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48. In 641942 lbs. ; how many barrels, stones, and pounds of wheat?

49. In 483104 lbs of barley; how many barrels, stones and pounds?

50. In 47712391 pounds of oats; how many barrels, stones and pounds?

51. In 64340 square yards; how many acres?

52. In 31419600 lines; how many English miles, and how many Irish miles?

53. From 641 3s 7ąd take 3 times 31 5s 104d, and divide the remainder by 15.

54. If 41lbs of tea cost 167 8s 4d; what is the price of one pound?

55. If 21 yards linen cost 21 4s 74d, what is that pr yard? 56. In 106756 grains of silver; how many lbs?

57. In 2858350 ounces; how many hundreds, &e.? 58. In 1233600 lb; how many tons, &c.?

59. Out of 6ct 2qrs and 201b of tea; how many canisters may be filled, each to hold 11 pounds?

60. In 180600lbs of sugar; how many hhds, each to contain 103 cwt.?

61. In 1096 cwt. of indigo; how many chests, each to contain 24 cwt.?

62. In 565810 grains; how many lbs Troy?

63. In 27160 English ells; how many yards ?

64. In 493550 nails; how many yards, qrs and nails ?` 65. In 11404800 inches; how many yards?

66. How many English miles, and how many Irish miles are in 8070400 feet?.

67. How many geographical miles between London and Pekin, in China, the distance suppose 5040 English miles, a degree being 60 geographical miles?

68. In how many steps, each 2 feet 8 inches, may a person walk one English mile?

69, If 10lbs of tobacco cost 17 13s. 9d; what is that per ib? 70. If 11ct of merchandize cost 227 14s 8d; what is that per cwt.?

71. If 16 moydores are worth 231 8s; what is the val. of 1? 72. If 20 cwt cheese cost 381 13s 4d; what is that percwt? 73. If 47 yds of diaper cost 31 128 54d; what is that pr yd? 74. If 24 cwt. of hops cost 104/ 12s; what is that pr cwt ?

75. What are coals per ton, if 89 ton cost 118 13s 4d? 76. If 123 doz of candles cost 687 1s 3d what is that pr doz? 77. If 60 lbs cost 71 38 84d; what is that per lb ?

78. If 644 tons hay cost 3341 2s Od; what is that per ton? 79. If 1454 gallons of brandy cost 1497 9s 104d; what is that per gallon?

80. If 80 yards of broadcloth cost 967 12s; what is that per yard?

81. If my yearly income be 1131 15s; what is that per day? 82. Suppose I have cleared by trade in 134 years, 4894/ 2s 34d; what is the average yearly increase of my property? 83. Divide 99ct 1qr 7lb 6oz by 7.

84. If I have 500 cwt. of tobacco; how many hhds may be filled, each to contain 8ct 1qr 21lb?

85. If the yearly rent of 69 acres be 1547 2s. 3d; how much is that per acre?

86. If on the whole earth there are 820 millions of people, and that each person could stand on 14 square feet; how many Irish square miles would hold them all?

87. Bought 2150 barrels of wheat, which cost me 4314! 13s 4d; if the same has reduced in preparing 105 barrels, what doth the remainder stand me in per barrel ?

88. A person by will left 150001, one-fourth thereof to his eldest son, one-fifth thereof to his second son, and the remainder to be divided between 3 other children, share and share alike; what was the share of each ?

89. Suppose two men purchase at auction, tobacco, to the value of 5471, and wt. 57ct 1qr 141b; one put in of the money, and the other the remainder; how much must each pay, and what weight is each to receive ?

90. Bought 5 hhds of tallow, wt. gròss 74ct 1qr 21lbs, but the brands being defaced, I agree to take them, on being allowed 141b per cwt; how much is the neat weight?*

91. How many yards can I buy for 247 at 6s per yard? 92. How many lbs of tea can I buy for 61 4s at 8s per lb ?t

90. From the gross weight subtract one-eighth part thereof, the remainder is neat weight, because 141b are of one cwt.

91. This question, and all similar oues, where the price yard, b, cwt is even shillings, may be easily resolved, by considering that 20s make a pound sterl. the half of which is 10s; therefore, add a cipher to the total price, and divide by half the price of one yard, , cwt, &c.

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93 How many cwt of starch can I buy for 407 at 36s prewt? 94. How many cwt of cheese can I buy for 1611, at 46s prewt? 95. How many yds of linen may be had for 291, at 4s pryd? 96. How many yards of cloth may be bought for 2041 at 12s. per yard?

97. Divide 12427 16s 8d between 9 men and 12 women, and give each man twice as much as each woman?

98. If one cwt. of hops cost 91 1s 4d; what are they per lb.?

99. If 7lbs of silver cost 21 guineas Irish money; what is the price of one ounce ?

100. Bought 1650 barrels of barley, which stand me in 1542/ 15s Od, it has reduced in preparing 102 barrels ; E have sold of the remainder 900 barrels, at the rate of 17 5sper barrel; what doth what I have on hands, stand me in per barrel?

