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RULE. Place the numbers alternately, beginning at the left hand, and let the last nuinber stand on the right hand, then multiply the first row for a divisor, and the second for a dividend.

EXAMPLES.

40

1. If 24 lb. at New-London inake 20 lb. at Amsterdam, and 50 lb. at Amsterdam 60 lb. at Paris ; how many at "Poris are equal to 40 at New-London ?

Left. Right.
24 = 20 20 X 60 X 40 48000
50 60

S 40 Ans.
24 x 50

1200 2. If 50 lb. at New-York make 45 at Amsterdam, and So lb. at Amsterdam make 103 at Dantzic; how many lb. at Dantzic are equal to 240 at N. York i Ans. 27870

3. If 20 braces at Leghorn be equal to 11 vares at Lisbon, and 40 vares at Lisbon' to 80 braces at Lucca ; how many braces at Lucca are equal to 100 braces at Leghorn?

Ans. 110.

EXCHANGE. BY this rule merchants know what sum of money ought to be received in one country, for any sum of different specie paid in another, according to the given course of exchange.

To reduce the monies of foreign nations to that of the United States, you may consult the following

TABLE: Shewing the value of the monies of account, of foreign

nations, estimated in Federal Money.* $ cts. Pound Sterling of Great Britain,

4 44 Pound Sterling of Ireland,

4 10 Livre of France,

Q 185 Guilder or Florin of the U. Netherlands, 0 39 Mark Banco of Hamburgh,

0 33 Rix Dollar of Denmark,

1 0

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O 10

Rial Plate of Spain,
Milrea of Portugal,
Tale of China,
Pagoda of India,
Rupee of Bengal,

I. OF GREAT BRITAIN.

1 48 1 94 0 555

EXAMPLES,

1. Iu 45l. 10s. sterling, how many dollars and cents :

A pound sterling being=444 cents, 721fore-is il. : 444cts. : : 45,51. : 20202cts. Ans.

2. In 500 dollars how many pounds sterling? As 44cts. : 11. : : 50000cts. : 1121. 12s. Sd.+ airs.

II. OF IRELAND,

EXAMPLES.

1. In 901. 103. 6il. Irish inoney, how many cents ?

11. Irisli=410cts.
£. cts.
£s cts.

Scts. Therefore-As 1 : 410 : : 90,525 : 371151=371, 154

2. In 168 dols. 10 cts. how many pounds Irish?
As 410cts. i 1l. : : 16810cts. : £,41 Irish. Ans.

III. OF FRANCE
Accounts are kept in livres, sols and deniers.
$ 12 deniers, or perice, make 1 sol, or shilling,

20 sols, or shillings, 1 livre, or pound.

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EXAMPLES.

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1. In 250 livres, 8 sols, how many dollars and cents ?

1 livre of France=184 cts. or 185 mills. £. F.

$. cts. 712. As 1 : 185 : : 250,4 : 46324=46, 32 4 Uns 2. Reduce 87 dois. 45 cts. T m. into livres of France

mills. lit. mills, lir. so. den. As 185 :1: : 87457 : 472 14 9+ Ans.

IV. OF THE U. NETHERLANDS Accounts are kept here in guilders, stivers, groats and phennings.

8 phennings make 1 groat.
2 groats

1 stiver.
20 stiver's

1 guilder, or florin. A guilder is=39 cents, or 390 mills.

EXAMPLES.

Reduce 184 guilders, 14 stivers, into federal money,

Guil. cts. Guil. S d. c. I.
As 1 : 59 : : 124,7 : 48, 63 S Ans.

mills. G. wills. G.
As 390 : 1 :: 48633 : 124,7 Proof

V. OF HAMBURGH, IN GERMANY. Accounts are kept in Hainburgh in marks, sous and deniers-lubs, and by some in rix dollars.

12 deniers-lubs make 1 sous-lubs.
16 sous-lubs,

1 mark-lubs.
3 mark-lubs,

1 rix-dollar. Note.--A inark s = ss} cts. or just of a dollar.

