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Denominator of the Quotient: Therefore is the Quotient fought.

Exam. 2. Multiplying 4 the Denominator of the Divifor by 1 the Numerator of the Dividend, it makes 4, for the Numerator of the Quotient; and 3 the Numerator of the Divifor multiplied by 2 the Denominator of the Dividend is 6, for the Denominator of the Quotient: So that the Quotient here is.

The Learner will probably obferve, that, as the Product in Multiplication was lefs than either of the given Fractions, the Quotient in Divifion is greater than either of the given Fractions. The Reafon is the fame; for every Divifion is a geometrical Proportion, or Rule of three; that is, as the Divifor is to 1, fo is the Dividend to the Quotient: If, therefore, the Divifor, or first Term, is less than 1 (as all proper Fractions are) then muft the Dividend be less than the Quotient.

Article 31. To divide compound Fractions and fimple Fractions.

Rule. Reduce the compound Fraction to a fimple Fraction; then proceed as at Art. 30.

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Exam. 1. The compound Fraction

of, reduced by

Art. 3, is; then 9 the Denominator of the Divifor multiplied into 3 the Numerator of the Dividend is 27, for the Numerator of the Quotient; and 4 the Numerator of the Divifor multiplied into 15 the Denominator of the Dividend is 60, for the Denominator of the Quotient.

The fecond Example is done in the fame Manner.

If a compound Fraction be given to be divided by a compound Fraction, reduce both the compound Fractions to fimple Fractions, by Art. 3; then proceed as at Art. 30.

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Exam. 1. The compound Fraction of is reduced to the fimple Fraction, and the compound Fraction of is reduced 45 to, by Art. 3; then proceed as in Art. 30, and we have 4 for the Quotient fought.

The fecond Example is done in the fame Manner.

Article 32. To divide a mixed Number by a fimple Fraction, or a fimple Fraction by a mixed Number.

Rule. Reduce the mixed Number to an improper Fraction, by Art. 2; then proceed according to the Directions at Art. 30.

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Exam. 1. The mixed Number 10 is reduced to the improper Fraction 97, by Art. 2; then the Denominator 6 multiplied by the Numerator 97 gives 582, for the Numerator of the Quotient; and the Numerator 5 multiplied by the Denominator 9 gives 45, for the Denominator of the Quotient: So is the Quotient fought.

The fecond Example is done in the fame Manner.

Article 33. To divide mixed Numbers and compound Fractions,

Rule.

Rule. Reduce the mixed Number to an improper Fraction, by Art. 2, and the compound Fraction to a fimple Fraction, by Art. 3; then proceed as at Art. 30.

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Exam. 1. The mixed Number 2 is reduced to, by Art. 2, and the compound Fraction of is reduced to the fimple Fraction, by Art. 3; then 18 the Denominator of the Divifor multiplied into 19 the Numerator of the Dividend is 342, for the Numerator of the Quotient: Laftly, 10 the Numerator of the Divifor multiplied into 9 the Denominator of the Dividend is 90, for the 'Denominator of the Quotient 342

Exam. 2. The mixed Number 9 is reduced to 47, by Art. 2, and the compound Fraction of to, by Art. 3; multiply the Denominator of the Divifor into the Numerator of the Dividend for the Numerator of the Quotient, and the Numerator of the Divifor into the Denominator of the Dividend for the Denominator of the Quotient ST.

Article 34. To divide fimple Fractions, mixed Numbers, or compound Fractions, by Integers; or Integers by fimple or compound Fractions, or mixed Numbers.

Rule. Make the Integers, whether they are the Divifor or Dividend, an improper Fraction, by putting an Unit for a Denominator, by Art. 1. If the Divifor or Dividend be a mixed Number, reduce it to an improper Fraction, by Art. 2: And, if the Divifor or Dividend be a compound Fraction, reduce it to a fimple Fraction, by Art. 3: After which, the Divifion must be performed as directed at Art. 30.

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Exam. 1. The Integer 4 is reduced to, by Art. 1; then multiplying the Denominator of the Divifor into the Numerator of the Dividend, it gives 7, for a new Numerator; and multiplying 4 the Numerator of the Divifor into 15 the Denominator of the Dividend, it gives 60, for a new Denominator: So is the Quotient.

Exam. 2. The compound Fraction of is reduced to, by Art. 2, and the Integer to 3, by Art. I; then multiply as before, and there is for the Quotient.

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Exam. 3. The mixed Number 7 is reduced to 22, by Art. 2, and 13 to, by Art. 1; multiply r the Denominator of the Divifor into 29 the Numerator of the Dividend for a new Numerator, and multiply 13 the Numerator of the Divifor into 4 the Denominator of the Dividend for a new Denominator, and the Quotient is 3.

Exam. 4. The Divifor 3 is reduced to, and the Dividend II to ; and, proceeding as in the other Examples, the Quotient will be

Thus

Thus having gone thro' the feveral Rules of adding, fubtracting, multiplying, and dividing Vulgar Fractions, we fhall now fhew the Learner how to find the Value of Fractions of Money, Weights, or Measures, and to reduce Fractions to their lowest Terms; thefe Articles are not neceffary to the learning the Rules of Addition, Subtraction, &c. but are neceffary, after the Operations are performed, to discover the Value and Refult of the Work.

Article 35. To find the Value of a Fraction in the customary Divifions of Money, Weights, Measures, and the like: As if it was required to find the Value of of a Pound Sterling.

Rule. Multiply the Numerator by 20, the Shillings in I Pound, then divide the Product by the Denominator, and the Quotient is Shillings, and, if nothing remains, is the true Value of the Fraction: If any Thing remains, multiply it by 12, the Pence in 1 Shilling, then divide the Product by the Denominator, and, the Quotient is Pence, and, if nothing remains, the Shillings before found, and the Pence now found, is the exact Value of the given Fraction: But, if any Thing remains, multiply it by 4, the Farthings in Penny, then divide the Product by the Denominator, and the Quotient is Farthings, which, being added to the Shillings and Pence before found, is the Value of the given Fraction; the Remainder, after the Multiplication by the smallest Divifion into which the Integer is divided, being generally neglected.

Let it be required to find the Value of the following Fractions of a Pound Sterling.

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