Proof of the foregoing Example. 47. How many quarters of sugar can you buy for 384 cents, at 6 cents a pound? OPERATION. 6) 384 28) 64 ( 2 qrs. 56 8 lbs. Ans. 2 qrs. 8 lbs. pounds by 28 pounds? A. Because quarter. Why do you divide 384 cents by 6 cents? A. Because, since there are 6 times as many cents as pounds, as often as 6 is contained in 384, so many pounds there will be. Why do you divide 64 every 28 pounds make 1 What, then, appears to be the method of proof? A. Reverse the operation; that is, make the divisors in the operation the. multipliers in the proof, and the multipliers the divisors. More Exercises for the Slate. 48. At 5 cents a gill, what will 8 pints of rum cost? A. $1,60. 49. How many gills in 20 pints? In 40 pints? A. 240 gills. 50. How many pints in 80 gills? In 120? A. 50 pints. 51. A merchant sold 5 hhds. of brandy at 3 dollars a gallon; how much did it amount to? A. $945. 52. How many hogsheads in 126 gallons? In 945? A. 17. 53. At 6 cents a quart, what will I hhd. of molasses come to ? * A. $15,12. 54. How many quarts are there in 3 hhds.? In 100? .A. 25956. 55. How many hogsheads are there in 756 qts.? In 252 qts.? A. 4. 56. Sold 1 tun of wine at 5 cents a gill; what did I get for it? A. $403,20. 57. How many gills in 10 tuns? A. 80640. 58. At 8 cents a pound, what will 3 cwt. 2 qrs. of raisins cost? A. $31,36. 59. How many pounds, in 15 cwt. 1 qr. A. 1708. 60. At 8 pence a peck, how many pence will 3 bushels of salt cost? A. 96. 61. How many pence are there in 20 shillings? 62. How many pence in 5£? In 10? 2. 3600. A. 240. 63. How many pounds in 480 d.? In 1440 d.? A. 8. 64. How many farthings in 4£? A. 3840. 65. At 6 pence per lb., what will 2 qrs. of rice cost? A. 336 pence. 66. How many qrs. of rice, at 6 pence per lb., may be bought for 336 pence? A. 2 qrs. 67. At 6 cents a gill, what will 1 tun of wine cost? A. $483,84. 68. How many tuns of wine, at 6 cents a gill, may be bought for $483,84. A. 1 tun. 69. At 9 pence per quart, what will 16 gals. 2 qts. of molasses come to in pence? A. 594 pence. 70. How many gallons of molasses, at 9 pence per quart, may be bought for 594 pence? A. 16 gals. 2 qts. 71. What is the value of a silver cup, weighing 10 oz. 5 pwts. 18 grs., at 5 mills per grain? A. $24,69. 72. At 5 mills per grain, what will be the weight of a silver cup that $24,69 will purchase? A. 10 oz. 5 pwts. 18 grs. 73. At 12 cents a pound, what cost 5 cwt. 2 qrs. 18 lbs. of sugar? A. $76,08 cts. 74. How many hundred weight of sugar, at 12 cents per lb., may be bought for $76,08? A. 5 cwt. 2 qrs. 18 lbs. 75. At 9 pence an hour, what will 2 yrs. 6 mo. 3 weeks, 6 da. 12 h. labour come to in pence? A. 187380. 76. How many years' work, at 9 pence per hour, may be obtained for 187380 pence? 4. 2 yrs. 6 mo. 3 weeks, 6 da. 12 h. 77. At 20 cents a nail, what is the price of 4 yds. of cloth? A. $12,80. 73. At 320 cents a yard, what will 64 nails of cloth cost? A. $12,80. 79. At 1£ 2 s. 6 d. per yard, what will 20 yds. of broadcloth cost in farthings? A. 21640. 80. At 6 cents a pint, what will 20 bu. 0 pks. 3 qts. 1 pt. of flax-seed cost? A. $77,22. 81. How many shillings, at 2 farthings a gill, will 5 T.1 p. 1 bhd. 2 gals. 2 qts. 1 pt. 3 gills, cost? A. 1935 s. 7 d. 2 qrs. 82. At 2 shillings a quarter, how many dollars will 8 yds. 1 qr. of broadcloth cost? Ꭿ. 11. 83. At 2 pence a gill, how many dollars will buy 50 gals. 2 qts. 1 pt. 2 gills of ale? 1. $45,055. 84. In 3600 dollars, how many farthings? A. 1036800. 85. In 1036800 farthings, how many dollars? A. 3600. 86. In 25 guineas, of 28 s. each, how many pence? A. 3400. 87. In 8400 pence, how many guineas? A. 25. 98. In 15 lbs. how many ounces, drams, scruples, and grains? A. 180 ounces, 1440 drams, 4320 scruples, 86400 grains. 89. In 86400 grains, how many scruples, drams, and ounces? A. 4320 scruples, 1440 drams, 180 ounces. 90. In 256 miles, 30 rods, how many rods? 4. 81950. 91. In 1950 rods, how many miles? 4. 256 m. 30 rods. 92. In 15 lea. 1 m. 6 fur. 23 rods, 4 yds. how many barley corns? A. 8803304. 93. In 8903304 barley corns, how many leagues? A. 15 lea. 1 m. 6 fur. 28 rods, 4 yds. 94. In 360 ells English, 4 qrs. 2 n. how many nails? A. 1804 qrs. 7218 na. 95. In 7218 na. how many ells English? A. 360 E. E. 4 qrs. 2 na. 96. In 3000 E. Flemish, how many nails? A. 36000. 97. In 36000 nails, how many E. Flemish? A. 3000. 98. In 500 acres, how many roods? A. 2000. 99. In 2000 roods, how many acres? A. 500. 100. In 15 tons of hewn timber, how many solid inches? A. 1296000. 101. In 1296000 solid inches of hewn timber, how many 102. In 20 cords of wood, how many solid inches? A. 4423680. 103. In 4423680 solid inches, how many cords of wood? A. 20. 