Note. In reducing the common fractions in this example, it will be sufficiently exact if the decimal be extended to three places. Ans. 1084 lb. 4. At 12 cents per lb. what will 37 lbs. of butter cost? 5. At $17'37 per ton for hay, what will 11 6. The above example reversed. At $201'92 what is that per ton? Ans. $4'7181. tons cost? 7. If '45 of a ton of hay cost $9, what is that T 65. Ans. $201'92. for 11 tons of hay, Ans. $17'37. Consult per ton? Ans. $20. 8. At '4 of a dollar a gallon, what will '25 of a gallon of molasses cost? Ans. $1. 9. At $9 per cwt., what will 7 cwt. 3 qrs. 16 lbs. of sugar cost? Note. Reduce the 3 qrs. 16 lbs. to the decimal of a cwt., extending the decimal in this, and the examples which follow, to four places. Ans. 71'035+. cwt.? Ans. $13. Ans. $16'10. 10. At $69'875 for 5 cwt. 1 qr. 14 lbs. of raisins, what is that per 11. What will 2300 lbs. of hay come to at 7 mills per lb. ? 12. What will 765 lbs. of coffee come to, at 18 cents per lb. ? Ans. $137'79. 13. What will 12 gals. 3 qts. 1 pt. of gin cost, at 28 cents per quart? .1 Note. Reduce the whole quantity to quarts and the decimal of a quart. Ans. $14'42. 14. Bought 16 yards 2 qrs. 3 na. of broadcloth, for $100'125; what was that per yard? Ans. $6. 15. At $1'92 per bushel, how much wheat may be bought for $72. Ans. 1 peck 4 quarts. 16. At $92'72 per ton, how much iron may be purchased for $60'268 ? Ans. 13 cwt. 17. Bought a load of hay for $9'17, paying at the rate of $16 per ton; what was the weight of the hay? Ans. 11 cwt. 1 qr. 23 lbs. 18. At $302'4 per tun, what will 1 hhd. 15 gals. 3 qts. of wine cost? Ans. $94'50. 19. The above reversed. wine, what is that per tun? At $94'50 for 1 hhd. 15 gals. 3 qts. of Note. The following examples reciprocally prove each other, excepting when there are some fractional losses, as explained above, and even then the results will be sufficiently exact for all practical purposes. If, however, greater exactness be required, the decimals must be extended to a greater number of places. 20. At $1'80 for 31 qts. of wine, what is that per gal. ? 22. If of a ton of potashes cust $60'45_what is that per ton? ། 21. At $2215 per gal., what cost 34 qts.? 23. At 96'72 per ton for potashes, what will of a ton cost? 24. If '8 of a yard of cloth cost $2, what is that per yard? 27. If 14 cwt. of potashes cost 19 £. 5 s., 25. If a yard of cloth cost $2'5, what will '8 of a yard cost? 26. At $2'5 per yard, how much cloth may be purchased for $2? 28. If a ton of pot- 29. At 27 £. 10 s., ashes cost 27 £. 10 s. a ton for potashes, what is that per ton? what will 14 cwt. what quantity may be bought for 19 £. 5 s.? cost? Note. After the same manner let the pupil reverse and prove the following examples: 30. At $18'50 per ton, how much hay may be bought for $12'025 ? 31. What will 3 qrs. 2 na. of broadcloth cost, at $6 per yard? 32. At $22'10 for transportation of 65 cwt. 46 miles, what is that per ton? 33. Bought a silver cup, weighing 9 oz. 4 pwt. 16 grs., for 3 £. 2 s. 3 d. 33 q.; what was that per ounce ? 34. Bought 9 chests of tea, each weighing 3 cwt. 2 qrs. 21 lbs., at 4 £. 9s. per cwt.; what came they to? 35. If 5 acres 1 rood produce 26 quarters 2 bushels of wheat, how mary acres will be required to produce 47 quarters 4 bushels ? Note. The above example will require two operations, for which consult ¶ 65, ex. 1. 36. A lady purchased a gold ring, giving at the rate of $20 per ounce; she paid for the ring $125; how much did it weigh? REDUCTION OF CURRENCIES. ¶ 78. Previous to the act of Congress, in 1786, establishing federal money, all calculations in money, throughout the United States, were made in pounds, shillings, pence and farthings, the same as in England. But these denominations, although the same in name, were different in value in different countries. New Jersey, S. Carolina and Georgia, } 7 s. 6 d., called Pennsylvania currency. 4 s. 8 d., called Georgia currency. 1. Reduce 6 £. 11 s. 64 d. to federal money. Note. To reduce pounds, shillings, pence and farthings, in either of the above-named currencies, to federal money,-First, reduce the shillings, pence and farthings (if any be contained in the given sum) to the decimal of a pound by inspection, as already taught, ¶ 76. = 6 £. 11 s. 64 d. = £6'576. ENGLISH MONEY. Now, supposing the above sum to be English money,-1 £. is 20 s. 240 pence, in all the above currencies. 