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

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

Note.-A miirea is 124 cents ; therefore to reiluce .nilreas 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 ?

340x12442160 cents,=8421, 60cts. Ans. 2. In 211 milreas, 48 rcas,

how NotE.When the reas are less than 100, place a cy. wher before them.—Thus 211,048x124=26169,952cts. 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 he tho

many cents ?

reas.

EXAMPLES.

1. In 4195 cents, how many milreas ?

4195+124–33,830+or 33 milreas, 330 reas. Ans. %. In 24 dols. 92 cts. how many milreas of Portugal

Ans. 20 milreus, 096 reas.
VIII. EAST-INDIA MONEY.
To reduce India Money to Federa., viz.
Tales of China, multiply with

148
Pagodas of India,

194 Rupee of Bengal,

554 EXAMPLES 1:1641 Tales of China, how many cents ?

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

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

Ang. 5439.

VULGAR PRACTIONS. HAVING briefly introduced Vulgar Practions immo. 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 immedi. ately to decimals; the learner is therefore requested to 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 numerator is less than the denominator, asi , &c.

2. An Improper Fraction, is when the nunierator exceeds the denominator, as *, &c.

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

4. A Nixed Namber, is composed of a whole number and a fraction, thus, 84, 147, &c.

5. Any whole number may be expressed like a fraction by drawing a line under it, and putting 1 for denominator, thus, 8=, and 12 thus, Y, &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 coinmun multiple of 2, 3 and 4; but their least coinmon 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 beneath.

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

continued product of the divisors and quotients, will give the 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 2 X 2 X 3=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 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 order to prepare them for the operation of Addition, Subtraction, &c.

CASE I. To abbreviate or reduce fractions to their lowest terms.

RULE. 1. Find a common measure, by dividing the greater term by the 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 common measure. *

2. Divide both of the teries of the fraction by the com. mon measure, and the quotients will make the fraction required.

* To find the greatest cominon ceasure 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 bunabers to the last, then will the grcatest common measure Ast found be the answer

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OR, It you chuse, you may take that easy metod in Problem 1. (page 74.)

EXAMPLES.
1. Reduce to its lowest terms.

Operation.
common mea. 8) = Ans.
**
2. Reduce to its lowest terms.

Ans. 3 3. Reduce 18 to its lowest terms. Ans. is 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.

LXAMPLES: 1. Reduce 451 to its equivalent improper fraction.

45 X8+7=7 Ans. 2. Reduce 1911 to its equivalent improper fraction. 3. Reduce 1610 ta an improper fraction.

Ans. 1613 4. Reduce 6136 to 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 18

5)48(93 Ans. 2. Find the value of 35.4

Ans. 19H 3. Find the value of 933

Ans. 844 # Jinri the value of 2005

Ans. 6114 360 sind the value of a

Ans. ***

360

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

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.

900

1. Reduce 7 to a fraction whose denominator shall be 9.

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

Ans. 216 3. Reduce 100 to its equivalent fraction, having 90 for #denominator.

Ans. 9200

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 a new nu. merator, and all the denominators for a new denominator; and they will form the fraction required.

EXAMPLES.

1. Reduce $ of off of fo to a simple fraction

1X2 X3 X4

==to Ars,

2X3X4X10 % Reduce of of to a single fraction. Ans. 10 3. Reduce of jj of jf to a single fraction. .

Ans. 336 4. Reduce off of 8 to a simple fraction.

Ans. 120

St .5. Reduce of 1; 42} to a simple fraction.

Ans. 12660 =2116 Note.--If the denominator of any member of a compound fraction be equal to the numerator of another mem

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