(1) Here we first multiply the £3 15s. 6d.-the price per cwt.-by 6, the highest number, or units in the multiplier; as by case VIII. (2.) We then resolve the 3qr. into the fractions of the denomination above, and 1; and take the parts of the multiplicand denoted by them, and write them under the corresponding denominations of the first product. (3.) Next we change the 14lb. to a fraction of the highest denomination, cwt., and take the part of the multiplicand denoted by it.. (4.) Having now multiplied by each part of the multiplier, (for it will be seen that the taking of parts of the multiplicand is the multiplication of a fraction by a fraction § 77. 1)), we add the parts and the first product together, and obtain the result required, £25 19s. 3qr. 3. Explanation. The exposition of the character of this multiplication already given (§ 114. 9), renders expla nation almost unnecessary. 4. It is proper, however, here to remind the pupil that in the first multiplication, that by the highest number or units of the multiplier, that number is regarded as a simple or abstract number; and that thus a rational product is obtained, and that it could be so in no other way;-the absurdity of saying, 6cwt. times £3 15s. 6d., for instance, is obvious. 5. The multiplication by the lower parts of the multiplier, has already been stated to be simply the multiplication of a fraction by a fraction (§120. (4)). This is apparent from the principle of this multiplication, which regards all the lower denominations in either of the given numbers, as fractional parts of the whole, or highest denomination (§ 114. 9). 6. For the distribution of the fractional parts of the multiplier into those most convenient and most easily taken, no special directions can be given; it must be left to the intelligence and dexterity of the pupil. 7. The great object is, in all cases, to obtain the rèquired result in the most concise manner. The pupil therefore should task his powers to obtain this unaided. 8. He will often find that when a part of the whole is wanted, and he already has a part from which the part wanted may easily be taken, that it will be expedient to take a part of that part for the required part of the whole (§ 64. 5.). 9. But, we say again, a choice of methods must be left to the pupil; and as he can acquire facility and accuracy in nọ class of arithmetical operations, without much exercise, so is this especially true here. 10. Another and better method of solving all questions of the character here involved, will be presented in Part IV. Yet it is well for the pupil to be acquainted with these operations, that he may, in a given instance, make his own choice. 11. Examples. (1.) What will be the cost of 55bu. 3pk. 5qt. of wheat at 10s. 2d. 3qr. per bushel ? Ans £28 11s. 10d 13 qr. (2.) What will 5yd. 3qr. 2na. 3s. 8d. per yard? of broadcloth cost at £2 Ans. £12 16s. 6d. 2qr. (3.) What is the value of 5cwt. 3qr. 14lb. of sugar at £2 4s. 6d. per cwt?: (4.) What is the value 7cwt. 3qr. 7s. 8d. per cwt? Ans. £13 1s. 5d. 1qr. (5.) What is the value of 37T. hemp at £89 6s. 8d. per ton? (6.) What will 57cwt. 3qr. 8lb. 17s. 9d. per cwt? (7.) What will 27T. 16cwt. 2qr. 18lb. of iron cost-at £90 10s. per ton ? Ans. £2520 0s. 5d+. (8.) What will 25A. 2sq. r. 25sq. rd. of land cost at $29 Ans. $744,03+ per acre? (9.) What will 121yd. 2qr. of broadcloth cost at $0,71 per yard? Ans. $86,265. (10.) What will 13lb. 10oz. 12pwt. 16gr. of silver cost at £4 7s. 6d. per pound? Ans. £60 14s. 11 d. (11.) What will 24lb. of tallów cost at $11,91 per cwt.? Ans. $2,552+. (12.) What will 1cwt. 3qr. 14lb. of raisins cost at £2 11s. 8d. per cwt? Ans. £4 16s. 10d. 2qr. (13.) What will 1ewt. 1qr. 8lb. of sugar cost at $8,65 per cwt? Ans. $11,42. (14.) What will 3624 bushels of wheat cost at $1,124 per bushel ? Ans. $407,53. (15.) What will 27gal. of brandy cost at $1,25 per