34. How does the product of any number of proper fractions compare with any one of its factors ? How of improper fractions ? 35. How does the quotient compare with the dividend, when the divisor is a proper fraction ? How when the divisor is an improper fraction ? 36. If } of a yard of cloth cost 63 cents, what will a yard cost ? Ans. 172 cts. 37. If of an acre of land cost $75, what will an acre cost? Ans. $120. 38. If of a farm is worth $4200, what is worth? Ans. $4000. 39. If f of an acre is worth $40, what is it worth? Ans. $35. 40. If of a yard cost $37, what will of a yard cost ? Ans. $41. 41. If it of a farm cost $8769, what will of it cost? Ans. $29230. 42. What is the rate per hour of a boat that goes 312 miles in 33} hours ? Ans. 9.48 miles. 43. In a garrison 480 men have provisions for 9 months; how many men must leave at the end of six months that the remaining provisions may last six months longer ? Ans. 240 men. 44. Divide 369 into three parts that shall be to each other as 2, 3, and 4. Ans. 82, 123 and 164. 45. Divide 1728 into four parts in the ratio of 2, 3, 4, and 9. Ans. 192, 288, 384, 864. -46. One-third is what per cent ? --47. One-ninth is what per cent ? 48. Two-ninths is what per cent? 49. Forty is how many per cent of 200 ? a 12 131. 50. Fifty is how many per cent of 400 ? 51. A note for $5000 dated April 1st, 1872, with interest at 6%, is endorsed as follows: May 1st, 1873, received $1025, June 1st, 1874, $1020, July 1st, 1875, $1015. What was due August 1st, 1876 ? Ans. $2956.30. 52. What is the bank discount of a note for $600 payable in sixty days, interest at 6%, 3 days grace ? and what are the proceeds ? Ans. Discount $6.30, and Proceeds $593.70. 53. What is the bank discount of $600 for 3 months at 6% ? Ans. $9.30. 54. What is the amount of $600 for 3 years and 4 months at 6 per cent simple interest ? At compound interest? Ans. $720, and $728.90. 55. A person owning & of a mine, sells of his share for $5130; what was the whole mine worth at that rate ? Ans. $10944. 56. What is the cost of 15 T. 12 cwt. 2 qr. 10 lb. coal, at $6 per ton ? Ans. $93.78. 57. How is a common fraction changed into a decimal ? 58. How many terms form a ratio ? 59. How many ratios may be formed of any two num. bers either integral or fractional ? 60. What is the present value of the following note to be discounted in bank, interest at 6%? Ninety days after date, I promise to pay to the order Ι of John Smith, three hundred dollars, value received. Thos. BROWN. Ans. $295.35. 61. Extract the square root'of .00012544. Ans. .0112. 1 62. How many steps of three feet each would a man take in walking a mile ? 63. By what process would 25643.21 be changed to 256.4321 ? 64. Reduce .625 lb. to ounces. Ans. 10 oz. 65. Reduce 12 lb. 8 oz. 4 drams to the decimal of cwt. Ans. .125+. 66. Solve the following by proportion, and explain the solution : If 27 acres of land cost $1350, what will 36 acres cost at the same rate ? Ans. $1800. 67. How many cords of wood can be put in a shed 256 ft. long 20 ft. wide and 8 ft. high? Ans. 320 cords. 68. How many shingles netting 6 in. by 4, will cover a house 50 ft. long and 40 ft. wide, with gable roof and the length of rafter 25 ft. Ans. 15000 shingles. 69. How many square ft. of lumber in one floor of the above house ? Ans. 2000 sq. ft. And how many square yards of plastering in a hall 15 feet high extending over the whole building ? Ans. 522% sq. yds. How many yards of carpeting one yard wide will cover the floor? Ans. 222; yds. 70. The product of two equal factors is 34225; what is each factor? Solve by factoring. By what other method may it be solved ? 71. What is the greatest common divisor of 72 and 1728 ? Ans. 72. 72. Find the least common multiple of 6, 9, 12, 18, and 36. Ans. 36. 73. Reduce lb. to the decimal of a ton. Ans. .0000625 ton. 74. What is the amount of $200 for 3 years at 6% compound interest, payable semi-annually? Ans. $238.81. a 75. If 12 men build a wall 36 yds. long in 30 days, working 8 hours a day, how many men can build a wall 84 yds. long in 60 days, working 7 hours in a day? Ans. 16 men. 76. What is the length of a side of a cubical box containing 48228544 cubic inches ? Ans. 364 in. 177. Extract the square root of g. Ans. .745 +. 78. In a series of equal ratios, the first term is 3, the ratio 2, and the last term 192 ; what is the sum of the series? Ans. 381. 79. A gentleman giving his daughter in marriage on New Year's day, gave her husband $100 toward her portion, promising to double it on the first day of every succeeding month during the year; what was her portion ? Ans. $409500. 80. If a man travel 540 miles in 30 days of 9 hours each, how far will he travel in 48 days of 12 hours each ? Ans. 1152 miles. 81. How many numbers form a proportion ? 82. What are the names of the terms ? 83. How many terms form a ratio ? and what are they called ? 84. The two means of a proportion are 3 and 6, and one of the extremes is 2; what is the other extreme? Ans. 9. 85. The two extremes of a proportion are 5 and 9, and one of the means is 3; what is the other mean? 86. In a series of ratios forming proportions, what name is given to the odd terms, and what to the even ones ? 87. In the usual method of numeration, how many figures in each period ? a 88. Name the first three periods of integers, and the first four places of decimals. 89. How does multiplying the numerator of a fraction affect the value of the fraction? How multiplying the ? denominator ? 90. How does a zero annexed to a decimal affect the value? If a zero is prefixed what is its effect ? 91. A father left to his four sons $38750, to be divided in such a manner that each one's share being placed at 5% simple interest shall amount to the same when he shall become 21 years of age, their ages at his death being 13, 15, 17 and 19 years respectively; what principal must be placed at interest for each ? Ans. $8580 youngest; $9240, $10010, $10920 oldest. 4, 18, 1= 486 4876, 8806, 1988 Hill * $$1$$ = $8580, etc. Reduce to a common denominator, and the numerators express the ratios. 92. The difference of time between Washington and Cincinnati is 29 min. 36 sec.; what is the difference of longitude ? Ans. n° 24'. 93. The difference of time between two places is 2 hours 20 min. 40 sec. ; what is the difference of longitude ? Ans. 35° 10'. 94. The difference of time between Baltimore and |