The dollar is considered to be the unit money, and all denominations below are decimal parts of a dollar. Thus, 1 dime is .1, or to of a dollar, 1 cent .01, or ido of a dollar, and 1 mill, .100 or robo of a dollar. The place next to dollars on the left hand, is eagles. Ang number of dollars, as 475, may either be read 475 dollars, or 47 eagles, 5 dollars; and the decimal parts of a dollar, as .865 may be read 8 dimes, 6 cents, 5 mills, or 86 cents, 5 mills, or 865 mills. Herice a sum expressed in Federal Money, is a mixed number in Decimal Fractions, and may be managed as such. Thus 25 eagles, 8 dollars, 4 dimnes, 6 cents and 3 mills are written 3 or 2 5 8. The usual way of reading sums in Federal Money is by naming only three of the denominations, namely, dollars, cents and mills. In this way, the above snm would be read 258 dollars, 46 cents, and 3 mills. The real coins in Federal Money are two of gold, the Eagle and half eagle, four of silver, the dollar, half dollar, double dime, and dime, and two of copper, the cent and half cent. The mill is only imaginary, there being no piece of money of that denomination. Addition, Subtraction, Multiplication and Division of Federal Money, are performed by the rules already given for Addition, Subtraction, Multiplication and Division in Decimal Fractions, and to these the scholar is referred. Examples. 1. What is the sum of 5 ea 4. A man bought 2; yds. broad. gles, 6 dollars, 8 dimes, 5 cents, cloth for $15.50, 6 yds. of silk, $9.444, $1.002, $25.22 and .867 | for 85.75, 7 yds. of cambrick for when added together? $5.25, and trimmings to the aE.D. d. ct.m. mount of 84.22; what was the 5 6. 8 5 amount of the purchase ? 9. 4 4 4 Ans. $30.72. 1. 0 0 2 2 5. 2 2 5. What will 47 yds. of cloth 8 6 7 cost, at .22 cents per yard ? Ans. $10.34. 9 3. 3 8 3 The scholar will bear in mind the 2. Suppose a man purchase 4 rule for pointing in the Multiplicahandkerchiefs at .62 cents each, tion of decimals. 8 yds. ribbon at .17 cts. per yard, 6. A man bought 24 yds. of and 5 yds. of lace at .44cts. per cloth at $1.50 per yard, and paid yard; what is the amount of the $26.55, how much remains due ? purchase ? Ans. 86.04. Ans. $9.45. 3. What will 156 yds. of cloth 7. If 24 lb, of tea cost $7.97, cost at $1.67 per yard ? what is it per pound? Ans. 8260.52 Ans. 80.392 8. If 125 bushels of wheat cost 11. Six men, in company, pur8200.50, what is it per bushel ? | chased 27 bushels of salt at81.67 Ans. $1.604. per bushel ; what did each man 9. If a man buy 154 bushels of pay, and what was each man's share of the salt? Ans. 87.515 wheat at 80.95 per bushel, and and his share 44 bushels. sell it at $1.125 per bushel, what is his gain? Ans $26.95. 12. A man dies leaving an es10. If $1268. be divided e tate of 835000, the deniands aqually among 15 men, what sum gainst the estate are $1254.65; does each receive ? the remainder, after deducting a Ans. $84.533. legacy of 83075, is divided e. When there is a remajoder after qually among his 6 sons; what dividing the dollars, the cents and is each son's share ? mills are obtained by annexing ci Ans. 85111.725. phers. QUESTIONS. 1. What is Federal Money? 8. What is a sum expressed in Fed2. In what proportion are its denom eral Money? inations ? 9. What denominations are gener3. How and when were they deter ally mentioned in naming a sum mined ? in Federal Money? 4. What is the table of Federal Mo 10. What are the real coins in Fed eral Money? 5. Which is the unit money? 11. What imaginary? 6. What are the denominations be. 12. How are Addition, Subtraction, low ? Multiplication and Division per7. What part of a dollar does one formed in Federal Money? dime express ? one cent? ney ? REDUCTION OF FEDERAL MONEY. Case I. To reduce New-England, &c. and New-York, &c. currencies to Federal Money.* Rule-If there be shillings, pence and farthings in the given sum, reduce them to the decimal of a pound by inspection, (see Case IJI. Reduction of Decimals,) and place it at the right hand of the pounds. Divide the given sum thus prepared, by .3, if New-England, and by .4 if New-York currency, and the quotient, pointed according to the rule for the division of decimals, will be the answer in dollars, and the decimal of a dollar. If pounds only be given, annex ciphers in the place of the decimal, and proceed as above directed. * Virginia and Kentucky currency is the same as New-England ; that of North-Carolina and Ohio, the same as New-York. } how many Examples. 1. In £22 how many dollars, 6. Reduce £25 15s. N.E. to cents and mills ? Federal Money. .41.3 ) 22.0000 Ans. $85.833. $73.333* if N.E. cur. dollars, cents, and 2. Reduce 516 78. 8ļd. in mills? Ans. $759 57cts. 8m. each currency to Federal Money. .41.3)16 385 8. Reduce £49 1s. in each currency to Federal Money. 