§ V. ADDITION AND SUBTRACTION OF ALGEBRAIC FRACTIONS. To add fractional quantities together. RULE. 154. Reduce the fractions, if necessary, to a common denominator, by the rules in the last case, then add all the numerators together, and under their sum put the common denominator; bring the resulting fraction to its lowest terms, and it will be the sum required. Or, the least common multiple of the denominators may be found, and then proceed, as in (Art. 153). It is generally understood that mixed quantities are reduced to improper fractions, before we perform any of the operations of Addition and Subtraction. But it is best to bring the fractional parts only to a common denominator, and to affix their sum or difference to the sum or difference of the integral part interposing the proper sign. Ex. 3. It is required to find the sum of a 3x2 b Or, bringing the fractional parts only to a com mon denominator, Ex. 4. It is required to find the sum of 5+ but we might change the fractions into other equivalent forms before we begin to add or subtract; thus, the fractional part of the proposed quantity may be transformed by changing the 4x 2x-3 signs of the numerator, (Art. 128), and the quantity itself can be written thus, 4x+ 3-2x 5x It is well to keep this transformation in mind, as it is often necessary to make use of it in performing several algebraical operations. |