1 dollar, in English money, is reckoned 4 s. 6 d. 54 pence, that is, 2540-40 of 1 pound. Now, as many times as 9 the fraction which I dollar is of 1 pound, English money, is contained in £6'576, so many dollars, it is evident, there must be; that is,-To reduce English to federal money,-Divide the given sum by the quotient will be federal money. £6'576 English money. 40 9) 263'040 29'226 federal money, Answer. Note. It will be recollected, to divide by a fraction, we multiply by the denominator, and dívide the product by the numerator. CANADA CURRENCY. Supposing the above sum to be Canada currency,—1 dollar, in this currency, is 5 s. = 60 pence, that is, = of 1 pound. Therefore,-To reduce Canada currency to federal money,-Divide the given sum by 4, and the quotient will be federal money; or, which is the same thing, multiply the given sum by 4. £6'576 Canada currency. 4 $26'304 federal money, Answer. = NEW ENGLAND CURRENCY. 1 dollar, in this currency, is 6 s. = 72 pence, that is, 72, or 3 of a pound. Therefore,-To reduce New England currency to federal money,-Divide the given sum by '3. '3) £6'576 New England currency. $21'92 federal money, Answer. NEW YORK CURRENCY. 1 dollar, in this currency, is 8 s. = 96 pence, that is, 9629480 or '4 of a pound. Therefore,-To reduce New York currency to federal money,-Divide the given sum by '4. A d. '4) £6'576 New York currency. $16'44 federal money, Answer. PENNSYLVANIA CURRENCY. = 1 dollar, in this currency, is 7 s. 6 =90 pence, that is 90 of a pound. Therefore,-To reduce Pennsylvania currency to federal money,-Divide by , that is, multiply the given sum by 8, and divide the product by 3. £6'576 Pennsylvania currency. 8 3) 52'608 that is, $17'536 federal money, Answer. GEORGIA CURRENCY. 1 dollar, Georgia currency, is 4 s. 8 d. — 56 pence, To of a pound. Therefore,-To reduce Georgia currency to federal money,-Divide by 3, that is, multiply the given sum by 30, and divide the product by 7. From the foregoing examples, we derive the following genera RULE: To reduce English money, and the currencies of Canada and the several states, to federal money,-First, reduce the shillings, &c., if any in the given sum, to the decimal of a pound; this being done, divide the given sum by such fractional part as 1 dollar, in the given currency, is a fractional part of 1 pound. EXAMPLES FOR PRACTICE. 2. Reduce 125 £., in each of the before named currencies, to federal money. Answers, 125 £. English money, 125 £. Canada currency, is $555'5553. $ 500. $416'666. $535'7142. 3. Reduce 1 s. 6 d., in the several currencies, to federal money. Answers, 1 s. 6 d. '075 £. English money, is $333; Canada currency, it is $30; New England currency, it is $25; New York currency, it is '187; Pennsylvania currency, it is $20; Georgia currency, it is $3213. 4. Reduce 75 £. 15 s., in the several currencies, to federal money, 5. Reduce 18 £. 0 s. 83 d., in the several currencies, to federal money. 6. Reduce 4 d., in the several currencies, to federal money. 7. Reduco 36 £. 3 s. 74 d., in the several currencies, to federal money. 179. To reduce federal money to any of the before named currencies, reverse the process in the foregoing operations; that is,Multiply the given sum in federal money by such fractional part as 1 dollar, in that currency to which you would reduce it, is of 1 pound. The product will be the answer in pounds, and decimals of a pound, which must be reduced to shillings, pence and farthings, by inspec tion, as already taught, ¶ 77. EXAMPLES FOR PRACTICE. 1. Reduce $118'25 to the several before named 'currencies. Answer, English money, 2. Change $250 to the several currencies. T80. It may sometimes be required to reduce one currency to par, or equality of another currency. the 1. Reduce 35 £. 6 s. 8 d., English money, to New England currency. $1 is 4 s. 6 d. 54 d. English money. $1 is 6 s. =72 d. New England currency; that is, the value of any number of pounds, shillings, pence, &c., English money, is of the same in N. England currency; consequently,-To reduce English money to N. England currency-Multiply by 4, or, which is the same, increase it by part of itself. Thus, 47 6 8 English money, is 15 6 2 2 2 2 New England currency, answer. Hence we have this general RULE for finding a multiplier to reduce any currency to the par of another : Make $1 in pence, of the currency to be reduced, the denominator of a fraction, over which write $1 in pence, of the currency to which it is to be reduced, for a numerator. This fraction may then be reduced to its lowest terms before multiplying. On the same principles, let the pupil form for himself multipliers, by which To reduce English money to Canada, N. York, Pennsylvania, and Canada currency to English, New England, New York, |