If 4 pipes of Holland gin coft 201£12/. fterling; what did it coft per gallon? gins. £ s. 4 p. x 2 x 63-504)201 12(0 8 A. When it is noon at Bofton, what time in the day is it at London, their difference of longitude being about 70° 58'? 15 )70° 58'(4 h. 43 mn. 52 fec. after noon A.. or 4 o'clock and 44 minutes, nearly. To divide by fractional parts; multiply by the lower and divide by the upper part of the fraction. To divide one compound number by another, increafing in the fame ratio.. RULE. Multiply the whole divifor by the firft figure or part of the quotient; fubtract each part of the product from the fame part of the dividend; in the fame manner multiply the whole divifor by the fecond figure or part of the quotient, always obferving to place the product or remainder of each denomination as far to the right (or left) of its part of the divifor, as its part of the quotient is to the right (or left) of the higheft denomination in the divifor. The names, of the feveral parts of the divifor and quotient. with the fign. x or of between them, reprefent every part of the dividend; as, (inches xd by inches i.e.) 12ths of 12ths reprefent 144ths, 144ths of 12ths 1728ths, &c. Alfo, the fums of the arithmetical indices of the and qt reprefent the feveral parts of the dividend, and determine the place which each part of the work must occupy taining 28 ft 11/? 70' 2° 3′ 4′′)28°11′ 6′′ 0" (12° 8'639" 7x7=49)274 7! 6′′(5 6 3936 234 12 in 24011 328" 12.808 (36340" A. 6528 Eight2/6d N.J.currency 10/N.E. what being worth 6 is 1 N.E. worth? 6£10′,8£2/10 (1£5/.N.J. A.. REDUCTION OF FRACTIONS, the changing or bringing them from one pofition to anr, retaining the fame value. ULE 1. To reduce fractions to their highest terms; Diboth the dividend and divifor by fuch a number as will without a remainder; in the fame manner divide their ients, &c. the leaft quotients poffible exprefs the given e in its fhorteft or highest terms. Revert the rule, to ce to lower terms. 4)146-36-3=3£. A. x4x3x4=144 proof. 24 72 170 6.0 8)= A. 25);;= A. Reduce 32, 11, 99, 188, 189, and 15 to their high196 125, terms.. 36 85 1 2 14 117 13 As. RULE 2. To reduce mixed or whole numbers to irregular tions. Multiply the integer by the divifor of the frac0, and add in the dividend, place this fum over the divifor the fraction required. Place 1 under any whole numand it becomes a fraction, Or multiply by any number I the product is the dividend and the multiplier the diviRevert the rule, to reduce fractions to integers. EXAMPLES. Reduce 7 lb to a fingle fraction. 7 x 2+1 lb A, 2)15(7 proof. If the reduction be ascending, (as that, by division, is called) the ult must be in higher terms instead of lower; if each one in the nd 1 far, and be reduced to 1 d. each i.e. bed by 4, the reduction is ending,. Reduce 141 to a fingle fraction. 14 x 20+15=23. A.-195 s.2014 proof. Reduce 5 galn. to a fraction having one, 2, 3, or 4 for its divifor. 4,5 x 210, 5 x 313, 5 x 4-2 gln. A. 5-10-14-20-20 quarts. Reduce to a fraction having 2 for its ÷nd. RULE 3. To reduce compound to fimple fractions; Multiply all the dividends together for the dividend, and all the divifors for the divifor of the fraction required. It is unneceffary to multiply by fuch numbers as are alike above and below the line. Revert the rule, to reduce fimple to compound fractions. This rule anfwers for xn.. 4 80 2)260(1973-33-proof. Reduce of S to a fingle fraction. proof. 1 x+x= bu. A. 32 2 32 1 of 1 of 133 gin. A. 10 T T duce of cts, of lb, of d of 15, 2 tun to fimple fractions. 10 3 cts. lb. s. tun. As. 192 ULE 4. To reduce one denomination, Coin, Weight, Meac. to any other; Multiply the denomination of the , &c. given by the proportion it bears to that which is ired, and the product is the answer divide the dividend ny fraction by its divifor, (multiply the remainder by the denomination or proportion, and divide as before quotient is equivalent to the primitive fraction. 2 EXAMPLES. and Reduce 30 s. to . and to S. (pro. between s. and is, between s. and . . T. 1. as 2; 9: 1 s. A I 3.0 £• 3.02 15.) 60 8. A. 4)3,00(,75 £= £. 323-18 A. 60,00(3,333 = {} 60 57 Reduce 2 lb. 3 oz. Troy to Avordupois (pro, $15T. 2.) oro. 391 T. 9.) — x 3'3 bu. A.-4 bu. 3191 pk. 371= 37 1 (pro. 62 T. 10) x = '14gln. A.=13134 What is the weight of 3 wine glns of water? (pro. 167 11) 167 3 x 20= 50 lb. Avor. A.—25,1 lb. The proportion, which one denomination, Coin, &c. bears to anoth may be found in the tables of the same name. In all cases if the deination, &c. given be larger than that which is required the nd of fraction or proportion must be larger than the r, if less the re se. |