galAns. $34,371. lon ? per (16.) What will 60 bushels of apples cost at 163 cents bushel? Ans. $10. Ans. $25,16. (17.) What will 75 bushels of potatoes cost at $0,331 per bushel? (18.) What will 463lb. butter cost at 12 cents per lb.? Ans. $5,793. (19.) What will 1gal. 2qt: 1pt. of wine cost at $3,62 per gallon? Ans. $5,89. (20.) What will fbu. 3pk. 6qt. of beans. cost at $1,12 per bushel ? (21.) What will 29yd. calico cost at $0,20 per yd.? Ans. $2,18. Ans. $5,95. (22.) What will 27yd. of silk cost at $1,12 per yd.? (23.) What will 1cwt. 16lb. of iron cwt.? (24.) What will 24lb. of sugar cost (25.) What will 1000 quills cost at Ans. $30,931. cost at $6,75 per Ans. $7,713 at $11,25 per cwt.? (26.) The interest on a certain sum $17,60, what is it for 7mo. 20da.? Aus. $2,41. ct. a piece? Ans. $5. for a year being Ans. $11,244. § 121. 1. While the United States were colonies of Great Britain, their currency was sterling. Each colony issued its own money in bills, the denominations to which were the pound, as the unit, with its subdivisions of shillings, pence and farthings. Some time after the separation of the colonies from the mother country, their bills depreciated; and in different degrees, in the different colonies. Hence arose an inequality in the value of the pound and its subdivisions in the different states.. 2. When therefore, the Federal Currency was adopted in 1786, the pound and its subdivisions in the several states had a different value in that currency; in some more and in others less. The fraction of a pound equalling a dollar, varied therefore, accordingly. 3. The value of the pound and its subdivisions in all the new states, that is, in the states added to the confeder acy since 1786, is the same as that in New-York and North Carolina. I. In English or Sterling Money; £1=20s.=240d. $1-4s. 6d. 54d.; therefore, £1=$4=$V. $1=££%; II. In Canada, Nova Scotia, and New-Brunswick; £1=20s. $1=5s.; therefore, £1=$=$ $1=£1⁄2=£1. III. In New-England, Virginia, Kentucky, and Ten nessee; £1=20s. $1=6s.; therefore, £1=$=$3. $1=£=£. IV. In New-York, North Carolina, and the new states; £1=20s. $1=8s.; therefore, V. In Pennsylvania, New-Jersey, Delaware and Maryland; £1=20s. 240d. $1=7s. 6d. 90d.; therefore, § 122. 1. To ascertain the comparative value of the unit or pound in the various currencies with regard to some fixed standard of estimation, and to change the denominations of one to those of another, are operations very frequently required. 2. The uniform standard of estimation is the dollar, the unit in Federal money. Its value, in parts of a pound, in the different currencies, is furnished in the tables; so is the value of the pound in parts of the dollar. 3. By the aid of the tables then-which the pupil should in every case be required to form for himself—and of the principles which they recognize, operations on the currencies are rendered comparatively clear and simple. 4. The three cases which follow, embrace all that is necessary for guidance in regard to such operations generally. §123. 1. CASE XIII. To change pounds, shillings, pence and farthings, in the different currencies, to Federal Money. RULE. Change all the lower denominations given to the decimal of a pound (§ 109. 1); divide by that fraction of a pound which equals a dollar in the required currency; and the quotient will be the result. 2. Illustration. Change £4 8s. 6d. English currency to Federal money. (1.) Here we first change the lower denominations, the shillings and the pence, to the decimal of a pound, which we annex to the pounds, and obtain £4,425. (2.) We then divide this result by, the fraction of a pound sterling, which equals a dollar, and we have $19, 666+, the result required. 3. Explanation. The principles involved in this operation are simply those of changing a denominate to a decimal fraction (§ 109.); and of division by a fraction; |