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 A R I T H M E T I C K. 373 In multiplying by 12, as in Ex. 8. it is more Ex. 8. I penny, and carry 6 to the place of {hillings, faying’3 tifual, and equally eafy, to proceed by faying, 48 7 times 8 is 56, and 6 that I carried is 62, which make twelve times 8 make 96, and, fetting down the 12 3 pc-nds and 2 (hillings; fet down the 2 (hillings, and carry 3 to the place of pounds which are integers. 6, fay, twelve times 4 is 48, and 9 carried is 2. If your multiplier confifts of two or more figures, 5.7J5. which down, and 576 multiply continually by its component parts, or by the If thefetmultiplier confifttheofproduct the fameis 576. figure repeated, as in, 222, 333, 777, &c. multiply by the unit’s fi- component parts of the compofite number that comes gure, and out of that produdl make up the total produdt, neareft to it, and then multiply the given multiplicand thus. Begin at the right hand, and firil take one figure, by the difference of the multiplier, and the neareft com-' then the fum of two, then the fum of three, <&c. repeating pofite number: the fum or difference of.thefe two prothe operation (till from the right hand, as often as there ducts is the anfwer. are figures in the multiplier; then negle<5Hng the right- Examp. I. What is the price of 56 C. tobacco, at hand figure, or figure in the firft place, take the fum of L. 2 : 14 : 9^ per C. as many figures toward the left hand a! the multiplier has Here the component parts are 8 and 7; for 8X7 = places ; and if there be not fo many, take the fum of all 56: therefore. the figures there are; then, neglecting the figures in the Multiply firft by 8, and that produCt by L. s. d. firft andfecond place, begin at the figure in the third place, 7; or, which will give the fame anfwer, 2 14 9!' 8 proceed as before; and thus go on till the laft or left-hand multiply firft by 7, and then that produCt figure is taken in alone; as in the following examples. by 8. Ex. 1. Ex. 2. Ex. 3. 21 186 7645 4983 38 7 33 666 4444 153 9 6 22935 pr. by 3. 29898 pr.by6. xya pr.by4. Examp. II. What is the price of 126 yards of velvet, at L. 3 : 8 : 4 per yard ? 252285 total. 3318678 total. 168872 total. Here multiply firft by 6, that produCt L. s. d. 6. The operation may frequently be rendered fhorter by 7, and that produCt again by 3 : but as 384 or eafier, either by addition, fubtraCtion, or a more the component parts are various, and may 6 Ample multiplication; and the cafes of this kind are fo be chofen at pleafure, you would have had —— numerous and various, that they admit of no limitation. the fame anfwer, had you multiplied by 20 10 Confult the following examples and directions. 9 X 7 X 2 ; or by 7 X 3 X 3 X 2. 7 Ex. 1. Ex. 2. Ex. 3. 143 10 438 374 746 87 56 84 3 3066 2244 2984 430 10 3504 1870 5968 From the above example may be deduced a general and eafy rule for working all queftions of this kind; and 38106 20944 62664 is of excellent ufe when the multiplier happens to be a Work the above examples as follows. number; viz. Ex. 1. Multiply by 7, and add that produCt to the Multiply continually fo many times by 10 .as there are multiplicand, inftead of multiplying by 8. figures in the multiplier, fave one; then multiply the giEx. 2. Multiply by 6, and out of that produCt fub- ven price by the right-hand figure of the multiplier; and traCt the multiplicand, inftead of multiplying by 5. again, the firft produCt of 10 by the following figure of Ex. 3. Multiply by 4, and double that produCt for 8. the multiplier; and fo on, till you have multiplied by all. the figures in the multiplier. The fum of thefe products. is the anfwer. II. Multiplication of the parts of Integers. Examp. III. What is the price of 8604 yards of cloth, Here there are three cafes. per yard ? 1. If your multiplier is a Angle digit, fet it under the atL.19 s.s. 64-d. d. Price of L. s. d. Price of units figure of the loweft denomination, multiply it into 19 64 I yd, X 4 = 3 18 2 4yds. all the parts of the multiplicand, beginning at the loweft, 10 and^arrying always as- in addition, or according to the value of the next luperior place. Examp. What is the price of 7 packs of cloth at 9155ip 10 yds, X 0 = L,. 64, 8 s. ioid. per pack ? L. s. d. Here fay, 7 times 2 is 14, which is ' 64 8 ioi 3 pence and 2 farthings over; fet down 97 14 to2 100 yds, X6= 586 5 600 yds. 7 ‘ the 2 farthings, and carry 3 to the place of pence, faying, 7 times 10 is 70, and 451 2 3 ,that I carried makes 73, which is 6 977 1 8 1000 yds, X8 = 7816 13 4 8000 yds. fliillings and 1 penny: fet down the Price of 8604 yards, 8406 166 Vol. I. No. 16. a 3. If S B