CASE III. To reduce a mixed quantity to an improper fraction. RULE. Multiply the infegral part by the denominator of the fraction, and to the product add the numerator, when it is affirmative, or subtract it when negative; then the result, placed over the denominator, will give the improper fraction required. To reduce an improper fraction to a whole or mixed quantity. RULE. Divide the numerator by the denominator, for the integral part, and place the remainder, if any, over the denominator, for the fractional part; then the two, joined together, with the proper sign between them, will give the mixed quantity required. To reduce fractions to other equivalent ones, that shall have a common denominator. RULE. Multiply each of the numerators, separately, into all the denominators, except its own, for the new nume rators, and all the denominators together for a common de. nominator (h). EXAMPLES. a b 1. Reduce and to fractions that shall have a comb C mon denominator. Here aXc ac b x b = b2 } the new numerators. txc bc the common denominator. (h) It may here be remarked, that if the nimerator and denominator of a fraction be either both multiphed, or both divided, by the same number, or quantity, its value will not be altered: thus 2 2×3 6 3 3×3 9 and 3 3-3 1 ac = ; or and 12. 12 3 4 b bc ab a bc C which method is often of great use in reducing fractions more readily to a common denominator. ing a common denominator. 3 2x 4x 5. Reduce and a += to fractions having a 4 3 Reduce the fractions, if necessary, to a common denominator; then add all the numerators together, and under their sum put the common denominator, and it will give the sum of the fractions required (i). (2) In the adding or subtracting of mixed quantities, it is best to bring the fractional parts only to a common denominator, and then to affix their sum or difference to the sum or difference of the integral parts, interposing the proper sign. |