101. Bought goods to the amount of 13411 17s 5d; how many guineas will discharge this debt ?*

102. In a park containing 545 Irish acres, how many English acres ?t

103. In 147a 2r 20p British statute measure; how many acres Irish plantation measure?

104. In a farm there is 66 Irish acres; how many English acres therein ?

105. Suppose the distance from Limerick to Dublin is 94 miles; how many English miles in the same distance?

106. Received invoice of iron, wt. 194 ton, 14ct 3qrs 14lb; how many ton long weight am I to be charged for freight? 107. With what number of sovereigns may I pay a debt of 395 guineas?

* 101. Bring £1341 17s 5d to pence, and divide by 273, the number of pence in one guinea, the remainder, if any, is pence.

+102, Multiply the given number of Irish acres by 196, and divide by 121 (see page 57.)

105. Multiply the given Irish miles by 14, and divide by 11,

106. Bring the given short weight to lb, and divide by 30, 4 and 20. 107. Multiply the given number of guineas by 21, and divide by 20, the remainder, if any, is pieces of 13 pence each,

108. Multiply 2050 by 54, the number of pence in a Spanish dollar, and divide by 273, the number of fence in a guinea, remainder, if any, is pence.

108. How many guineas are equal in value to 2050 Spanish dollars, at 4s 6d each?

109. How many cwt. long weight in 145ct 1qr 14lbs common weight?

110. In 173ct 1qr 291b long weight; how many cwt, qrs and lbs common weight?

111. In 245 ells English, 3qr 2n; how many yards, qrs and nails ?

112. In 138 yards 1qr 3n; how many ells Flemish, qrs. and nails?

113. In 174yds 1qr 3n; how many ells Eng. qr and nl? 114. In 169e.f. 2qr 1n; how many ells Eng. qr and nl? 115. In 135e.f. 2qr In; how many yards qrs and nails? 116. In 2287 square perches; how many acres?

117. If a park containing 500 acres, is to be divided into portions of 2a 3r each; how many such will it make, and what will remain ?*

118. From the 19th December 1819, till the 29th of September in the following year, both days inclusive; how many days and weeks?

119. If a sailor serve from 1st of February, 'till the 20th of October following; how many months, each month 28 days? 120. Divide 357 between 2 men, and give one 5 guineas more than the other ?

121. If in the City of Dublin there are 250,000 individuals, and each consume of flour when made into bread, each day; what quantity would be sufficient to last them 7 days? 122. In 74ct 1qr 181b of wheat; how many barrels, stones and lbs?

123. In 83bls 11 stone of oats; how many cwt. ?

124. In 45ct 3qr 15lb of oats; how many barrels, stones and pounds?

117. Bring the given number of acres to roods, which divide by 11 the number of roods in 2a 3r. the remainder, if any, will be roods. 120. Divide 351 by 2, also divide 5 guineas by 2; the two quotients added together, will give the greater share, and this subtracted from the given sum, will give the less share.

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1F any whole thing, a foot, a yard, a pound, &c. is divided into three equal parts, any of those parts is one-third of the whole, written thus, . If two of them are taken, they are two-thirds, or such expressions are called fractions: the number above the line is called the numerator of the fraction, and the number below the line the denominator.

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A proper fraction is that whose denominator is greater than its numerator, If the numerator be equal to the denominator, or greater, the fraction is called improper.

The denominator always denotes the number of equal parts into which the whole thing or integer is conceived to be divided, The numerator denotes the number of those parts which are taken in the fraction; thus, the fraction intimates that the integer is divided into 7 equal parts, and that we take three of those parts in the fraction.

Any improper fraction, whose numerator and denominator are equal, such as 4, 7, 8, &c. is equal to one integer, which we suppose to be divided into equal parts, Thus, if a pound is divided into 7 equal parts, and that 7 of those parts are taken, the whole pound is taken, neither more nor less. It is therefore, manifest, that or any proper fraction is less than the whole, and that or any improper fraction, whose numerator is greater than its denominator, is greater than the whole. Here it is to be understood, that one whole thing divided as one integer is meant, whether a pound, a foot, a yard, &c. or ever so many pounds, feet, yards, &c.

When we consider any fraction, such as, we conceive it "to be two-thirds of one. But there is another view, to which it will be proper to attend. It may be considered as the third part of 2, for as two-thirds are twice as great as one-third, and 2 twice as great as one, it is evident that two-thirds of 1 and one-third of 2, are equivalent expressions. In like manner, the fraction may be considered, either as three-sevenths of one, or as the seventh part of 3; the latter being three times greater than the seventh-part of one. Thus, any frac tion may be considered as a quotient, arising from the division of its numerator by its denominator, and hence fractional notation is commonly employed to express division.

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