; what did he gain by his purchase? Ans. $36,125. ADDITION. 101. Addition of Compound Numbers is the process of finding the amount of two or more denominate numbers of the same kind, when one or more of them is compound. ENGLISH MONEY. Ex. 1. Paid a London tailor 7£ 13s. 6d. 2far. for a coat; 2£ 17s. 9d. 1far. for a vest; 3£ 8s. 3d. 3far. for pantaloons; 9£ 11s. 8d. 3far. for a surtout; what was the amount of the bill? Ans. 23£ 11s. 4d. 1far. OPERATION. d. far. £ 8. 3 8 3 9 11 8 3 Having written units of the same denomination in the same column, we find the sum of the farthings to be 9 farthings, equal to 2d. and 1far. We write the 1far. under the column of farthings, and carry the 2d. to the column of pence; the sum of which is 28d., equal to 2s. 4d. We write the 4d. under the column of pence, and carry the 2s. to the column of shillings; the sum of which is 51s., equal to 2£ 11s. We write the 11s. under the column of shillings, and carry the 2£ to the column of pounds; and have for the whole amount, 23£ 11s. 4d. 1far. Ans. 23 11 4 1 The same result can be arrived at by reducing the numbers as they are added in their respective columns. Thus, we can, beginning with farthings, add in this way: 3far. and 3far. are 6far., equal to 1d. 2far., and 1far. are 1d. 3far., and 2far. are 1d. 5far., equal 2d. 1far. Writing the 1far. under the column of farthings, carry the 2d. to the column of pence; add 2d. (carried) and 8d. are 10d., and 3d. are 13d., equal to 1s. 1d., and 9d. are 1s. 10d., and 6d. are 1s. 16d., equal to 2s. 4d. Writing the 4d. under the column of pence, carry the 2s. to the column of shillings; add 2s. (carried) and 11s. are 13s., and 8s. are 21s., equal to 1£ 1s., and 17s. are 1 18s., and 13s. are 1£ 31s., equal to 2 11s. Writing 11s. under the column of shillings, carry the 2£ to the column of pounds, and so find the whole amount to be as before. Thus the adding of compound numbers is like that of simple numbers, except in carrying according to a varying scale (Art. 82, Note) A like difference holds in subtracting, multiplying, and dividing of compound numbers. 101. What is addition of compound numbers? How do you arrange compound numbers for addition? Why? What is the difference between addition of compound and addition of simple numbers? RULE. Write all the given numbers so that units of the same denomi nation may stand in the same column. Add as in addition of simple numbers; and carry, from column to column, one for as many units as it takes of the denomination added to make a unit of the denomination next higher. The proof is the same as in addition of simple |