40.962 49 1sN.E163.50 Here 3, half the greatest even £49 1s. N.Y.=$122.625 number of shillings, is the first decimal figure. 8ld.=34qrs. This 9. Reduce £8 7s. 2 d. in each is increased by 1, because over currency to Federal Money. 12, making it 35, and 3 is increas £878. 41d.N.E.=$27.87 Ans. were odd, making it 85. 10. Reduce £111 11s. 114d. 3. Reduce 591 in each cur- N.Y. to Federal Money. rency to Federal Money. Ans. $278 99cts. 2m. 11. Reduce 86 68. 5 d. in currency to Federal Money. 4. Reduce £125 N.E, to Fed N.E. 8287.74 eral Money Ans. 8416.366. S } Ans. N.Y. } Ans. 5. Reduce £33 13s. N.Y. to Federal Money. Ans. $84.125. 12. In £365 N.Y. how many dollars, &c. Ans. 912.50. Tbe reason of this rule will be obvious by considering that in N.E. currency, 6s. or of a pound, are equal to $1, and y=16, or .3 of a pound; and that in N.Y. currency, 8s. or 2 of a pound=1 dollar, and b=1, or .4 of a pound. Hence, in the former case, there are evidently as many dollars in the pounds, as there are 1, and in the latter, as many as there are to. Therefore, dividing the pounds by 3 in one case, and .4 in the other, and pointing according to the rule for the division of decimals, the quotient is evidently dollars and the decimal of a dollar.--If, after reducing the shillings, &c. to the decimal of a pound by inspection, the separatrix be removed one place to the right hand, the sum will be 2 shilling pieces and the decimal of a 28. piece, and this divided by 3 and 4, as whole numbers will evidently give dollars and deci. mals of dollars in the two cases, because in the former, 3 two shillings, and in the latter, 4, are equal to a dollar. . Case II. To reduce Federal Money to New-England, g c. to New York, &c. currencies. Rule.* _Multiply the given sum by.3 for New England currency, and by .4 for New York currency, and the product, pointed accord ing to the rule for the multiplication of decimals, will be pounds and the decimals of a pound. Then find the value of the decimal by inspection. (See Reduction of Decimals, Case V.) how many Examples. 1. In $25.964, how many 4. In 86.753 pounds, shillings, pence, and far- pounds, shillings, pence, and farthings ? things? 25.964 25.964 .3 €2 0s. 61. N.E. Ans. .4 £2 14s. 04d. N.Y. £7.7892 £10.3856 S£7 15s. 9 d. N.E. Ans. <£10 7s. 8 d. N.Y. 5. In $1.612 how many shil lings, pence and farthings? 2. In 8912.50 how many pounds, shillings, pence and farthings ? 12s. 104d. N.Y. { Ans. { £365 Os. N.Y. 5. In $1111.111 how many 3. In 49 cents how many shil pounds, shillings, pence and farlings, pence and farthings ? things ? £333 6s. 8d. 3s. 11d. N.Y. £444 10 Ans. {2144 8s. 104d. N.Y. Case III. To reduce Pennsylvania, New Jersey, Delaware and Maryland cur. rency to Federal Money. Rule.t-Reduce the given sum to pence, and if there are farthings, for 1 qr. place 2 at the right hand of the pence; for 2 qrs. write 5, and for 3, write 7; but if there are no farthings, annex a cipher to the pence. Divide this sum by 9, and add the quotient to the dividend. From the sum point off three figures for cents and mills; those on the left hand will be dollars. * As this rule is the converge of the preceding, the truth of it must be sufficiently obvious from what has already been said. † A dollar in Pennsylvania, &c. currency, is 7s.6d.=90d. which, increased by one ninth of itself, is 100= to the number of cents in a dollar. Hence the reason of the rule is obvious. Examples. 1. In €25 6s 5d 2qrs how 2. In €86 6s 5d how many many dollars? dollars, cents and mills ? £s d qrs Ans. $230.191. 25 6 5 2 20 3. Reduce 736 to Federal money. Ans. $1962,666. 506 12 4. Reduce £42 128 8d to 9)60775 Federal money. 6752 Ans. $113.688. Ans. $67.527 Case IV. Rule. If there be no mills in the given sum, reduce it to mills by annex. ing ciphers; from the sum subtract one tenth of itself, and the remainder, excepting the right hand figure, will be pence, which must be reduced to pounds. If the figure cut off from the right hand be 2, call it 1qr. if 5, 2qrs. and if 7, 3qrs. Examples. 1. In 867.527 how many pounds, 2. In 8230.191 how many shillings, pence and farthings ? pounds, shillings, pence and far 67.527 To get one tenth, things ? Ans. £86 6.54d. a sum is divided by 12)6077.5 10, by cutting off the right hand figure ; 3. In 8200 how many pounds ? 2|0)50/65{d, hence we have only Ans. €75. to drop the right hand figure and subtract 4. In 814.25 how many pounds, the others from the shillings, pence and farthings? given sum. Ans. £25 6s. 5 d. Ans. 5 6. 10 d. Rule. * £25 68 * Here the shillings, pence, &c. are reduced to the decimal of a pound, and the whole multiplied by 4, because £l=4 dollars ; a dollar in that currency being equal to 5 shillings. The currency of Nova Scotia is the same as Capada. |