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CHAPTER III-FRACTIONS.
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67 to 71. The denomiuntors of certain given fractions aro stated to he 19, 23, 62, 29, 123, 35, 188, 37, 9, 17, 140, 141, 116. 31, 92, 57, 73, 55, 110, 19, 74, 219, in orler); and the numorators begin with 1 and rise accessively in value by in order. Add (all) these (fractions) and give the result, () you who have reached the other shore of the ocean of simple fractions.
Here, the rule for arriving at the numerators, when the deno. inators and the sum of a muinber of fraction are given, in an
Make one the numerater in relation to all the given deno.
6); then, multiply by means of such numbers us are Ally chosen those numeriutors which are derived from these
18 go as to have a common denominator, llere, those ors) turn out to be the reynirl nuncrators, the son of the
hereof, obtained by multiplying them with tho numeraved its above, is equal to f lumerator of the given I the fractions concerned.
The rule for arriving at the numerater's, the denominators and ar sum being given as before in relation to such fractional) quantities an have their inmerator'L ively rising in value by one, when, in the given: oan if these fractions, the denominator is higher in value than the morator:
73. The quotient obtained by dividing tho (given him (of tho fractions conoernod) by the sum of those (tentative fructions)
73. This rule will become clear from the king of the example in stansu No. 74, wherein weilsaume 1 to be the provisional meritor in ration to each of the given denominator ; thun we get to and ;', which, being record so as to haron common denoininator, become , and .. When the numerators are multiplied by 3, 3 und 1 in order, the sum of the products thus obtained becomes equal to the numarrator of the riven uni, tinmols, 477. Hence, 2, 3, and 4 are the required namerators. Here it may be pointed out that this givon sum aluo muat be understood to bave the same denominator in the common denominator of the fractions.
78. To work out the sum given under 74 below, according to thin rule: ..
Rodaoing to the sam, denominator the fractions formed by umowning 1 to be the apmerator in relation to each of the given denominators, we get 19. apdoh. Dividing the giren kam #1 by the nom of thoso fractions 18%, we get the quotient 1, which is the namerutnr in relation to the first denominator. The remaindet 279
