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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.

EXAMPLES.

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 x 20 20 X 60 X 40 = 48000 50 60

40 Ans. 40 24 x 50

1200 2. If 50 lb. at New-York make 45 at Amsterdam, and 80 lb. at Amsterdam make 103 at Danızic; how many lb. at Dantzic are equal to 240 at N York ?

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

ins. 110.

Ans. 27870

EXCHANGE. By this rule merchants know what sun of meney 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 moreys of foreign nations to that of the United States, you may consult the following

TABLE: Showing the value of the moi eys of .ccount, of foreign nations, estimated in futral money.*

$ cts. Pound Sterling of Great-Britain,

4 44 Pound Sterling of Ireland,

4 10 Livre of France, Guilder or Florin of the U. Netherlands, 0 39 Mark Banco of Hamburgh,

033 Rix Dollar of Denmark,

* Lazos U. S. A,

0 18}

1

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

I, OF GREAT BRITAIN.

0 10 1 24 1 48 1 94 0 557

EXAMPLES.

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

A pound sterling being=444 cents, Therefore-As il. : 444cts. : : 45,5l. : 20202cts. An.

2. In 500 dollars how many pounds sterling ? As 444cts. : 11. : : 50000cts. : 1121. 12s. 3d. + Ans,

II. OF IRELAND.

EXAMPLES.

1. In 901. 10s. 6d. Irish money, how many cents ?

11. Irish =410cts. £. cts. £.

cts. $ cts. Therefore--As 1 : 410 : : 90,525 : 371151=371, 151

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

III. OF FRANCE.
Accounts are kept in livres, sols and deniers.
S 12 deniers, or pence, make 1 sol, or shilling,
220 sols, or shillings, 1 livre, or pound.

EXAMPLES.

m.

m.

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

1 livre of France=18} cts. or 185 mills.
£.
£.

$ cts. m. 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, groats and phennings.

8 phennings make 1 groat.
2 groats

1 stiver.
20 stivers

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

EXAMPLES.

C.

m.

:

Reluce 124 guilders, 14 stivers into federal money.

Guil. cts. Guil.
As 1 39 : : 124,7 :

48, 6 3 3 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 and
eniers-lubs, and by some in rix doilars.

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

3 mark-lubs, 1 rix-dollar NOTE.--A mark is a 33} cts. or just } of a dollar,“

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

EXAMPLES.

Reduce 641 marks, 8 sous, to federal money.

3)641,5

$213,833 Ans. But to reduce federal Money into Marks, multiply the gix en sum by 3, &c.

EXAMPLES.

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

3

365,7v=365 marks 11 sous, 2,4 den. Ans.

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

$ 34 marvadies of plate make 1 rial of plate.
28 rials of plate

1 piastre or piece oi 8. 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. 50 cts. &c.

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

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

NOTE.-A milea is = 124 cents ; therefore to reduce milreas into Federal Money, multiply by 124, and the pro duct will be cents, and decimals of a cent.

EXAMPLES. 1. In 340 milreas how many cents ?

340x124=42160 cents=$421, 60cts. Ans. 2. In 211 milreas, 48 reas, how many cents ?

NOTE.—When the reas are less than 100, place a ci pher before them.—Thus, 211,048X124=26169,952 cts, or 261 dols. 69 cts. 9 mills. + 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.

EXAMPLES.

1. In 4195 cents, how many milreas ?

4195*124=33,830 +or 33 milreas, 830 reas. Ans 2. In 24 dols. 92 cents how many milreas of Portugais

Ans. 20 milreas, 096 reas.
VIII. EAST-INDIA MONEY.
To reduce India Money to Federal, 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. 94068 2. In 50 Pagodas of India, how many cents ?

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

Ans. 5499

VULGAR FRACTIONS. HAVING briefly introduced Vulgar fracti uns immeiately after reduetion of whole numbers, and given some eneral definitions, and a few such problems therein as "vere necessary to prepare and lead the scholar immediately o decimals ; the learner is therefore requested to read thuse eneral definitions in page 74.

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

1. A single, simple, or proper fraction, is when the nu gerator is less than the denominator, as } . &c.

2. An Improper Fraction, is when the numerator exeeds the denominator, as 4, &c.

3. A Compound Fraction, is the fraction of a fraction, oupled by the word of, thus, of i'u of of, &c.

4. A Mixed Number, is composed of a whole number nd a fr.ction, thus 8., 14 fe, &c. 5. Ary whole number

may be expressed like a fraction y drawing a line under it, and puiting 1 for denominator, aus, 8=\, and 12 thus, 1, &c.

6. The common measure of two or more numbers, is jat number which will divide each of them without a relainder ; thus, 3 is the common measure of 12, 24, and 0; and the greatest number which will do this is called the reatest common measure.

7. A number, which can be measured by two or more umbers, is called their common multiple : and if it be the ast number that can be so measured, it is called the least ommon multiple: thus 24 is the common multiple of 2, 3 ad 4 ; but their least common multiple is 12.

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

RULE. 1. Divide by any number that will divide two or more f the given numbers without a remainder, and set the

uotients, together with the undivided numbers, in a line Jeneath.

2. Divide the second lines as before, and so 2 lere are no two nunibers that can be divided ; then the

on till

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