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 arithmetics:. 379 Examp. I. If L. 274! 13 : 8 : 3 be equally divided the right hand as there are ciphers in the faid divifor; the among 8 men, what will each man’s fhare be t figures thus pointed off are to be efteemed a remainder, Here firft divide the inand the other figures on the left hand are to be accounted tegers L. 274 by 8, and the L. s. d. f. a quotient; then multiply this quotient by the comple- quotient L. 34, and L. 2 8)274 8 3 dividend, ment, placing the units of the produft under the units of remains; iswhich reduced to 34 6 8 2-^ quotient, the former remainder; again, divide this product by the the denomination makes new divifor, by pointing off from the right hand the fame 40 next fhillings; and thefe added to 13 {hillings make 53 number of figures as in the former remainder, and the fi- {hillings divided by 8 gives 6 {hillings to the quogures to the left are to be eftemmed another quotient; tient, and; which remains ; which 5 {hillings reduced which quotient you- are again to multiply by the comple- make 6od 5and{hillings added to 8d. make 68 d.; which diviment, and divide as before. And in this manner proceed ded by 8 gives 86od. to the quotient, and 4d. remains, fee. till the laft quotient is nothing; then add as in addition The operationd. may, if you pleafe, be drawn out at of integers, obferving the carriage from the left lund coas in the following lumn of the remainders; to the remainders add the pro- large; II. If C. 42 :-2 : 8 of tobacco be made up dudt of the faid carriage and complement, and the fum intoExamp. is the total remainder; and the fum of the feveral quo- hhd .5? equal hhds, what will be the neat weight of each tients is the total quotient required. Here divide the C. 43 by C. lb. C. lb. Example. 5, and the quotient is C. 8, 5)43 2 8 ( 8 2 24, Divide 74678 by 98. and C. 3 remains; which 40 New divifor xoo 100)746.98 reduced, and added to the — Given divifor 98 14.92=746X2 2 makes 14 C^_ which 3 rem, — .28=14X2 divide by 5, fee. 4 Complement 2 Tot. quot. 762.18+4=22 total rem. Carriage 2X2 complement —4 Explication. Firft, to unity annex two ciphers, becaufe the given di4 rem,. vifor confifts of two figures, and lb the new divifor is 28 1O0: from which fubtraft the given divifor 98, and there remains 2 for the complement. 120Next divide the, given dividend by the new divifbr, 10 viz. point off 98, the two figures next the right hand, for the firft remainder; and the figures on the left, name20 ly, 746, is the quotient. 20 Then multiply the faid firft quotient 746 by the complement 2 ; and by the new divilor divide the product 1492, viz. point off 92 for the fecond remainder, andi 2. If the divifor confifis of two qr more figures,, andi 14 is the feconcf quotient. number, refolve it into its component Again, multiply the fecond quotient 14 by the com- 'be-a compofite and divide the given dividend by one of thefeplement 2, and the product 28, divided by 100, gives parts, parts, the quotient 28 for the third remainder, but nothing to the quotients tient is the anfwer.. by another, fee. and the laft quoThen add the feveral remainders and quotients, and If the divifor confifts of integers and parts, reduce find the total quotient amounts to 762, and the remain- both3. divifor and dividend to the fame denomination, and: ders to 18. Laftly, multiply 2, the carriage from the' left-hand- then proceed as in divifion of integers. column of the remainders, by the complement 2 ; and III. The Proof of Ditsifon. the product 4 add to the remainders 18, and the fum 22. is the total remainder. Division.may he proved feveral ways, viz. by multiplication, by divifiqn, and by calling out the 9’s. 1- Byormultiplication: Multiply the and quotient by the II. Divi/ion of the parts if Integers. divifor, the divifor-by the quotient; the.product Here there are three cafes. with the remainder added to it, wall be equal to the dix. If the divifor be a digit, by it divide the integers
 * Or, take the produdls of the quotient-figures in^o

of the di v idend, reduce the remainder to the parts of vidend the divifor,. add them jn the order they Hand under the the next inferior denomination, 'and add it, when thus dividuals; and their fum, with the remainder,. will be ,vuuev.,l, ’ ' ..rts ; then divide the fum, reduto the dividend. cing and adding the 1retnainder to the parts of the follow- equal 2. By divifion; Divide the difference of the dividend ing denomination, £sc. and remainder by the quotient, and your next quotient , It the integral part of the dividend be lefs than be equal to your firft divifor, without any remainder. «b for, you mull, j. the firft place, reduce it to the will But this method is tedious. parts of the next denomination. 3. By calling out the 9’s: Caft the 9’s.out of the dU vifoK