Exam. 3. Reduce and and to Fractions of the fame Denominators. 44 Exam. 1. The Numerator I multiplied by the Denominator 4 is 4, for a new Numerator to the Fraction: The Numerator 3 multiplied by the Denominator 2 is 6, for the new Numerator to the Fraction : Then the Denominator 2 multiplied by the Denominator 4 is 8, for the common Denominator to both the Fractions. The fecond Example is done in the fame Manner. Exam. 3. The Numerator 3 multiplied by the Denominator 3, and that Product by the Denominator 5, is 45, the new Numerator for the Fraction: The Numerator 2 multiplied by the Denominator 4, and that Product by the Denominator 5, is 40, the new Numerator to the Fraction: Then the Numerator 4 multiplied by the Denominator 3, and that Product by the other Denominator 4, is 48, the new Numerator to the Fraction : Laftly, multiply all the Denominators together, and the Product is 60, the common Denominator; which, being put under each of the Numerators before found, gives the Fractions 45, 40, and 48, equal to the given Fractions. The following Examples are done in the fame Manner. Article 5. To reduce compound Fractions and fimple Fractions to Fractions of the fame Denominator. Rule. First reduce the compound Fraction to a fimple Fraction, by Art. 3; then reduce that and the given fimple Fraction, to Fractions of the fame Denominator, by Art. 4. Answer 21 40 56 16845 Answer and . 45 112 168 4 and 1. Exam. 1. The Numerators 1 and 3 of the compound Fraction multiplied together give 3, for a new Numerater; and the Denominators 2 and 4 multiplied together produce 8, for a new Denominator; which reduces it to the fimple Fraction, by Art. 3: Then the Numerator 3 of this new Fraction multiplied into the Denominator 7 of the given simple Fraction is 21, for a new Numerator to the Fraction ; and the Numerator 5 multiplied into the Denominator 8 is 40, for the other new Numerator: Laftly, the Denominators 8 and 7 multiplied make 56, for the common Denominator; over which placing the Numerators before found, these are the two new Fractions fought. Exam. 2. Multiplying 3 and 5, the Numerators of the compound Fraction, the Product is 15; multiplying 7 and 8, the Denominators of the compound Fraction, the Product is 56; and is the fimple Fraction: Hence the two fimple Fractions are and. Now, 15 multiplied by 3 is 45, one of the new Numerators; and 2 multiplied by 56 is 112, the other new Numerator; and 56 multiplied by 3 is 168, the common Denominator: Hence and are the two new Fractions fought. 2 The two following Examples are done in the fame Manner. C Exam. 3. Article 6. To reduce mixed Numbers and fimple Fractions to Fractions of the fame Denomination. Rule. First reduce the mixed Number to an improper Fraction, by Art. 2; then reduce that improper Fraction and the given fimple Fraction to a common Denominator, by Art. 4. Exam. 1. Reduce 9 and Ex. 2. Reduce 7 and 3 and to the fame Denominator. to a common Denominator. TO I 2 Exam. 1. The Integer 9 multiplied by 5 the Denominator of the Fraction is 45; to which 4 the Numerator being added, is 49, for a new Numerator; under which placing the Denominator 5, the improper Fraction is 49, by Art. 2. Then multiplying the Numerator 49 by the Denominator 10 of the given fimple Fraction, the Product is 490; and the Numerator 7 multiplied by the Denominator 5 of the improper Fraction is 35; these are the new Numerators. Laftly, the two Denominators 5 and 10 multiplied give 50 for the common Denominator. Whence 49 and 35 are the Fractions fought. 30 30 Exam. 2. The mixed Number being reduced to the improper Fraction, and the other mixed Number 3 to 4, by Art. 2; multiply the Numerator 31 into the two Denominators 2 and 7, which makes 434, for a new Numerator to the Fraction; and the Numerator 7 multiplied into the Denominators 4 and 7 is 196, for a new Numerator to the Fraction; alfo the Numerator 6 multiplied by the Denominators 4 and 2 is 48, for a new Numerator to the Fraction Laftly, the Denominators 4, 2, and 7, multiplied, give 56 for a common Denominator to the Fractions 434. and 4%. Exam. 3. Exam. 4. 196 These Examples are done as the first and second. Article 7. To reduce a mixed Number and a compound Fraction to the fame Denomination. Rule. Reduce the mixed Number to an improper Fraction, by Art. 2; then reduce the compound Fraction to a fimple Fraction, by Art. 3; laftly, reduce these two Fractions to the fame Denomination, by Art. 4, and they will be the new Fractions fought. Exam. 1. Exam. 2. Reduce 3 and of to the Reduce 96 and of to fame Denomination. the fame Denomination. Exam. 1. The Integer 3 multiplied by 7 is 21; to which add 3, and it makes 24; thus is 3 reduced to 2+. Then the Numerators 2 and 3 of the compound Fraction multiplied give 6, and the Denominators 3 and 4 multiplied give 12; therefore is the fimple Fraction to which the compound Fraction is reduced. The Numerator 24 multiplied into the Denominator 12, and the Numerator 6 into the Denominator 6 7, give |