RULE. Diviile the marks by '3, the quotient will be dollars.

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EXAMPLES.

Reduce 641 marks, 8 sous, to tederal money.

5)641,5

$213,835 Ans. But to reduce Federal Money into Marks, multiply the given sum by 3, &c.

EXAMPLES.

Reduce 121 dollars, 90 cts. into marks banco. 121,90

3

363,70=365 iarks 11 sous, 2,4 den. Ans.

VI. OF SPAIN.
Accounts are kept in Spain in piastres, rials and marvadies.

SS4 marvadies of plato make 1 rial of plate.
* 8 rials of plate

1 piastre or piece of To reduce rials of plate to Federal Money. Since a rial of plate is 10 cents, or 1 dime, you need only call the rials so many dimes, and it is done.

EXAMPLES.

485 rials=485 dimes 48 dols. 30 cts, &c.

But to reduce cents into rials of plate, divide by 16Thus, 845 cents:10=84,5=84 rials, 17 marvadies, &si

VII. OF PORTUGAL. Accounts are kept throughout this kingdom in milreas, and reas, reckoning 1000 reas to a millea.

Note.--A inirea is = 124 cents; therefore to reiluce milreas into Federal Money, multiply by 124, and the product will be cents, and decimals of a cent,

EXAMPLES.

1. In 340 milreas how many cents ?

340 x 124=42160 cents,=8421, 60cts. Ans. 2. In 211 milreas, 48 rcas, how many cents ?

Note.- When the reas are less than 100, place a cyidher before them. Thus 211,048 X 124=26169,952cts. or 261 dols. 69 cts. 9 milis. + Ans.

But to reduce cents into milreas, divide them by 124 ; and if decimals arise you must carry on the quotient as far as three decimal places; then the whole numbers thereof will be the milreas, and the decimals will be the

reas.

reas,

EXANPLES. i. In 4195 cents,

how
many

milreas ? 4195=124=33,830+or 35 milrras, 330 reas. Ans. 2. In 24 dols. 92 cts. how many milreas of Portugal ?

Ans. 20 milrens, 096
VIII. EAST-INDIA MONEY.
To reduce India Money to Federa, viz.
Tales of China, multiply with 148
Pagodas of india,

194
Rupee of Bengal,

555

EXAMPLES.

1. In 641 Tales of China, how many cents ?

Ans. 94868. 2. In 50 Pagodas of India, how many cents ?

Ans. 9700. 3. In 98 Rupees of Bengal, how many cents ?

Ans. 5439.

VULGAR FRACTIONS. HAVING briefly introduced Vulgar Fractions immodiately after reduction of whole numbers, and given some general definitions, and a few such problems therein as were necessary to prepare and lead the scholar immediately to decimals; the learner is therefore requested to read those general definitions in page 74.

Vulgar Fractions are either proper, improper, single, compound, or mixed.

1. A single, simple, or proper fraction, is when the numerator is less than the denominator, as it &c.

2. An Improper Fraction, is when the numerator exceeds the denominator, as { } 4, &c.

S. A Compound fraction, is the fraction of a fraction, coupled by the word of, thus, of , $ of of }, &c.

4. A Mixed Næmber, is composed of a whole number and a fraction, thus, 8, 1415, &c.

. 5. Any whole number may be expressed like a fraction by drawing a line under it, and patting 1 for denominator, thus, 8=4, and 12 thus, , &c.

6. The common measure of two or more numbers, is that number which will divide each of them without a remainder; thus, 3 is the common measure of 12, 24 and 30; and the greatest number which will do this, is called the greatest common measure.

7. A number, which can be measured by two or more numbers, is called their common multiple : and if it be the least number that can be so measured, it is called the least common multiple: thus, 24 is the common multiple of ?,

but their least common multiple is 12. To find the least common multiple of two or more Aumbers.

RULE. 1. Divide by any number that will divide two or more of the given numbers without a remainder, and set the quotients, together with the undivided numbers, in a line beneath.

2. Divide the second lines as before, and so on till there are no two numbers that can be divided; then the

3 and 4;

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