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In the tenth Example, the Anfwer is 2 Feet, 1 Inch, and 2 Quarters, or 1 Half; or exactly 2 Feet, 1 Inch, 2 Quarters, and of Quarter of an Inch. In the eleventh Example, the Answer is I Foot, I Inch, and of 1 Quarter of an Inch. And, in the twelfth Example, the Answer is 8 Inches, I Quarter, and of 1 Quarter of an Inch.

And, in general, to find the Value of any Vulgar Fraction, is only to multiply the Numerator into the feveral Denominations that compofe the Integer of which the Fraction is a Part, beginning with the Denomination which comes next to the Integer, and dividing by the Denominator, as in the foregoing Examples, which will give the Value fought.

When the Value of an improper Fraction is required, divide the Numerator by the Denominator, and the Quotient will be Integers, and is the true Value, if there is no Remainder; if there is any Remainder, multiply it, and divide by the Denominator, as before taught, by which Means we shall have the Value of the improper Fraction.

Find the Value of the following Fractions of a Pound Sterling. Exam. 2. Of.

Exam. 1. Of 27.

8) 27 (31.

24

3

20

9) 34 (31.

27

7

20

Exam. 3. Of.. 7) 13 (17.

7

6

20

7) 120 (17 s.

7

50

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Exam. 1. The Numerator 27 being divided by 8 gives 3 in the Quotient, which is 3 Pounds; after this the Operation is the fame as before; and fo we find the improper Fraction? of a Pound, is 31. 7 s. 6d.

And fo of the other two Examples; where, in the Answers, the Remainders 2 and 6 are neglected.

If the Value of a compound Fraction is required, reduce it to a fimple Fraction, by Art. 3, and then proceed as before taught.

Required the Value of the following Fractions.

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Anfwer 1 F. 6 Inch.

The compound Fraction is reduced to the fimple Fraction by Art. 3; afterwards its Value is found as before taught, and is 35. 9d. Which is fhewn to be the true Value thus: The eighth Part of a Pound is 2s. 6d. whence three Eighths are 7 s. 6d. but the one Half of 7 s. 6d. is 3s. 9d. as in the Answer. And, as to the other Example, the two Thirds of a Yard are 2 Feet, but the three Fourths of 2 Feet are 18 Inches, or 1 F. 6 Inch. as before found.

The great Variety in Vulgar Fractions makes them appear with fome Difficulty to a Learner; but I would not have him

be

be difcouraged, if he does not at firft remember every Rule; it will be fufficient, for his prefent Purpose, if he fees how the Operation is performed by the Rule, for then he will quickly recover the Manner of any Operation by having Recourfe to the Directions.

Article 36. To reduce a Fraction to its lowest Terms.

Rule. Divide the Denominator by the Numerator; if any Thing remains, divide the Numerator by the Remainder; and, if any Thing yet remains, divide the laft Divifor by fuch Remainder, 'till nothing remains; then is that Divifor the greatest common Measure which will divide both the Numerator and the Denominator without a Remainder. By the common Measure fo found divide the Numerator, and the Quotient is a new Numerator; then divide the Denominator by the fame Number, and the Quotient is a new Denominator; and this new Fraction is equal to the given Fraction.

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189) 513 (2

Exam. 2. Reduce to its lowest Terms,

27) 189 (7 a new Numerator.

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Exam. 1. The Denominator 315 being divided by the Numerator 252, there remains 63; by which divide the Divifor 252, and nothing remains; therefore 63 is the common Measure fought: Then divide the Numerator 252 by this common Measure 63, and the Quotient is 4, for the new Numerator; and dividing the Denominator 315 by the fame 63, the Quotient is 5, for a new Denominator: So is the Fraction equal to 3, the loweft Terms to which it can be reduced.

252

Exam. 2. The Denominator 513 being divided by the Numerator 189, the Remainder is 135; by which divide the Divifor 189, and there remains 54; and dividing the laft Divifor by 54, there remains 27; then divide the last Divifor 54 by 27, and there remains nothing: Therefore 27 is the greatest common Measure; by which divide the Numerator 189, and the Quotient is 7, for the new Numerator; and dividing 513 the Denominator by the fame 27, the Quotient is 19: Therefore, is the lowest Terms of the given Fraction.

The third Example is done in the fame Manner; only as the fecond Divifion, not having any Remainder, fhews, that the Divifor 57 is the common Measure; and, as the Dividend was the Numerator, it was not neceffary to divide the Numerator again by it, as is done in the firft Example, fince it might there have been omitted: Whence 3 is the new Numerator; and dividing 399 by 57, it gives 7 for a new Denominator: And fo is reduced to its lowest Terms.

Exam. 4.

Exam. 4. Reduce 33 to its loweft Terms.

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But if, in dividing to find a common Measure, the Remainder happens to be an Unite, then the Fraction is already in its lowest Terms.

There are other Methods of reducing Fractions to their lowest Terms: For if the Numerator and Denominator of a Fraction have each one or more Cyphers on the right Hand, the fame Number of Cyphers in the Numerator and Denominator may be cut off, and the remaining Fraction will still be of equal Value: Thus, in the first Example of Art. 35, is the fame with, the taking away the Cyphers not altering the Value of the Fraction. So again, in the fourth Example

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