104. In 500 bushels, 3 pecks, 7 qts. 1 pt. how many pints? A. 32063. 105. In 32063 pints, how many bushels? A. 500 bu. 3 pks. 7 qts. 1 pt. 106. In 20 tuns of wine, how many gills? A. 161280, 107. In 161280 gills of wine, how many tuns? A. 20. 108. In 366 years, 300 days, 20 hours, 50 minutes, and 37 seconds, how many seconds? A. 11378955037. 109. In 11378955037 seconds, how many years? A. 360 yrs. 300 days, 20 hours, 50 minutes, and 37 seconds. 110. In 8 signs of the Zodiac, how many seconds? A. 864000. 111. In 20 purses, each containing 21 guineas, how many shillings, pence, and farthings? A. 11760 s. 141120 d. 564480 far. 112. In 5 ingots of silver, each 5 lbs. 6' grains? A. 158500. oz. 20 grs., how many 113. In 239130 grains, how many ingots, each 6 lbs. 11 oz. 15 grs.? A. 6. 114. A lady sent a tankard to a silversmith, that weighed 5 lbs. 3 oz. and ordered it to be made into spoons, each to weigh 2 oz. 2 pwts.; how many spoons did it make? A. 30. 115. A goldsmith, having 15 ingots of silver, each weighing 2 lbs. 7 oz. 3 pwts. which he wishes to make into bowls of 2 lbs oz., tankards of 1 lb. 10 oz., salts of 11 oz., and spoons of 1 oz. 15 pwts., and of each an equal number, how many will there be of each sort? Bring 2 lbs. 8 oz., 1 lb. 10 oz., 11 oz., and 1 oz. 15 pwts., into pennyweights; add them up for a divisor; then bring 2 lbs. 7 oz. 3 puts. into pennyweights, multiply by 15 for a dividend, divide, and the quotient will be the answer. Ꭿ. 7. 116. In 26880 lbs. of sugar, how many hhds., each 12 cwt.? A. 20. 117. How many barley corns will reach round the globe, it being 360 degrees? A. 4755801600. 118. In running 300 miles, how many times will a wheel 9 feet 2 inches in circumference, turn round? A. 172800. 119. In 172800 turns of a wheel measuring 9 feet 2 inches, how many miles? A. 300. 120. How many times will a wheel, which is 15 feet 9 inches in circumference, turn round in going from Providence to Norwich, it being 45 miles? A. 15085+ 121. A farmer rents a plantation of 400 acres, of which no more than 200 are to be tilled; how many poles are there in the remainder? A. 32000. 122. In a lunar month, of 27 days, 7 hours, 43 minutes, 5 seconds, how many seconds? A. 2360585. 123. How many seconds is it from the birth of our Saviour to Christmas, 1828, allowing the year to contain 365 days, or 365 days, 6 hours? A. 57687292800. 124. When a person is 21 years old, how many seconds old is he? A. 662709600. 125. It is supposed the wars of Bonaparte, in 20 years, caused the death of 2000000 of persons; how many was this per hour, allowing the year to contain 365 days 6 hours? A. 117714 71480 175320 COMPOUND ADDITION. ¶ XXX. 1. William bought an arithmetic for 2 s. 6 d., and an inkstand for 6 d.; how many shillings did both cost? 2. Harry purchased a vest; the cloth and making cost 5s., the buttons 9 d., and the thread 3 d.; how much did the vest cost? 3. William, Harry, and Thomas gathered some nuts; and when they measured them, it was found that William had 2 qts. and 1 pt., Harry 3 qts. 1 pt., and Thomas 2 qts.; how many pecks did they gather in all?' 4. How many pecks are 3 qts. + 1 qt. + 4 qts.? 9. How many pounds are 10 s. + 18 s. + 12 s. ? 12. How many minutes in 45 sec. + 15 sec. +10 sec.? 15. Sold a Virgil, that cost me 12 s. 6 d., so as to gain 1 s. 6 d. ; how much did I get for it? Q. What is this, which you have now been doing, called? A. Compound Addition. Q. Why do you call it Compound? why not Simple Addition ? A. Because there are more denominations than one. Q. What do you mean by more denominations than one? A. Shillings, pence, &c. in one sum; pecks, quarts, pints, &c. in another sum. Q. What, then, is the collecting numbers of different denominations into one sum called? A. Compound Addition. Operation by Slate illustrated. 1. A man bought a cart for 6£ 12 s. 3 d., a load of hay for 3£ 9 s. 7 d., and a cow for 4£ 4 s. 1 d.; what did he pay for the whole ? OPERATION. 20 12 £ S. d. 6 12 3 3 4 9 17 4 1 Ans. £14 5 11 How do you write the numbers down? A. Pounds under pounds, shillings under shillings, &c. How do you get the 11 d. in the answer? A. I find, by adding up the column of pence, that it makes 11 d., which I write under the column of pence. How do you get the 5 shillings? A. Adding up the column of shillings, I find it makes 25 s. = 1£5 s. (for 20 s. in 25, 1 time, and 5 over), writing the 5 s. under the column of shillings. What is to be done with the 1£? A. I must, of course, add pounds to pounds, and, to do this, I join, or carry it to the next column, which is pounds. How do you get the 14£? A. Adding up the column of pounds makes 13 pounds, and 1£ (to carry) makes 14£. |