When the Multiplier is a composite Number, i. e. if any two Figures, being multiplied together, will make that Number, then multiply by one of those Figures, and the Product by the other will give the answer. Multiply 771039 by 35, or 7 times 5 7 5397273 5 26986365 Multiply 921563 by 32. TO PROVE MULTIPLICATION. (T.S.) Cast all the 9's out of the sum of the Multiplicand, sna also out of the Multiplier, set down the remainders. Then multiply the first remainder by the second, and cast out the 's from the Product of these two remainders. Then cast out the 9's from the Product of the question. If the third and fourth remainders are equal, the work is right. 473457896 by 963 943446788 by 987 49416739 by 298 89743849 by 8743 87321219 by 4781 18731842 by 3274 14731942 by 5781 27891934 by 5843 TE 47892894 by 6974 151344999 by 55879 EACHETH to find how often one Number is contained in another; or to divide any Number into what Parts you please. In this Rule there are three Numbers real, and a fourth aceidental: viz. 1, The Dividend or number to be divided: 2, The Divisor or Number by which you divide: 3, The Quotient, or Number that shews how often the Divisor is contained in the Dividend: 4, Or accidental Number, is what remains when the Work is finished, and is of the same Name as the Dividend. RULE. When the Divisor does not exceed 12, find how often it is contained in the first Figure of the Dividend; set it down under the Figure you divided, and carry the overplus (if any) to the next in the dividend, as so many Tens: then find how often the Divisor is contained therein, set it down, and continue the same till you have gone through the Line: but when the Divisor is more than 12, multiply it by the Quotient Figure, the Product subtract from the Dividend, and to the remainder bring down the next Figure in the Dividend, and proceed as before, till the Figures are all brought down. PROOF. Multiply the Divisor and Quotient together, adding the Remainder (if any), and the Product will be the same the Dividend. Dividend. Rem. as When there are Cyphers at the End of the Divisor, they may be cut off, and as many places from off the Dividend, but must be annexed to the Remainder at last. 271,00)25473221(939 273,000)752473|729(2756 5721|00)7253472|16(1267 215 000)6325104,997(29+19 When the Divisor is a composite Number, i. e. if any two Figures, being multiplied together, will make that Number, then, by dividing the Dividend by one of those Figures, and that Quotient by the other, it will give the Quotient required. But as it sometimes happens that there is a Remainder to each of the Quotients, and neither of them the true one, it may be found by this RULE. Multiply the first Divisor into the last Remainder, to that Product add the first Remainder, which will give the true one. Div. 3210473 by 27 7210473 by 35 6251043 by 42 5761034 by 54 118906. 11 Rm. 206013. 18 Rm. 148834. 15 Rm. 106685. 44Rm. TO PROVE DIVISION. (T. S.) Cast out the 9's in the Divisor and also in the Answer, and multiply one by the other and cast out the 9's from the Product; to which add what remains after casting out the 9's from the remainder of the question, which sum will be equal o the excess of nines in the Dividend. |