Daboll's Schoolmaster's Assistant, Improved and Enlarged

But to reduce cents into rials of plate, divide by 10 Thus, 845 cents÷-10-84,5-84 rials, 17 marvadies, &ca VII. OF PORTUGAL.

Accounts are kept throughout this kingdom in milreas, and reas, reckoning 1000 reas to a milrea.

NOTE. A miirea 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 540 milreas how many cents?

640X12442160 cents,=$421, 60cts. Ans.

2. In 211 milreas, 48 reas, how many cents? Norn-When the reas are less than 100, place a cypher before them. Thus, 211,048×124-26169,952 or 261 dols. 69 cents, 9 mills. + Ans.

cts.

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

rens.

EXAMPLES.

1. In 4195 cents, how many milreas ?

4195÷124=35,850+ or $3milr. 830reas. Ans. 2. In 24 dols. 92 cts. how many milreas of Portugal P Ans. 20 milreas, 096 reas.

VIII. EAST INDIA MONÉY.

To reduce india honey to Federal, viz.

Tales of Cina, multiply with

Pagodas of India,

Rupee of Bengal,

EXAMPLES.

148

194

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

Ans. 94868

2. In 50 Pagodas India, how many cents?

Ans. 9700

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

Ans. 5439

VULGAR FRACTIONS.

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 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, as † 1†, 16. &c. 2. An Improper Fraction, is when the numerator exceeds the denominator, as ¥, 8 7 12, &c.

3. A Compound Fraction, is the fraction of a fraction, coupled by the word of, thus, of 12, of 3 of 1, &c. 4. A Mixed Number, is composed of a whole number and a fraction, thus, 8, 14, &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, 12, &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 50; 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, 3 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 beneath.

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

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

EXAMPLES.

1. What is the least common multiple of 4, 5, 6 and 10 ? Operation, X5)4 5 6 10

X2)4 1 6 2

X2 1x3 1

5X2X2XS=60 Ans.

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

Ans. 24

5. 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 terms of the fraction by the common measure, and the quotients will make the fraction required.

*Fo 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 measure last found be the answer.

ORIf you choose, you may take that easy method in Problem I. (page 74.)

EXAMPLES.

1. Reduce 48 to its lowest terms.

48) 18 (1

0848/6

48 Rem.
00

Operation.

common mea. 8)8- Ans.

2. Reduce to its lowest terms. 3. Reduce 182 to its lowest terms.

4. Reduce 3798 to its lowest terms.

7596

CASE II.

Ans.

fins. 13 Ans.

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.

EXAMPLES.

1. Reduce 45 to its equivalent improper fraction.

45x8+7=367 Ans. 2. Reduce 1912 to its equivalent improper fraction.

3. Reduce 161, to an improper fraction.

Ans. 356

Ans. 1618 100

4. Reduce 61 to its equivalent improper fraction.

360

CASE IN.

Ans. 22085

380

To find the value of an improper fraction.