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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 69. 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 , , 3, 4, &c. 2. An Improper Fraction, is when the numerator ex *eeds the denominator, as , , ,”, &c. 3. A Compound Fraction, is the fraction of a fraction, oupled by the wood of, thus, of so, of 3 of , &c. 4. A Mired Number, is composed of a whole number and a fraction, thus, Sł, 14", &c. 5. Any whole number may be expressed like a fraction by drawing a line under it, and putting 1 for denominator, thus, 8–1, and 12 thus, a, &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 leas common multiple: thus 24 is the common multiple 2, 3 ane 4; but their least common multiple is 12. To find the least common multiple of two or more num

bers.

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

2. Divide the second lines as before, and so on till there are no two numbers that can be divided; then the continued product of the divisors and quotients, will give the multiple required.

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| 44 nEDUCTION OF volcan Faactions.

Ex-------

1. What is the least common multiple of 4,5,6 and 101 Operation, ×5)4-5-6 10

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5x2x2 x3–60 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 WULGAR 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 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.

* 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 unmbers, and so on through all the numbers to the last; then will the greatest common mea sure lost found be the answer

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145 Re-LUCTION or vuluan Fra A.C.T.u.Ns. 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.

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

12. Ans. ** 3. Reduce 100 to its equivalent fraction, having 90 for a denominator. Ans. ****=***=" to CASE W.

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 numerator. and all the denominators for a new denominator; and they will form * sinction required.

Ex-MPLEs. 1. Reduce of 3 of , of on to a simple fraction 1 x2 x3 × 4 —=*-* Ans. 2x3 × 4 × 10 2. Reduce 5 of of to a single fraction. Ans. * 3. Reduce of of 18 to a single fraction.

Ans, too, 4 Reduce of ; of 8 to a simple fraction. Ans. *=34 5. Reduce : of 13 of 42+ to a simple fraction. Ans. *****=21 to *** -—If the denominator of any member of a com * * *ction be equal to the numerator of another mem.

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