191. When the fractions are such as will not reduce to known quantities without remainder. RULE. Reduce the given fractions to fractions of the highest denomination mentioned, (Art. 183.) then reduce these to a common denominator, (Art. 180.) add the numerators together, as in Art. 187, and reduce the sum to its proper quantity, (by Art. 186.) which will be the answer2. 5 7 I first reduce shill. and d. to fractions of a pound, which is the z This rule will be readily understood; for it is plain, from what has been shewn in the preceding notes, that in order to add fractions together, they must be reduced first to parts of the same whole, and then to parts of the same denomination; after which the sum is evidently found (as before) by adding all the new numerators together, placing the common denominator under the sum, and reducing this fraction to its equivalent value in known denominations. tions of a pound, these I reduce to a common denominator, and add as in Art. is next reduced to its lowest terms, and lastly to its pro Then 1 x 108 x 1200 = 129600 1 x 7 x 1200= 1 x 7 x 108= 756 30. Add 19 of a week, of a day, and ther. Sum 21h, 55m. 12′′. 10 SUBTRACTION OF VULGAR FRACTIONS. 192. When the given fractions are both simple. RULE I. Reduce the fractions to a common denominator, beginning with the numerator of the greater fraction. II. Subtract the lower new numerator from the upper, and under the remainder place the common denominator; this fraction being reduced to its lowest terms will be the answer". a As fractions of different denominations cannot be added, so neither can they be subtracted; we must first reduce them to a common denominator, and then it is plain that their difference is found by taking the difference of the new numerators, and placing it over the common denominator. Thus in Ex. 1. 193. When there are mixed numbers, compound or complex fractions. RULE I. Reduce mixed numbers to improper fractions, compound and complex fractions to simple ones, reduce these to a common denominator, and proceed as before. Nothing can be plainer than this rule; for if one fraction be subtracted from another of the same denomination, the remainder is evidently a fraction of the same denomination with both; thus, if two fifths be taken from three fifths, the remainder will be one fifth; and the same of other fractions. II. If the answer be an improper fraction, reduce it to its equivalent whole or mixed number ". First, I reduce the mixed number to an improper fraction Secondly, 13 4 the compound fraction to a simple one Thirdly, I reduce these two to a 15 24 common denominator, and subtract, which gives the fraction 21 I reduce this fraction to its lowest terms and this to a mixed number. 13 16 The two complex fractions are first reduced to the simple ones and these are next reduced to a common denominator; and all the rest as before. This rule is sufficiently plain from what is shewn in the note on the similar rule in Addition of Fractions, (Art. 189.) |