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

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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
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 Dantzic ; how mang lb. at Dantzic are equal to 240 at N. York ? Ans. 278,6

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

Ans. 110.

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

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

TABLE: Showing the value of the moneys 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,

0 39 Mark Banco of Hamburgh,

5 0 33 Rix Dollar of Denmark,

1 0

* Laws U. S, A.

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

1.- OF GREAT BRITAIN.

0 10 1 24 1 43 1 94

0 55)

EXAMPLES.

1. In 451. 10s. sterling, how many dollars and cents ?

A pound sterling being=444 cents, Therefore-As 11. : 444 cts. : : 45,51. : 20202 cts. Ans.

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

II.-OF IRELAND,

: EXAM'LES. 1. In 901. 10s. 6d. Irish money, how many cents ?

11. Irish=410 cts. £. cts. £.

cts. $ cts. Therefore--As 1 : 410 : : 30,525 : 37115!=371, 151

2. In 168 dols. 10 cts. how many pounds Irish? As 410 cts. : 11. : : 16810 cts. : £41 Trish. Ans.

III.-OF FRANCE.
Accounts are kept in livres, sols and deniers.

12 deniers, or pence, make l sol, or shilling.
20 sols, or shillings, 1 livre, or pound.

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

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

£.

m.

Octs, m. As): 185 : : 259,1 : 46324 46 32 4 Ans. 2. Keduce 87 dols. 45 cts. 7 m. into livres of France,

mills. liv, mills. liv. 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 croats

I stiver.
20 stivers

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

m.

sn. den.

EXAMPLES.

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:

Reduce 124 guilders, 14 stivers, into federal money.

Guil. cts. Guil. $ d.
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 de
niers-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 mark is = 331 cts. or just of a dollar. RULE.—Divide the marks by 3, the quotient will be 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 given sum by 3, &c.

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

3

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

VI.OF SPAIN.
Accounts are kept in Spain in piastres, rials, and mar-
Tadies.

| 34 marvadies of plate 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. 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 milrea.

Note.-A mirea is 124.cents; therefore to reduce 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=$421, 60 cts. Ans. 2. In 211 milroas, 48 reas, how many cents ?

NOTE.When the reas are less than 100, place a cipher before them.--Thus, 211,048 x 124=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, aud 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 Portual?

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,

554 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 Ropees of Bengal, how many cents ?

Ans, 5439

VULGAR FRACTIONS.

8 7
3) 55

HAVING briefly introduced Vulgar Fractions immediately 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 69.

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 s, i, j, 2,

1, , , &c. 2. An improper Fraction, is when the numerator exceeds the devoninator, as

4. &c. 3. A Compound Fraction, is the fraction of a fraction, coupled by the word of, thus, ofia, of jof?, &c.

4. A Mixed Number, is composed of a whole number and a fraction, thus, 37, 141, &c.

5. Any whole number may be expressed like a fraction by drawing a line under it, and putting 1 for denominator, thus, 8=i, and 12 thus, ?,

12, e. 6. The cominou measure of two or more vumbers, is that number which will divide each of them without a remainder; thus, 3 is the common measure of 12, 21, 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 multi-le 2, 3 and 4; but their least commou inultiple is 12.

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

Rule.-). Divide by any number that will divide two or more of die given vumbers without a remainder, and sct 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 continued product of the die visors and quotients, will give the multiple required.

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