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 3^2 A R I T H M stick:. Note i. Tnftead of working divifion of fraftioris as Or, Divide the giten multiplicand by the numerator , taught above, you may invert the divifor, and then mul- cf the fradtion, and miultiply the quot by the denomi> t, tiply it into uthemadividend. Thus, in Example r. inftead nator. i Divide L. 276 : 16 : 8 among four men, y° number y ^y.be -fx#—?o—iA= v- fradlion, the A,Exam*. 2. If any divided by a proper B, C, D, fo that A, B, C, may have equal lhares, quot will be greater than the dividend: for in divifiofl and D only two thirds of one of their fhares. the quot ftiews how often the divifor is contained in the 1 + 1 + 1 +y=-f-f-f+-!+!=44 dividend ; and confequently if the divifor be greater than L. s. d. L. s. d. L. s. d. unity, the quot will be lefs than the dividend; if the di- 11)276 16 8 (25 z 4X2—75 ro Avifor be unity, the quot will be equal to the dividend ; X3 = 75 10 B. and if the dmfor be lefs than unity, the quot will, in X 3 = 75 ia G. the fame proportion, be greater than the dividend. Thus, X 2 = 50 6 8 D. fuppofing the divifor to be -£» or j-, the quot in this cafe Proof 376 16 8 will be double or triple of the dividend. 3. To divide a fradtion by an integer,- is only to mul- The reafon of the rule will appear by* confiderirvg, tiply the integer into the denominator of the fradlion, that the method here ufed is nothing elfe but the reducing the divifor and dividend to a common denominator, the numerator being continued. Thus, 7):|viV 4. A mixt number may fometimes be divided by an and then dividing the one numerator by the other. Thus, integer, with more eafe, in the following manner. Di- ■i) T (l'> ^or re^ucing the divifor and dividend to a comvide the integral pa-1 of the mixt number by the given mon denominator, we have y?r) -A (=|. integer: and if there be no remainder, divide likewife The truth of the rule may alfo be proved by afluming the fradtion of the mixt number by the given integer, and two fradlions equal to two integers, fuch as, -f- and ^, annex the quot to the integral quot formerly found. equal to 2 and 4, and the quot of the fradions will be But if, in dividing the integral part, there happen to be equal to the quot of the integers. Thus, |-) (4!;= a remainder, prefix this remainder to the fradtion for a 2, and 2)4(2. new mixt number; which reduce to an improper fraction : then divide the improper fradtion by the given inThe Simple Rule of Three in Vulgar Fraflions. teger, and annex the quot to the integral quot formerly found. Thus, if it be required to divide 15^ by 8r The queftion is ftafed as formerly taught in the rule fay, 8) 15(1, and 7 remains; which 7, prefixed to the of three. The extremes muft be of one denomination. fradtion, gives 7^-for anew mixt number; and this, re- Reduce mixt numbers and integers to improper fradiions, duced to an improper fradtion, is ^, and 8) y (yr: fo compound fradlions to Ample ones, and then Work by the following rule, viz. the complete quot is 5. If the fadtors of the numerator and denominator Multiply the fecond and third terms, and; divide the by the firft term ; that is, multiply the numeraof the quots, inftead of being adtually multiplied, be produdl of the firft term into the denominators of the feeond only connedted with the fign of multiplication, it will be tor and third, for the denominator of the anfwer; and muleafy to drop fuch fadtors, above and below, as happen tiply the denominator of the firft term into the numerato be the fame, thus: of tors of the fecond and third, for the numerator of the anfwer. s=f. Or a fadtor above and below may be divided byr the fame number thus : v(^° I. Direft. the fadtors of the numerator of the quot may be ex- Quest. If 4 yard coft 4 !• what will yard coft ? Yd. L. Yd. changed, .W.52? = ^ ?-=5®. 6 the,, T'MaXp 2X9 = 2X3 If 1 : 1 : : tV 6. To divide an integer by a fradtion, is to divide the 4 =? =:!_= produdt of the denominator and integer by the numerator, •/ 3X8X10 3X2X10 3X2X2 2X2 thus: y)s( =^^=5 X 2 —10. 4 7. If the divifor and dividend have the fame denominator, you have only to divide the numerator of the diIT. Inverfe. vidend by the numerator of the divifor, thus: ^-g-C^r; Quest. If 4 yard1 of cloth that is 2 yards wide, Will for much of any other cloth that it! 8. If a dividend of two or more denominations be make a garment, how the fame garment ? given to be divided by a fradtion, reduce the higher part •f yard wide will make Bread, len. Bread. or parts of the dividend to the lowed fpecies, and then divide. Thus, to divide 61. p^s. by 4, fays9 61= j$X20s.= i2o; and 120 + 9^= i'>9^s.=i^r ; and 8-=mTsl|>1"- 14s- 7-fd.