Page:Encyclopædia Britannica, first edition - Volume I, A-B.pdf/477

 ARITHMETIC K. 395. Ex. 2. Ex. 1. Rule III. If the rate be no aliquot part of a pound, 37, at 3I. 8s and cannot readily be divided into fuch parts, divide it 213, at il. 13: d iot d. into parts whereof one at lead: may be an aliquot part of a pound, and the fubfequent part, or parts, each an ali106 10 4i quot part of fome prior part. 21 6 3l 6s, 10 13 d Fk. i. Ex. 2. 2s. 6d, 412 6 3 3 9(5, at x s. ltd. 21 136 7t 3yo|6, at i s. 3d. 9 3 lot d. 3 * L.355 8 iof 6 6 d id9t 43 16 3 4276 15 L.127 7 L.219 2 6 Case VIII. When the given number confills of in tegers and parts. Work for the price of the integers as alreaL.8 18 it dy Rule. taught; and for the part or parts, take a proportional Case VI. When the rate is pounds. part or parts of the rate. Rule. Multiply the given number by the rate, and the product is the price in pounds. Ex. 1. i Ex. 2. Yards. Yards. Ex. 1. Ex. 2. T20, at 6s. 8d. n6f, at 4 s. 6d. 42, at 2 !. 13, at 8 I. per yd. per yd. L. 84 L. 104 240 as. 6d. 14 10 Case VII. When the rate is pounds and (hillings, 6s.i 8d. 2 s. yd' or pounds, {hillings, pence, and farthings. 4. yd. Rule I.. If the rate he pounds and (hillings,-multiL. 240 ply the given number by the pounds, and work for the L.26 4 3 /hillings as in Cafe IV. An operation in the rules of practice may be proved Ex. 1. Ex. 2. running over the feveral (leps a fecond time, by 46, at 1 1. 4 s. 82, at 41. 10 s. by working the fame queftion a different way, or by the: 9 4 rule of three. 328 41 L- 55 L 369 Chap. XI. Q/-Decimals. Note. When the rate is more than 1 1 and lefs thanI. Notation. 2 l. as in Ex. 1. we have no occafibn to draw a line under the given number, it being efteemed fo many pounds,, A Fraction having 10, 100, 1000, or .unity with: and the parts for the (hillings or pence are added up aftiy number of ciphers annexed to it, for a denominawith it. 2. deci?nal fraftion; fuch as, T7^-, Rule II. If the rate be pounds, with (hillings and tor, is* 1called a oio pfence that make fome aliquot part of a pound, or are di- 1000 fra&ions, as in vulgar, the denominator vifible into aliquot parts, or into (hillings and fome ali- In decimal into how many parts the unit or integer is diviquot part or parts ; then multiply the given number by (hews ded, and the (hews how many of thefe the pounds, and work for the (hillings and pence as in parts the fractionnumerator contains. Thus, if the fradion be Cafe V. Rule L or II. the unit is divided into ten equal parts, and the Ex. 1. 1 Ex. 2. contains nine of thefe parts; and confequently, 54, at L, 3:2:6/ 43,atL. 5:3 :4. fradion if the unit or integer be a. pound Sterling, the value of fuch a fradion is eighteen (hillings. 215 31- 1626 15 We may conceive the denominator of a decimal 28.6d. 3s. 45ld. 7 3 4 fradion to be formed by dividing the unit into 10 equal parts, and each of thefe parts into 10 other equal parts, L.I68 15 L.222 3 4 of thefe again into 10 other equal parts, and fo on, Rule III. If the rate be poundsi, with (hillings, each as far as pence, and farthings, that cannot readily be refolved in- always beneceffary fo many tenths, or fo many tenths of T'^, or to aliquot parts of a pound ; multiply the given number fo many tenths of -Ay and by reducing the by the pounds; and then work for the (hillings, pence, compound fradion to aoffimple <bc.; one, we have the decimal. and farthings, as in Cafe V. Rule III. Thus, A of Ay of -j’-j- = t'A'uOr
 * 75
 * 3 9
 * and hence a decimal fradion will