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 3 Bo A R I T H M E T I C K. vifor and quotient, place the excefles on the right and left lides of a crofs; then multiply thefe two figures inProof by Reduction afcending. to one another, and caft the 9’s out of their product; add the excefs to the remainder; and, carting out the In 45:3120 farthings how many pence, ftiillings, and 9’s if need be, place the fum or excefs at the top of the pounds ? crofs ; then caft the 9’s out of the dividend, and fet the Here divide the farthings by 4)453120 farthings. excefs at the bottom. If the work be right, the figures 4, becaufe 4 farthings make x <!t the top and bottom of the crofs will agree, or be the penny, and the quotient is 12)113280 pence. fame. pence : then divide the pence Thefe methods of proof are a proper exercife to the by 12, becaufe 12 pence make 210)944)0 (hillings. learper in fchools ; but, in bufinefs, the only proof ufed 1 (hilling, and the quotient is is a careful revifal of the operation. (hillings: lartly, divide the (hil472 pounds. lings by 20, becaufe 20 (hillings make 1 pound, and the quotient is pounds. Note 1. To reduce pounds to pence at one operation, Chap. VI. Reduction. multiply by 240, the number of pence in 1 pound 2. To reduce pounds to farthings at one operaReduction teacheth how to bring a number of one tion,Notemultiply by 960, the number of farthings in 1 name or denomination to another of the fame value; and pound. is" either defcending, afcending, or mixt. Note 3. To reduce (hillings to farthings at one opeI. Redudtion defcending brings a number of a .higher ration, multiply by 48, the number of farthings in 1 denomination to a lower, when the lower is fome aliquot part of the higher; as pounds to ftiillings, pence, or far- (hilling. Note 4. To reduce pence to pounds at one operation, things; and is performed by multiplication. by 240, the pence in 1 pound. II. Reduction afcending brings a number of a lower divide Note 5. To reduce farthings to pounds at one opedenomination to a higher, when the lower is fome aliquot ration, by 960, the farthings in 1 pound. part of the higher; as (hillings, pence, or farthings, to Note divide 6. To reduce farthings to (hillings at one opepounds ; and is performed by divifion. ration, divide by 48, the farthings in 1 (lulling. III. Mixt reduftion brings a number of one denomifollows the farthings of Queft. 1. reduced back nation to another, when the one is no aliquot part of the to Here other; as pounds to guineas, and requires the ufe of pounds by thefe notes. both multiplication and divifion. By note 5. In treating of reduftion we ftiall conjoin the defcend- By note 4. 96)0)45312)0(472 L. ing and afcending, the one ferving as a proof of the 4)453120 farthings. other ; and ftiall afterwards treat of mixt reduftion by 24|o)ii328|od. (472L. 384” itfelf. 691 In working reduction, of whatever kind, the following 96 672 rule is to be obferved, viz. Multiply or divide as the tables of money and weights 172 192 dire£t. 168 192 Reduction defcending and afcending. 48 (o) 48 x. M O N E Y. Quest, i. In L. 472 how many (hillings, pence, (°) and farthings ? This reduction is defcending, 472 pounds, By note 6. therefore multiply the pounds by 20 2)0) 20, becaufe 20 (hillings make 1 48)453120(94 |o (hillings. pound, and the produft is (hillings: 944° (hillings, then multiply the (hillings by 12, 12 432 472 pounds. becaufe 12 pence make 1 (hilling, and the product is pence : lartly, 1888 211 multiply the pence by 4, becaufe 944 192 4 farthings make 1 penny, and the product is farthings. 113280 pence. 192 192 453120 farthings. 2. AVOIR-