of a crown to its proper sum. Ans. 2s. 11d. 7 of a cwt. to its proper quantity. An 129. Reduce 7 swer 5s. 8d.7 4. 7 130. Reduce 12 131. Reduce 8 19 134. Reduce of a week to its proper time. Answer 20 6d. 15h. 36m. | of a quarter of corn to its proper quantity. of an acre to its proper quantity. An ADDITION OF VULGAR FRACTIONS. 187. When simple fractions are to be added together. RULE I. Reduce the given fractions to a common denominator, by Art. 180. II. Add the new numerators together, under their sum place the common denominator, and reduce the fraction to its lowest terms for the answer, by Art. 170. III. If the resulting fraction be an improper one, reduce it to its equivalent whole or mixed number, by Art. 173. As whole numbers of different denominations cannot be added or subtracted, so dissimilar fractions (namely, such as are not like parts of the same 2 3 whole) cannot; so, in Example 1, cannot be added to until they are 8 7 2 reduced to the same denomination: this reduction being performed, becomes Nothing can be plainer than the grounds of this process; for since the denominator only indicates what parts the fraction consists of, therefore, when several fractions having the same denominator are proposed, the comparative value of each will be expressed by its numerator. Thus, let the fractions 1 -2 3 7? and 2 1 3 be proposed; it is plain that is double of and 7? 7 triple of it, and that the sum of all three can be nothing but sevenths, that is, it will consist of as many sevenths as there are units in all the numerators 188. When there are whole or mixed numbers to be added. RULE I. Add the fractions together by the preceding rule. II. Add the whole numbers together, and prefix their sum to the sum of the fractions (found by the preceding rule) for the answer ". 67 378 126 sum of the fractions, Art. 187; also 3+ 4 1 2 the sum required. 8. Add 2 and 3 together. Sum 620 9. Add 1- 11 20 3 11 4 12 189. When compound or complex fractions are to be added. RULE. Reduce the compound and complex fractions to simple ones, reduce their equivalent simple fractions to a common denominator, and proceed as before*. u This rule is evident; for if the sum of the whole numbers be prefixed to the sum of the fractions, it is plain that the result will be the sum of all the given numbers, both whole and fractional. * Fractions cannot be added together until they are first reduced to simple VOL. I. N 14 thirdly, I reduce the two complex fractions to and their respective 35 simple ones. Fourthly, I reduce these three fractions, common denominator. Lastly, I reduce the answer 3402 and to a -" to its lowest terms by dividing successively by 7, 3, and 3, and then I reduce the improper frac fractions of the same whole, and then to similar parts of the same whole, namely, to a common denominator; when all this is effected, the sum of the whole is evidently found by adding all the numerators of the reduced fractions together, and placing under the sum the common denominator, as in Art. 187; wherefore the rule is manifest. 190. When the fractions to be added are of different denomi nations in money, weights, or measures. RULE. Reduce the fractions to their proper quantities, by Art. 186. then add the proper quantities together by the rules of Compound Addition". y It is plain that the fractions treated of in this rule being dissimilar cannot be added together until they are reduced as the rule directs; when this reduction is performed, the remainder of the operation (depending on the rules of Compound Addition) is sufficiently obvious. |