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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 milrea 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?

340×124=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, 211,048×124-26169,952 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, 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 Portuga Ans. 20 milreas, 096 reas.

VIII. EAST-INDIA MONEY.

To reduce India Money to Federal, viz.

Tales of China, multiply with

Pagodas of India,

Rupee of Bengal,

EXAMPLES.

148

194

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

55

Ans. 94568

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 fractions 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 those eneral definitions in page 74.

H

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

1. A single, simple, or proper fraction, is when the nu aerator is less than the denominator, as ¦ ¦ §. &c.

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

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

4. A Mixed Number, is composed of a whole number nd a fraction, thus 81, 141⁄2, &c.

5. Any whole number may be expressed like a fraction y drawing a line under it, and putting 1 for denominator, hus. 8, and 12 thus, 12, 12, &c.

6. The common measure of two or more numbers, is hat number which will divide each of them without a reainder; 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 mmon multiple: thus 24 is the common multiple of 2, 3 nd 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 eneath.

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

continued product of the divisors and quotients, will the multiple required.

EXAMPLES.

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

×5)4 5 6 10

×2)4 1 6 2

X2 1x3 1

5×2×2×3=60 Ans.

2. What is the least common multiple of 6 and 8 .

Ans. 2

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

4. What is the least number that can be divided the 9 digits separately, without a remainder? Ans. 252

REDUCTION OF VULGAR FRACTIONS,

IS the bringing them out of one form into anothe order to prepare them for the operation of Addition, traction, &c.

CASE I.

To abbreviate or reduce fractions to their lowest ter

RULE.

1. Find a common measure, by dividing the g term by the less, and this divisor by the remainder, a on, always dividing the last divisor by the last rema till nothing remains; the last divisor is the common

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2. Divide both of the terms of the fraction by the mon measure, and the quotients will make the fracti quired.

*To find the greatest common measure of more than two numb must find the greatest common measure of two of them as per rule then, of that common measure and one of the other numbers, an through all the numbers to the last; then will the greatest commo ure last found be the answer.

OR, you choose, you may take that easy method in

Problem I. (page 74.)

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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.

EXAMPLES.

1. Reduce 451 to its equivalent improper fraction. 45X8+7-367 Ans 2. Reduce 191 to its equivalent improper fraction.

3. Reduce 16 to an improper fraction.

18 100

Ans. 35

19

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4. Reduce 611 to its equivalent improper fraction.

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.

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CASE IV.

To reduce a whole number to an equivalent fraction, having 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.

12.

EXAMPLES.

1. Reduce 7 to a fraction whose denominator will be 9 Thus, 7×9=63, and 3 the Ans. 2. Reduce 18 to a fraction whose denominator shall be

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

Ans. 9000

CASE V.

90

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To reduce a compound fraction to a simple one of equal

value.

RULE.

1. Reduce all whole and mixed numbers to their equ.valent fractions.

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

EXAMPLES.

1. Reduce of of of to a simple question.

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2. Reduce of of to a single fraction. Ans. 3. Reduce of of to a single fraction.

4. Reduce of of 8 to a simple fraction.

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Ans. 120=31

5. Reduce of 12 421 to a simple fraction.

0

36

Ans. 1388-21% NOTE. If the denominator of any member of a com pound fraction be equal to the numerator of another mem

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