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


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

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

40 Ans. 40 24 x 50 s 1200 2. If 50 lb. at New-York make 45 at Amsterdam, and 80 lb. at Anisterdam make 103 at Dantzic; how many Ik. at Dantzic are equal to 240 at N. York ?

Ans. 27876 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,

0 181 Guilder or Florin of the U. Netherlands, 089 Mark Banco of Hamburgh,

O S3 Rix Dollar of Denmark,

1 0

Laws U. 8. A.

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


0 10
1 24
1 48
1 94


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

A pound sterling being=444 cents, Therefore- As il. : 444cts. : : 45,51. : 20202cts. Ana

2. In 500 dollars how many pounds sterling? Ans 444cts. : 11. : : 50000cts. • 1121. 128. 3d. + Ans.



£ cts.

t. In 901. 108. 6d. Irish money, how many cents ?

11. Irish 410cts.

cts. $ cte Therefore--As 1 : 410 : : 90,525 : 371151=371, 154

2. In 168 dols. 10 cts. how many pounds Irish ?
As 410cts. : il. : : 16810cts. : £41 Irish. Ans.

Accounts are kept in livres, sols and deniers.
S 12 deniers, or pence, make 1 sol, or shilling,
20 sols, or shillings,

1 livre, or pound.


£. m.


1. In 250 livres, 8 sols, how many dollars and cents : 1 livre of France=18} cts. 'or 185 mills. £

$. ets. 11. As 1 : 185 : : 250,4 : 46324=46, 32 4 Ans. 2. Reduce 87 dols. 45 cts. 7 m. into livres of France mills. liv. mills.

liv. so. den. As 185 :1: : 87457 : 472 14 9+ Ans.

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

8 phennings make 1 groat. 2 groats

1 stiver. 20 stivers

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


Reduce 12A guilders, 14 stivers, into federal money.

Guil. cts. Guil. S d. c. m.
As 1 : 39 : : 124,7 : 48, 6 S S Ans.

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

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

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

1 mark-lubs.
3 mark-lubs,

1 rix-dollar.
Note. A mark :s = S3} cts. or just of a dollar.

Divide the marks by 3, the quotient will be dollars.


Reduce 641 marks, 8 sous, to federal money.


$213,8SS 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


365,70=365 marks 11 sous, 2,4 den. Ans.

VI. OF SPAIN. Accounts are kept in Spain in piastres, rials and marvadies, SS4 marvadies of plate make 1 rial of plate. 8 rials of plate

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


485 rials485 dimes -48 dols. 50 cts. &e.

But to reduce cents into rials of plate, divide by to Thus, 845 cents+10=84,584 rials, 17 marvadies, &

VII. OF PORTUGAL. Accounts are kept throughout this kingdom in mireas, und reas, reckoning 1000 reas to a milrea.

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


1. In 340 milreas how many cents ?

340x124=42160 cents,=8421, 60cts, Ans. 2. In 211 milreas, 48 rcas,

how many cents ? Note. When the reas are less than 100, place a cy: wher before them. Thus 211,048 X 12426169,952cts. or 261 dols. 69 cts. 9 mills. + Ans.

But to reduce cents into milreas, divide them by 184, 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



1. In 4195 cents, how many milreas ?

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

Ans. 20 milreas, 096 reas.
To reduce India Money to Federa, viz

Tales of China, multiply with 148
Pagodas of Iridia,

Rupee of Bengal,



1, 1,2641 Tales of China, how many cents ?

Ans. 9486& %. In 50 Pagodas of Indid, how many cents ?

ns. 9700. 3 In 98 Rupeos of Bengal, how many cents ?

Ang. Mso.

VULGAR YRACTIONS. HAVING briefly introduced Vulgar Fractions imme diately 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 + is, &c.

2. An Improper Fraction, is when the numerator exceeds the denominator, as *, &c.

3. A Compound Fraction, is the fraction of a fraction, coupled by the word of, thus, of t, of of #, &c.

4. A Mixed Number, is composed of a whole number and a fraction, thus, 8}, 1412, &c.

5. Any whole number may be expressed like a fraction by drawing a line under it, and putting 1 for denominator, thus, 8=, 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 cominon multiple : and if it be the least number that can be so measured, it is called the least common multiple: thus, 24 is the coinmun multiple of 2. 3 aud 4; but their least coinmon multiple is 12.

To find the least common multiple of two or more numbers.

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 Knes as before, and so on til There are no two numbers that can be divided; then the

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