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Of Algebżalck Fractions, or Broken Duantitics.

Sect. 1. Notation of Fractional Quantities.

Raftional Quantities are expressed or fet down like Vulgar Fractions in common Arithmetick.

Th..sa 2 bc5b-4a Numerators.

Dus I To ď: 4d +77 Denominators. How they come to be fo, fee Cafe 4, in the last Chapter of Divison. These Fractional Quantities are managed in all re: Spects like Vulgar Fractions in Common Arizhmetick. Y 2

Scet.

Sect. 2. To alter or Change different fractions into

one Denomination, retaining the same Value,

RUL E. G U LTIPLY all the Denominators into each other for a

V new Denominator, and each Numerator inte all the Denominators but it's own for new Numerators.

E X A M P L ES.
Let it be required to bring and into one Denomination.

First a xc, and d x b, will be the Numerators, and b xc will be the common Denominator, viz.com and are the two Fractions required : that is, te , and be

btc Again, let and be brought in one Denomination,

bd
, 6b+bc-bd-dc ,adactbdbc

and they will be bat-bb-da-be

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Sect. 3. To Bring whole Duantities into fractions

of a given Denomination.

RUL E.
MULTIPLY the whole Quantities into the given Dena-

VW nominator for a Numerator, under which subscribe the given Denominator, and you will have the Fraction required.

E Y A M P L E S. Let it be required to bring a tob into a Fraction, whose Denominator is d - A. First a +bxd--a is datbd-a b a:

Denominazominator for a Newhole Quantities

datbd--aaba is the Fraction required. Thendra

Again b ta will be 00:42. Andant - a will be a cada

aatbb Allo a tota

200

Will be

When

When whole Quantities are to be set down Fraction-wife, subscribe an Unit for the Denominator. Thus ab is -, And aabb, is a 4 B5, &c.

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Sect. 4. To abbreviate, or Reduce Fractional Quantities into their lowest Denomination.

RUL E. Dlvide both the Numerator and Denominator by their greatest

common Divisor, viz. by such Quantities as are found in both; and their Quotients will be the Fraction in it's lowest Term.

аас, aa abbb. Bb . . bac Thusis do " abc "T

+7 =atd.. In such single Fractions as these, the common Divisors (if there be any) are easily discovered by Inspection only; but in compound Fractions it often proves very troublesome, and must be done either by dividing the Numerator by the Denominator, until nothing remains, when that can be done : or else finding their common Measure, by dividing the Denominator by the Numerator, and the Numerator by the Remainder, and so on, as in Vulgar Fractions (Sect. 4. Page 51.)

É X Å MP LE S. a acaad Suppose nd were to be reduced lower.

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Hence it appears that - 2 a ab- 2 abb is the common Measure; by which a aa-abb being divided.

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a

Viz. — 2 a ab- 2 abb) a aa-abb (-4 I

aaa taab 277

aab-abb -aabab b

Oo Then this the new Numerator ; and 67 - is the new Denominator. But + ==20 = 'the Numerator; and

- 2026 ==

4 ba = = the Denominator. Let both be multiplied with 2 ba,

zba and you will have a

-amb the Denominator.

waarab the Signs of all the Quantities, it will be

the new Frace:

ato

aa a b aaa — abь tion required. That is,

atba a + 2ab +66.

da bb Again, let it be required to reduce

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a a tab the Numerator.

Or changing

The common Measure of this Fraction will be the easiest found (as appears from Trials) by dividing the Denominator by the Numerator, &c. Thus,

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Hence it appears that bdbb is the common Measure that will divide both the Numerator and the Denominator.

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