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 387 A R I T H M E T I C K. Quefi. 2. A put into company jbol. for 8 months,. L. Stock, gain. Stock, B 279 1. for 10 months, and C 735 1. for 6 months ; A's flock 12 A. If 20 : 5 :: 12 they gained 10001.: What (hare of the gain muft each B’s flock 8 S hare ? A 560X 8=4480, third term for A’s lhare. Total flock 20 2|o)6]o B 279X10=2790, third term for B’s lhare. C 735X 6—4410, third term for C’s fnare. Stock, gain. Stock. A’s gain 3.I, B. If 20 : 5 :: 8 L. 11680, firft term. 8 X. L. s. d. f. Rem. — A’s gain 3 A If 11680 : 1000 j: 4480 : 383—xi — 2—3 208 2|o)4fo B’s gain 3 B If 11680 : 1000 :: 2790 : 238—17—4—3 80 C If X1680 : 1000 :: 44x0 : 377—n—4—i— 88d B’s gain 21. Total gain 5 proof. 1. When, in any queftion there happen to be Proof 1000—00—o—o—u68. remainders, they muft be reduced equally low, fo as to. be all of one name ; and then their fum will be either equal to the divifor, or exact!y double, triple, <bc, of Ghap. IX. Vulgar. Fractions. it: and accordingly x, 2, 3, 6r. carried from the fum of the remainders, and added to the particular gains,, will make up the total gain ; or the divifor will always A Fraction is a part or parts of an unit, or of any divide the fum of the remainders exaftly, and the quot integer or whole; and is exprelfed by two numbers,. added to the particular gains will give the total gain. one above and the .other below a line drawn between Note 2. When the partners have equal fhares of flock them ; as, or capital, their lhares of gain,, lofs, or neat proceeds, The number under the line fnews into how many is found readily by dividing the total gain, lofs, (drc. by parts the unit or integer is divided; and is called the denominator, becaufe it gives name to the fradhon : The the number of partners. number above the line fhews or tells how many of thefe II. Felli'wJJjip with time. parts the.fradtion contains; and is therefore called the In fellowlhip with time, the gain or lofs is divided a- numerator. mong the partners, both in proportion to the flocks In the fraftion ^1. a pound Sterling is the unit, in-• themfelves, and alfo in proportion to the times of their teger, or whole and-the denominator 4 Ihews that thecontinuance in company : For the fame flock continued pound is broken or divided into four equal parts, viz.. a double time, procures a double (hare of gain ; and 4 crowns ; and the numerator 3 Ihews that the fraftion ■ continued a triple time, procures a triple (hare of gain ; contains three of thefe parts, that is, .three crowns ; and . that is, the fhares of gain or lofs are as the produdts of fo the value of this fraction is fifteen fhillings;. the feveral flocks multiplied into their refpedtive times : Cor. 1. Hence it follows, 1. When the numeraand accordingly queftions belonging to. this rule are tor of a fraflion is lei's than the denominator, the va-wrought by the following proportion. lue of fuch a fradtion is lefs than unity, or the integer., As the fum of the products of. the.feveral flocks into, 2. When the numerator is equal to the denominator, the their refpeAive times value of the fradtion.is exadlly an unit or integer. 3. When To the total gain or lofs,. the numerator is greater than the denominator, the value So the product of each man’s flock into his time of the fradhon is more than an unit ; and fo often as the • To his lhare of the gain or lofs,. is contained in the numerator,Fo many units • Queft. 1. A put into company 401. for. 3 months, denominator or wholes are contained in the fradlion. If, therefore B 75I. for 4 months; they gain 70I. : What fhare.muft, the numerator of a fradtion be divided by the denominaeach man have ? tor, the quot will be a number of units or integers, and A 40 X 3 = 120,. third term for A’s lhare.. the remainder fo. many pants.■ ' , B 75X4 = 300, third term for B’s fhare.. The numerator of a fra'dlion is to be confidered as a dividend, and the denominator as a divifor; and the fradfion itfelf may be taken to denrite the quotient. 420, firft term. Cor. 2. From this view of a fradtion, it is evident, x. r. A. If 420. : 70 :: 120 B. If 420. : 70 :: 300 ■ that if the numerator and denominator, of a fradlion be 120 300 either both multipled or both divided by the fame number, the produdls or quotients will retain the fame pro42|o)84o]d(2oL 42]6)2ioo]o(59 IV. portion to one another; and confequently the new frac84 210 tion thence arifing wrl! be of' the fame value with the given one. Thus the numerator and denominator of the fradtioh multiplied by 2 produces ^ and divided by (9) A’s gain. 20x: (o) 2 quots both which fx addons are cf the fame value B’s gain 50 with A. Fradlions having 10, ioq, 1000; or 1, with any numTcial gain 70 proof.'. . ber of ciphers annexed tc it, for a denominator, arc called-