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H m & Ds h m
195. 11 27 48 x 8 196. 4 13 19 x 16 * . Dr. h. m. - Prs. do. h. m. 197. 5 19 12 - 34 198. 1 137 5 35 - 21
Though Compound Multiplication is seldom employed, ercept in relation to money, yet as it may be usefully applied in the solution of many examples in the Rule of Proportion, p; ve enlarged upon it, rather more than some may think necessary. Should the teacher
find the eramples here given, too many, it is left to his discretion to direct the number the pupil may omit.
Drvision of DIVERS DENOMINATIONs, *.
Place thc divisor on the left hand, as in simple division.
Begin at the left of the dividend, and divide the highest denomination by the divisor, and write down the quotient; multiply, the remainder, if any, by as many as make one of the next lower denomination, taking the number of the same denomination in the dividend, and divide the result as before, this will give that part of the quotient which belongs to this denomination; if there is again a remainder, multiply by the parts in the next lower denomination, and proceed as before directed, until all the denominations are gone through, annexing the fractional part, if any, to the last quotient, as before explained in simple division. If in any of those divisions, there should be no remainder, divide the next denomination of the dividend by the divisor, and proceed as if commencing a new operation, placing a cipher in the quotient, when any denomination of the dividend is less than the divisor, and taking the whole of said denomination as a remainder; proceed with it as before directed. Note:-The quotients are always of the same name as the respective dividends. Compound Division is proved by the multiplication of the quotient or answer by the divisor, and in general, one variation of the rule may be applied to prove another.
From the illustrations gives of Simple Division, and Compound Multiplication, this rule is evident, as to divide any compound quantity; or number whatever, is the same as dividing the component parts - of the compound quantity or number, seperately by the given divisor.
When the divisor is a composite number, divide by one of the component parts, and the quotient arising by the other, and this by the third if the divisor consists of more than two parts, but in general, when this is the case, it may be as concise to proceed as in long division. When there are only two component parts, the rule already given in simple division, must be strictly observed, when determining the fractional parts, that is, to multiply the second remainder by the first divisor, and to the product add the first remainder. When there are three component parts, multiply the third remainder by the second divisor, and to the product add the second remainder; then multiply the result by the first divisor, and to the product add the first remainder, and the last sum will be the whole remainder, the same as if long division had been employed.