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

I.- OF GREAT BRITAIN.

O 10
1 24
1 48
1 94
0 55

EXAMPLES.

4

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

A pound sterling being=444 cents, Therefore-As 1l. : 444 cts. : : 45,5l. : 20202 cts. Ans.

2. In 500 dollars how many pounds sterling? ds 444 cts. : 1l. : : 50000 cts. : 1121. 12s. 3d. t. Ans.

II.-OF IRELAND.

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

11. Irish=410 cts. £. cts. £.

cts.

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

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

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

12 deniers, or pence, make I sol, or shilling. 120 sols, or shillings, I livre, or pound.

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

1 livre of France =184 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. As 185 : 1:.: 87457 : 472 14 9+ Ans.

IV._OF THE U. NETHERLANDS. Accounts are kept here in guilders, stivers, groats and hennings.

8 phennings make i groat.
2 groats

1 stiver.
20 stivers

I guilder or dorin.
A guilder is=39 cents, or 390 mills.

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EXAMPLES.

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m.

mills.

Reduce 124 guilders, 14 stivers, into federal money:
Guil. cts. Guil.

d.
As 1 : 39 :: 124,7 : 48, 6 3 3 Ans.
mills. G.

G.
As 390 : 1 :: 48633 : 124,7 Proof.
V.-OF HAMBURGH, IN GERMANY.
Accounts are kept in Hamburgh in marks, sous and de-
(s-lubs, and by some in rix dollars.

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

I mark-lubs.
3 mark-lubs, I rix dollar.
Ilote. A mark is 334 cts, or just 4 of a dollar.
KULE.--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. vadies.

34 marvadies of plate make 1 rial of plate.
8 rials of plate

1 piastre or piece of 8. To reduce rials of plate to federal money. Since a rial of plute is 10 cents or 1 dime, you need only call the rials so many dimes, and it is done.

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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 me and reas, reckoning 1000 reas to a milrea.

NOTE.—A milrea is 124 cents; therefore to r race milrcas into federal money, multiply by 124, and th pro: duct will be cents, and decimals of a cent.

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EXAMPLES.

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1. In 340 milreas how many cents ?

340 x 124=42160 cents=$421, 60 ct Ins. 2. In 211 milreas, 48 reas,

how many

cents ? NOTE:-When the reas are less than 100, place i cipher before thein.—Thus, 211,048 x 124=26169,952 ct . or 261 dols. 69 cts. 9 mills. + Ans.

But to reduce cents into milreas, divide them by J24; 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-tor 33 milreas, 830 rcas. 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,

55) EXAMPLES.

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

1

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

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

Ans. 5430

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SULGAR FRACTIONS. HAVING briefly iytroduced Vulgar Fractions iume 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

69. Vulgar Fractions are either proper, improper, sing.c, compound, or mixed.

1. A single, simple, or proper fraction, is when the nu. nicrator is less than the denominator, as į á, , , &c.

2. An Improper Fraction, is when the numcrator ex occds the denominator, as $, , ,

3. A Compound Fraction, is the fraction of a fraction, coupled by the word of, thus, i of ta, į of jy of , &c.

4. A Mixed Number, is composed of a whole nuinber and i fraction, thus, 8!, 14,', &c. 1-5. Any whole number may be expressed like a fraction by drawing a line under it, and putting 1 for denominator, thus, S=1, and 12 thus, ?, &c.

6. The common measure of two or more numbers, is that number which will divide each of them without a rcmainder; thus, 3 is the cominon measure of 12, 24, and 30; and the greatest mmber 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 leas common multiple : thus 24 is the common multiple 2, 3 ani 4; but their least common multiple is 12.

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

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

2. Divide the second lines as before, and so on till there aro no two numbers that can be divided; then the continued product of the di. visors and quotierits, will give tlic multiplo required.

EXAMPLES.

1. What is the least common multiple of 4, 5, 6 and 101

Operation, x 5)4 5 6 10

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5x2x2x3=60 Ans. 2. What is the common multiple of 6 and 8?

Ans. 24. 3 What is the least number that 3, 5, 8 and 12 wil measure ?

Ans. 120. 4. What is the least number that can be divided by the 9 digits separately, without a remainder? Ans. 2520.

REDUCTION OF VULGAR FRACTIONS,

IS the bringing them out of one form into another, in or der to prepare them for the operation of Addition, Sul, traction, &c.

CASE I.

To abbreviate or reduce fractions to their lowest terms.

RULE.-1. Find a common measure, by dividing the greater term by tho less, and this divisor by the remainder, and so on, always dividing the last divisor by the last remainder, till nothing remains ; the last divisor is the cominon measure.*

2. Divide both of the terms of the fraction by the common mea. euro, and the quotionts will make the fraction required.

* To find the greatest common measure of more than two numbers, you must find the greatest common measure of two of them as per rule above; then, of that common measure and one of the other numbers, and so on through all the numbers to the last; then will the greatest common mea our last found be the answer.

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