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

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

Note.A milrea is 124 cents; therefore to reluce ilreas into Federal Money, multiply by 194, and the oduct will be cents, and decimals of a cent.

EXAMPLES, 1. In 340 milreas how many cents ?

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

how

many cents ? Note. When the reas are less than 100, place a cy. er before them.-Thus 211,048 X124=26169,952cts. 261 dols. 69 cts. 9 mills. + Ans. But to reduce cents into milreas, divide them by 124 ; d if decimals arise you must carry on the quotient as - as three decimal places; then the whole numbers ereof will be the mịlreas, and the decimals will be the

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1. In 4195 cents, how many milreas ?

4195=12433,830+or 33 milreas, 330 reas. Ans.
2. In 24 dols. 92 cts. how many milreas of Portugal ?

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.

. In 641 Tales of China, how many cents ?

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

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

Ans. 5439.

to

8 7

, &c.

VULGAR FRACTIONS. HAVING briefly introduced Vulgar Fractions imm diately after reduction of whole numbers, and given som general definitions, and a few such problems therein a were necessary

prepare

and lead the scholar immed ately to decimals; the learner is therefore requested t 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 nu merator is less than the denominator, as 1 2 , &c.

2. An Improper Fraction, is when the numerator ex geeds the denominator, as

S. A Compound Fraction, is the fraction of a fraction coupled by the word of, thus, of jy i of of *, &c.

4. A Mixed Number, is composed of a whole number and a fraction, thus, 81, 1470, &c.

5. Any whole number may be expressed like a fraction by drawing a line under it, and putting 1 for denominator, thus, 85, 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 2, S and 4; but their least common 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 beileath.

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

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ntinued product of the divisors and quotients, will give
e multiple required.
1. What is the least common multiple of 4, 5, 6 and 107
Operation, X5)4 5 6 10

EXAMPLES.

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5 X 2X2 X3=60 Ans. 2. What is the least common multiple of 6 and 8?

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

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

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REDUCTION OF VULGAR FRACTIONS, IS the bringing them out of orie form into another, in ler to prepare them for the operation of Addition, Subction, &c.

CASE I. o abbreviate or reduce fractions to their lowest termis.

RULE. 1. Find a common measure, by dividing the greater in by the less, and this divisor by the remainder, and art, always dividing the last divisor by the last remain-, till nothing remains ; the last (livisor is the common 2. Divide both of the terins of the fraction by the comn ineasure, and the quotients will make the fraction uired.

astre. *

1 que

To find the greatest cominon measure of more than two nbers, you must find the greatest common measure of

of them as per rule above: then, of that common meae and one of the other numbers, and so on through all the abers to the last, then will the greatest common mcasurç found be the answer

56

48

Ans. 35
Ans. 1 3

Or, If you chuse, you may take that easy method in
Problem I. (page 74.)

EXAMPLES.
1. Reduce to its lowest terms.

Operation.
05486

common mea. 8*= Ans.

Rein.
2. Reduce 12 to its lowest terms.
3. Reduce 182 to its lowest terms.
4. Reduce, 3798 to its lowest terms. Ans.

CASE II.
To reduce a mixed number to its equivalent improper

fraction.

RULE. Multiply the whole number by the denominator of the given fraction, and to the product add the numerator, this sum written above the denominator will form the fraction required.

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EXAMPLES.

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1. Reduce 453 to its equivalent improper fraction.

45x8+7=357 Ans. 2. Reduce 1974 to its equivalent improper fraction.

Ans. 354 3. Reduce 16118 to an improper fraction.

Ans. 1618
4. Reduce 614to its equivalent improper fraction.

Ans. 22085
CASE III.
To find the value of an improper fraction.

RULE.
Divide the numerator by the denominator, and the
quotient will be the value sought.

EXAMPLES. 1. Find the value of 48

5)48(9; Ans. 2. Find the value of 35.4

Ans. 1913 S. Find the value of 933

Ans. 845 4. Find the value of 2208.5

Ans. 611 5. Find the value of 72

Ans, 8

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CASE IV.
To reduce a whole number to an equivalent fraction, hav

ing a given denominator.

RULE. Multiply the whole number by the given denominator ; place the product over the said denominator, and it will form the fraction required.

EXAMPLES. 1. Reduce 7 te a fraction whose denominator shall be 9.

Thus, 7x9=63, and the Ans. 2. Reduce 18 to a fraction whose denominator shall be 12.

TZ 3. Reduce 100 to its equivalent fraction, having 90 for a denominator.

Ans. 998°='60=100

CASE V.
To reduce a compound fraction to a simple one of equal

value.

RULE. 1. Reduce all whole and mixed numbers to their equiva. lent fractions.

2. Multiply all the numerators together for å new numerator, and all the denominators for a new denominator; and they will form the fraction required.

Ans, 21.6

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EXAMPLES.

288

1. Reduce } of of of mo to a simple fraction i

1x2x3X4

== Ans.

2X3 X4X10 2. Reduce of of to a single fraction. Ins. 7. S. Reduce of il of 1 to a single fraction .

115, 836

1500 4. Reduce of of 8 to a simple fraction.

Ins. 1=S! 5. Reduce 6 of 11 42} to a simple fraction.

Ans. 12699 Note. If the denominator of any member of a Ci....o pound fraction be equal to the numerator of another 2011

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