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 390 A R I T H M E T I C K. to the integers. The above example wrought in this fractions, by Prob. II; then reduce the fradlions to a common denominator, by Prob. VIII. and fubtradt the manner follows. one numerator from the other. Ex, What=:is the fum::=of 7! + 5 * ? Ex. From 74 xfubtradt ji. ^+T — tTT" and 7 + TT'"^TT 5 + itjt =44 I3tV 74. 5tV.= V > xA> byY»Prob. II. VIII. and by Prob. Rule IV. If any, or all of the given fra&ions, be and V — V = V = 2| = 24, by Prob. I. and VII. compound, firft reduce the compound fractions to Ample Rule If it be required to fubtradt a mixt numones, by Prob. IV.; then reduce the Ample fradtkms to ber, or aIV.fradtion, an integer, Arfl fubtradt the a common denominator, by Prob. VIII. and add the nu- fradtion from an unit from borrowed ; that is, fubtradt the numerators. merator from the denominator, and place the remainder, Ex. What is the fum of y-of as a numerator, over tlie denominator, for the fradtional y of £8 —tV, by Prob. IV. part of the anfwer: Then, for the unit borrowed, add 1 and T r -f +fs., by Prob. VIII. anc to the integral part of the mixt number*, fubtraft the ^ — I'5^» hy Prob. I. fum from the given integer; and prefix the remainder to Rule V. If the given fradtiorrs be of different de- fradtional part of the anfwer. But when a fradtion nominations,. Arfl reduce them to the fame denomination, thefubtradted from an integer, for the unit borrowed, take by Cor. of Prob. IV. or by Prob. V.; then reduce the isj from the given integer, and prefix theremainder to fradlions-, now of one denomination,, to a common deno- the fradtional part of the anfwer. minator, by Pfob. Vlfl. and add the numerators ; or Ex. 1. From 14 fubtradt 74. reduce each of the giv,en fradlions feparately to value, Here fay, 5 — 3=2 ; fo 4 is the fradtional part of by Prob. VI. and then add their values. the anfwer : Then fay, 1 borrowed and 7 make 8, and Ex. What is the fum of |s. and-^1. ? 8 fubtradted from 14 leaves 6 ; which prefix to the fracMethod I. tional part : So the difference or anfwer is 64|-s. = ^ of i*-Ql.=-^l. by Con Prob. IV. Ex. 2, From is fubtradt 4and ^ + | = ^ by Prob. VIII. Here fay, 7 — 3 ^ 4 J fo 4 is the fradtional part; then —+ and — 185. 3d. by Prob. VI. fay,. 1 borrowed from 12, and 11 remains : So : 14 is the difference, or anfwer. MeVhod II. Note, When an integer is given to be fubtradted from ^ 1. =, o r=J , 0 by Prob. V.. a mixt nnmber, you have only to fubtradt the given integer from the integral part of the mixt number ; and the= remainder annex the fradtional part. Thus, and 4 4*'x 't - ^s. 3d. by Prob.I. .and VL. to9t—5 Rule4t*V. If one or both of the given fradtions b© Method III. compound, firft reduce the compound fradtions to Ample ones, by Prob. IV.; then reduce the Ample fradtions to = Vd.= 9 a common denominator, by Prob. VIII. j and fubtradt 4 the one numerator from the other. Ex. From 4 fubtradt 4 of J. 4I. = Z*££?s. zeJ-^a-s. = 17—6 by Prob. VL 4 of |=A. by Prob. IV. and 4, A= = 44, -iA by Prob. VIII. an( 18-3 J i 44— T® ~ by Prob. VII. Rule VI. When the given fradtions are of different Sublrafiion of Vulgar Frations. denominations, firft reduce them to the fame denominaby Cor..of Prob. IV. or by Prob. V., then reduce Rule I. If the given fraftions have the fame deno- tion, the fradtions, now of one denomination, to a common minator, fubtradl the leffet numerator from the greater, denominator, by Prob. VIII.; and fubtradt the one nuand place the remainder over the denominator. merator from the other. Or, reduce each of the given Ex-. From 4 fubtraft 4* fradtions, feparately, to value, by Prob. VI. j and fubT 4II.— T*If the ■ given*fractions hare different deno- tradt the one value from the other. s Rule minators, reduce,.them to a common denominator, by Ex. From 41- fubtradt4 Method I; Prob. VIII.: then fubtraft the leffer numerator from the greater, and place theiremainder over the common 4s.=4 of =Al- by Cor. Prob. IV. denominator. and 4, ^4£§, by Prob. VUI. and 44^—irt'5,~T*4Trb — *4s.* 4^* byPr°b.I. andVI. Ex, From fnbtracft 4M E T H O.D II. 4,and4 -jt:—dx* -^, A, by Prob. ■ VIII.. Rule III. If it be required to fubtraft one mixt 4l-1^2Si 8= <^s; by Prob. V. number from another, or to fnbtraft a fradtion from a and %°,0 4=V A A, by Prob VJIL raixt number, reduce the mixr numbers to improper and ‘A — A= A* s. = l4S. 4c!. by Prob. I. and VI, Method ■
 * and 4+ 40 =:= 4 -4-6 s 4=, by Prob. VIII.
 * ,s. = ^d.